# Computation-Efficient Era: A Comprehensive Survey of State Space Models in
Medical Image Analysis

Moein Heidari
School of Biomedical Engineering
University of British Columbia
British Columbia, Canada
&Sina Ghorbani Kolahi11footnotemark: 1
Department of Industrial and Systems Engineering
Tarbiat Modares University
Tehran, Iran
Sanaz Karimijafarbigloo
Faculty of Informatics and Data Science
University of Regensburg
Regensburg, Germany
&Bobby Azad
Electrical Engineering and Computer Science Department
South Dakota State University
Brookings, USA
&Afshin Bozorgpour
Faculty of Informatics and Data Science
University of Regensburg
Regensburg, Germany
&Soheila Hatami
Faculty of Mechanical Engineering
Tarbiat Modares University
Tehran, Iran
&Reza Azad
Faculty of Electrical Engineering and Information Technology
RWTH Aachen University
Aachen, Germany
&Ali Diba
Lunit Inc.
Amsterdam, The Netherlands
&Ulas Bagci
Department of Radiology
Northwestern University
Chicago, USA
&Dorit Merhof
Faculty of Informatics and Data Science
University of Regensburg
Regensburg, Germany, and
Fraunhofer Institute for Digital Medicine
MEVIS, Bremen, Germany
&Ilker Hacihaliloglu
Department of Radiology, Department of Medicine
University of British Columbia
British Columbia, Canada
Indicates equal contributionCorresponding author: Ilker Hacihaliloglu,
<EMAIL_ADDRESS>
###### Abstract

Sequence modeling plays a vital role across various domains, with recurrent
neural networks being historically the predominant method of performing these
tasks. However, the emergence of transformers has altered this paradigm due to
their superior performance. Built upon these advances, Vision Transformers
(ViTs) have conjoined Convolutional Neural Networks (CNNs) as two leading
foundational models for learning visual representations. However, transformers
are hindered by the $\mathcal{O}(N^{2})$ complexity of their attention
mechanisms, while CNNs lack global receptive fields and dynamic weight
allocation. State Space Models (SSMs), specifically the Mamba model with
selection mechanisms and hardware-aware architecture, have garnered immense
interest lately in sequential modeling and visual representation learning,
challenging the dominance of transformers by providing infinite context
lengths and offering substantial efficiency maintaining linear complexity in
the input sequence. Capitalizing on the advances in computer vision, the field
of medical imaging has heralded a new epoch with Mamba models. Intending to
help researchers navigate the surge, this survey seeks to offer an
encyclopedic review of Mamba models in medical imaging. Specifically, we start
with a comprehensive theoretical review forming the basis of SSMs, including
Mamba architecture and its alternatives for sequence modeling paradigms in
this context. Next, we offer a structured classification of Mamba models in
the medical field and introduce a diverse categorization scheme based on their
application, imaging modalities, and targeted organs. Consequently, we explore
various applications and their practical use cases in medicine, such as image
segmentation, reconstruction, registration, classification, language
processing, multi-modal understanding, and other medically related challenges.
Finally, we summarize key challenges, discuss different future research
directions of the SSMs in the medical domain, and propose several directions
to fulfill the demands of this field. In addition, we have compiled the
studies discussed in this paper along with their open-source implementations
on our GitHub111https://github.com/xmindflow/Awesome_mamba repository. We plan
to update this page regularly with the latest relevant research papers.

_K_ eywords State Space Model $\cdot$ Mamba $\cdot$ Linear, Computer Vision
$\cdot$ Medical imaging $\cdot$ Medical applications $\cdot$ Survey

##  1 Introduction

Figure 1: Algorithms and methods trilemma. Despite CNN’s ability to
efficiently process local information with high computational efficiency, they
often struggle with capturing long-range dependencies due to their inherent
architectural constraints. On the other hand, transformers excel at capturing
long-range dependencies and have demonstrated high performance in various
tasks. However, they are computationally expensive and potentially inefficient
when processing local information. The Mamba model emerges as a promising
alternative by balancing these trade-offs. It offers a method that maintains
computational efficiency while effectively capturing local information and
long-range dependencies.

Due to ongoing advancements in computer technology and the increasing
computing capabilities of the hardware, computer-aided diagnosis (CAD) with
deep learning methods has found widespread application in medical image
analysis [1, 2, 3]. In the medical domain, particularly for mobile medical
devices, developing artificial intelligence (AI) models with limited
computational memory for deployment in resource-limited settings, such as
small towns without large hospital systems or in developing countries is
crucial. Most contemporary deep learning methods, including those applied to
medical imaging, are built upon the foundational architectures of
convolutional neural networks (CNNs) [4, 5, 6] and transformers [7, 8, 9, 10].
As convolutional filters designed to identify and extract necessary features
from medical images, extensive research has been dedicated to CNNs, and thanks
to their progressively enlarged receptive fields and excelling at obtaining
local characteristics, they have been the de facto standard in CAD problems so
far [11]. This research spans a range of applications, including the detection
and classification of tumors [12], identification of skin lesions [13], and
segmentation of target tumors [14], to list just a few examples. CNNs have
also significantly enhanced the analysis of various imaging modalities in
clinical medicine, including X-ray [15], CT scans [16], MRI [17], ultrasound
[18], and digital pathology [19]. However, CNNs fail to capture long-range
dependencies and spatial correlations, limiting their capacity to accurately
distinguish the shape and structural details essential for effective medical
image analysis across various applications [20]. On the other hand,
transformers have proven to be a formidable force in the modern medical image
analysis stack with tremendous impact in many applications ranging a broad
area [21, 22]. In contrast to CNNs, transformers, first developed for language
processing and then transferred to vision domain [23, 7], approach images not
by processing spatial hierarchies but by treating them as sequences of
patches. This criterion enhances their ability to capture global information
and long-range dependencies by its elegant design of the self-attention
mechanism [3]. However, the self-attention module usually introduces more
computational load due to its quadratic complexity related to image size [24]
despite strategies such as Parameter-Efficient Fine-Tuning (PEFT) [25], and
Pre-training [26] paradigm. Despite all the progress, it is proven that both
local and global information is of paramount importance in medical image
processing due to the complexity of lesion distribution or organ shape [27].
Furthermore, enhancing the precision of CAD frequently involves increasing the
algorithmic model’s parameters to boost its predictive capabilities. Yet, it
is important to consider computational power and memory limitations in
practical clinical and healthcare settings. For mobile health applications, it
is critical to utilize models that require fewer parameters and minimal memory
usage. Consequently, there is a pressing need for algorithmic models that are
both efficient and perform well on future mobile medical devices [28].

Here, we highlight that these requirements present a trilemma, as current
models typically make trade-offs among them. Figure 1 summarizes how
mainstream frameworks tackle the trilemma. Transformer models [23] learn the
long-range feature representations well but have computational constraints and
inefficiency in local information processing, CNNs, and Recurrent Neural
Networks (RNNs such as Long Short-Term Memory (LSTM) [29] and Gated Recurrent
Unit (GRU) [30]) face limitations like solely capturing local connections,
restricted memory capacity, vanishing gradients, and the incapacity to
parallelize, respectively [31]. Recently, State Space-based Mamba model [32]
has emerged as a promising alternative to these models to enhance
computational efficiency while maintaining the ability to capture long-range
dependencies and sustain high performance. They demonstrate surprisingly good
results in capturing long-range and local information [33] while scaling
linearly or near-linearly with sequence length [34]. To date, Mamba models
have proven beneficial across computer vision (CV) domains, broadly
encompassing image segmentation [35], restoration [36], generation [37],
classification [38], video [39] and point-cloud analysis [40] to name a few.
The medical imaging field has recently seen a significant increase in adopting
Mamba-based techniques. As illustrated in Figure 6, extensive research focuses
on applying Mamba models to various medical imaging scenarios. The recent
surge of Mamba model variations has been so substantial that researchers and
practitioners may struggle to keep up with the rapid pace of innovation. This
trend underscores the extensive research efforts dedicated to exploring the
applications of Mamba models across various medical imaging contexts. Given
the current substantial attention garnered by these models, there has been a
notable influx of research contributions in this domain, prompting the need
for a comprehensive survey to synthesize the existing literature and offer
timely insights. Hence, this survey endeavors to provide a thorough overview
of the latest advancements in this category of models within medical imaging.
We hope this work will point out new research directions, provide a guideline
for researchers, and initiate further interest in the medical image analysis
community to leverage the potential of Mamba models in the medical domain. Our
major contributions are as follows:

$\bullet$ We first present the background and theory behind State Space Models
(SSMs) briefly cover their foundation in the general formulation and the Mamba
model. Then, we conduct a systematic and exhaustive examination of Mamba’s
uses in medical imaging, offering respective taxonomies and discussions of
various aspects of these methods. In particular, we delve into over 35 papers
in a structured and hierarchical fashion.

$\bullet$ Our work provides a taxonomized (Figure 6), in-depth analysis (e.g.,
task/organ-specific research progress and limitations (Figure 2)) of these
models. Specifically, we group the applications of Mamba papers into eight
categories: medical image segmentation, classification, synthesis,
registration, reconstruction, language processing, multi-modal understanding,
and multi-task learning applications.

$\bullet$ Finally, we address challenges and unresolved issues, highlighting
emerging trends, research questions, and future directions related to the
Mamba model.

Relevant Surveys.

Even though the Mamba network was introduced recently, related surveys and
contributions to the literature have already significantly increased.
Specifically, Mamba-360 [34] provides a holistic review of applications of
SSMs across different domains while presenting the performance evaluation of
SSMs compared to state-of-the-art (SOTA) transformers. Concurrently, the work
of [41, 42] carries out an extensive survey and presents a taxonomy study of
Mamba models concentrating on its application across various visual tasks and
data types and discusses its predecessors as well as recent advancements.
Lastly, Wang et al. [43] deliver a comprehensive survey of research, including
both the natural language processing (NLP) and CV domains, and present
statistical comparisons and analysis of these models. While some of these
works touch upon the medical domain, we introduce the first comprehensive
survey paper that thoroughly explores the applications of Mamba models in
medical imaging. Our taxonomy systematically categorizes research on medical
Mamba models and their applications, the targeted organ, and the imaging
modality. We delve into SSMs’ underlying concepts and theoretical principles
and provide an extensive and up-to-date review of recent advancements in
medical Mamba models (until June 2024), presented in Figure 6.

Search Strategy.

We performed a detailed search on DBLP, Google Scholar, and Arxiv Sanity
Preserver using specialized search phrases to compile a list of academic
papers. This collection encompassed peer-reviewed journals, conference and
workshop papers, non-peer-reviewed articles, and preprints. Our search terms
included combinations of keywords like (mamba* $|$ deep* $|$ medical* $|$
{Task}), (mamba $|$ medical*), (state space model* $|$ medical* $|$ image* $|$
{Task}*), (V(U)mamba* $|$ vision* $|$ {Task}* $|$ medical*), with {Task}
representing a specific application discussed in this review (refer to Figure
6). To select the most pertinent papers, we thoroughly assessed their
originality, contributions, and impact, giving preference to pioneering works
in medical imaging. Based on these evaluations, we selected the most highly
ranked papers for detailed analysis.

Paper Organization.

The structure of the remaining sections of the paper is as follows: Section 2
presents the background theory behind SSMs, covering Mamba architecture and
beyond. Section 3 discusses diverse variants of the Mamba model, which guide
most medical domain contributions, highlighting its relevance in clinical
settings. From Section 4.1 through Section 4.8, we extensively cover the use
of Mamba across various medical imaging tasks, detailing technical innovations
and primary applications as illustrated in Figure 6. In Section 5, we
comprehensively discuss the approaches presented in this work and offer
detailed comparisons that suggest insights into key aspects such as
contributions and core ideas. Finally, we offer a detailed discussion on open
challenges and potential research directions of Mamba models in medical domain
in Section 6, and Section 7 provides a conclusion to this study.

(a) Applications

(b) Modalities

(c) Organs

Figure 2: The diagram illustrates the distribution of the analyzed papers,
categorized as follows: (a) by their applications, (b) by their imaging
modalities, and (c) by the type of organ studied.

##  2 Preliminaries

This chapter defines the necessary preliminaries of SSMs and their key
features. First, a comprehensive background of SSMs is presented. Then, a
unified sequence modeling formulation is introduced, describing the
fundamental objectives of SSMs in processing 1-D input sequences irrespective
of the input type. This is followed by an overall SSM formulation from the
continuous-time system to the discretized form based on S4 [44]. Next, the
differences between SSMs and transformers in context learning are explored,
highlighting the weaknesses of SSMs in this area that led to the development
of Mamba. Lastly, the architecture of Mamba is thoroughly examined.

###  2.1 Background on State Space Models

The foundational concept of the SSM is rooted in Kalman filtering [45], which
introduces a linear filtering and prediction method divided into prediction
and correction steps. The prediction phase estimates the current state based
on the previous state, and the correction phase refines this estimate by
assimilating the observed state, aiming for an optimal state estimation. This
mathematical framework describes dynamic systems through first-order
differential equations for continuous-time systems or difference equations for
discrete-time systems, representing internal state evolution and output
relations in matrix and vector formats, thus accommodating multivariable
systems. Enhancing this model, Gu et al. [46] developed the Linear State Space
Layer (LSSL), which synergizes the strengths of recurrent neural networks,
temporal convolutional networks, and neural differential equations, overcoming
their individual limitations in terms of model power and computational
efficiency.

Like the challenges, RNNs face, SSMs struggle with vanishing or exploding
gradients, particularly when modeling extensive sequences. Addressing this,
the HiPPO model [47] integrates concepts of Recurrent Memory with Optimal
Polynomial Projections, significantly boosting the performance of recursive
memory crucial for handling long sequences and dependencies. The S4 model
[44], a novel sequence modeling approach, employs three innovative mechanisms
to manage long dependencies effectively: the Higher-Order Polynomial Project
Operator (HiPPO) for effective signal history retention, Diagonal Plus Low-
Rank Parametrization for stabilizing the state transition matrix (A), and
efficient kernel computation using Fast Fourier Transforms (FFTs), which
optimizes computational complexity to $O(N\log(N))$.

H3 [48] identifies and addresses two significant challenges traditional SSMs
encounter: difficulty retaining information from earlier tokens and comparing
tokens across different sequences. To overcome these, H3, as illustrated in
Figure 4, proposes a novel approach by stacking SSMs with multiplicative
interactions between input and output projections, enhanced by a FlashConv for
training efficiency and a State-Passing Algorithm for scaling, which together
improve memory retention and facilitate cross-sequence comparisons.

Exploring the initialization and parameterization of SSMs, Gu et al. [49] and
Gupta et al. [50] delve into Diagonal State Space Models (DSSM), demonstrating
the critical importance of proper initialization for performance optimization.
Gupta et al. [50] further present the DSS model as a simpler yet effective
alternative to structured SSMs like S4, capable of achieving comparable
performance without low-rank modifications.

Expanding the application scope of SSMs, the S5 model [51] extends the
principles applied in RNN-based multiple-input multiple-output Linear
Dynamical Systems to SSMs, allowing for the concurrent processing of multiple
inputs and outputs. Addressing training stability, Long Convolution [52] notes
the dependence of SSMs on complex mathematical frameworks and proposes the
direct parametrization of convolutional kernels to stabilize deep network
training. This idea parallels innovations such as Structural Global
Convolution (SGConv) [53] and Hyena Hierarchy (HH) [54], which seek to address
the perplexity gap observed with attention-based transformers by employing
sub-quadratic convolutions and data-gating mechanisms.

Moreover, models such as RWKV [55, 56], Mega [57], GSS [58], and RetNet [59]
illustrate the adaptive use of SSM principles. RWKV merges the benefits of
transformers and RNNs, offering efficient parallelizable training and
inference. RetNet, termed Retentive Network, focuses on combining training
parallelism with low-cost, high-performance inference across varying
computational paradigms. Gated State Spaces (GSS) further enhance this by
incorporating gating units to reduce dimensionality during FFT operations,
optimizing the efficiency for longer input sequences.

This enhanced detailing provides a clearer understanding of the developments
in SSMs and highlights their broad applicability and ongoing evolution, as
comprehensively overviewed in additional literature [60, 61]. These insights
are foundational for advancing the application and theoretical understanding
of SSMs in handling long sequential data.

SSMs General Formulation

In this subsection, we introduce the general form of causal sequence modeling
tasks with one-dimensional (1-D) sequence inputs, using language modeling as
an illustrative example. This framework helps establish the foundational goals
of SSM applications in 1-D sequence modeling.

Sequence modeling can be viewed as a mapping between input and output signals,
represented by the function $f$:

$\textbf{y}(t)=f(\textbf{x}(t),\dots,\textbf{x}(t-T);\theta),$ (1)

where $\textbf{y}(t)$ is the output at time $t$, and
$\textbf{x}(t),\dots,\textbf{x}(t-T)$ are the input signals up to time $t$.
The parameters $\theta$ are optimized for specific tasks to enhance model
performance. Due to the extensive search space of $f(\cdot;\theta)$, various
parameterizations are used to simplify the problem. The architecture of
$f(\cdot;\theta)$ significantly affects its ability to learn data structures
effectively.

The model $f(\cdot;\theta)$ learns by being exposed to input-output pairs
$(\textbf{x}(t),\textbf{y}(t))$ for all $t$, and iteratively updates
parameters $\theta$ to minimize the loss function $\mathcal{L}(\cdot)$ as
follows:

$\bm{\min_{\theta}}\;\mathcal{L}(\textbf{y}-f(\textbf{x};\theta)).$ (2)

In language modeling, inputs $\textbf{x}(t)$ are tokenized sentences, and
outputs y are shifted versions of the inputs, forming an auto-regressive
model.

SSMs, inspired by the Kalman filter, represent a continuous-time system that
maps a 1-D sequence from $\textbf{x}(t)\in\mathbb{R}$ to
$\textbf{y}(t)\in\mathbb{R}$ through a hidden state
$\textbf{h}(t)\in\mathbb{R}^{N}$ as depicted in Figure 3. These models are
typically defined by linear ordinary differential equations (ODEs):

$\displaystyle\dot{\textbf{h}}(t)$
$\displaystyle=\textbf{A}\textbf{h}(t)+\textbf{B}\textbf{x}(t),$ (3)
$\displaystyle\textbf{y}(t)$
$\displaystyle=\textbf{C}\textbf{h}(t)+\textbf{D}\textbf{x}(t),$ (4)

where $\textbf{A}\in\mathbb{R}^{N\times N}$, $\textbf{B}\in\mathbb{R}^{N\times
1}$, $\textbf{C}\in\mathbb{R}^{1\times N}$, and
$\textbf{D}\in\mathbb{R}^{1\times 1}$ are the state, input, output, and feed-
forward matrices, respectively, assumed to be time-invariant. The state
equation (Equation 3) involves multiplying matrix B with the input
$\textbf{x}(t)$, followed by matrix A with the previous state $\textbf{h}(t)$.
The matrix A stores all previous information and determines the influence of
the previous hidden state on the next hidden state. The matrix B determines
how the input $\textbf{x}(t)$ affects the hidden state. The output equation
(Equation 4) describes how the hidden state transforms into output via matrix
C and how the input affects the output via matrix D. In the absence of direct
connections ($\textbf{D}(t)=0$), the system further simplifies.

Figure 3: SSM can be represented and computed in three different forms:
continuous-time, recurrent, or convolutional models. Redrawn from [46]

For discrete-time applications, SSMs use a timescale parameter
$\mathbf{\Delta}$ to convert continuous parameters into discrete ones. The
zero-order hold (ZOH) technique is commonly used for this transformation:

$\displaystyle\mathbf{\overline{A}}$
$\displaystyle=\exp{(\mathbf{\Delta}\mathbf{A})},$ (5)
$\displaystyle\mathbf{\overline{B}}$
$\displaystyle=(\mathbf{\Delta}\mathbf{A})^{-1}(\exp{(\mathbf{\Delta}\mathbf{A})}-\mathbf{I})\cdot\mathbf{\Delta}\mathbf{B}.$

The discrete model then operates stepwise:

$\displaystyle\textbf{h}_{t}$
$\displaystyle=\overline{\textbf{A}}\textbf{h}_{t-1}+\overline{\textbf{B}}\textbf{x}_{t},$
(6) $\displaystyle\textbf{y}_{t}$ $\displaystyle=\textbf{C}\textbf{h}_{t}.$
(7)

However, this recurrence form (Figure 3) does not allow for parallel
computation. To address this, the model can be expanded to show each output as
a function of all previous inputs:

$\displaystyle\textbf{y}_{0}$
$\displaystyle=\textbf{C}\overline{\textbf{A}}^{0}\overline{\textbf{B}}\textbf{x}_{0},$
(8) $\displaystyle\textbf{y}_{1}$
$\displaystyle=\textbf{C}\overline{\textbf{A}}^{1}\overline{\textbf{B}}\textbf{x}_{0}+\textbf{C}\overline{\textbf{A}}^{0}\overline{\textbf{B}}\textbf{x}_{1},$
$\displaystyle\textbf{y}_{2}$
$\displaystyle=\textbf{C}\overline{\textbf{A}}^{2}\overline{\textbf{B}}\textbf{x}_{0}+\textbf{C}\overline{\textbf{A}}^{1}\overline{\textbf{B}}\textbf{x}_{1}+\textbf{C}\overline{\textbf{A}}^{0}\overline{\textbf{B}}\textbf{x}_{2}.$

Alternatively, using a convolutional approach simplifies the computation to a
single convolution operation:

$\displaystyle\overline{\textbf{K}}$
$\displaystyle=(\textbf{C}\overline{\textbf{B}},\textbf{C}\overline{\textbf{A}}\overline{\textbf{B}},\ldots,\textbf{C}\overline{\textbf{A}}^{L-1}\overline{\textbf{B}}),$
(9) y $\displaystyle=\textbf{x}*\overline{\textbf{K}},$

where $\overline{\textbf{K}}\in\mathbb{R}^{L}$ is a structured convolutional
kernel that encapsulates the combined effect of the system’s dynamics over the
input sequence of length $L$, and $*$ denotes the convolution operation
(Figure 3).

While facilitating certain computations, these models’ linear time-invariant
(LTI) nature introduces significant limitations in dynamic learning contexts,
such as those required by deep learning frameworks. Subsequent sections of
this paper will address this fundamental challenge in applying SSMs to deep
learning by introducing the Mamba model. This advanced model seeks to mitigate
the contextual learning deficiencies observed in traditional SSM frameworks.
While the Transformer architecture stores context information in the
similarity matrix, SSMs lack a similar module, adversely affecting their
performance in contextual learning scenarios.

Mamba

Figure 4: The Mamba block (right) is a streamlined component that combines the
H3 (left) and MLP (center) blocks. From [32]

To address the limitations of traditional SSMs characterized by LTI
parameters, Gu et al. [32] have developed the Mamba architecture. This model
introduces a Selective Scan Mechanism, enabling dynamic filtering of inputs
based on their relevance to the task. Unlike traditional SSMs, in Mamba, the
matrices B, C, and $\Delta$ in S4 are functions of the inputs $\textbf{x}(t)$,
enhancing the model’s responsiveness and allowing it to adapt its behavior
based on the input with batch size $B$, length $L$, and $D$ channels. The
discretization process after incorporating the selection mechanism is as
follows:

$\displaystyle{\overline{\textbf{B}}}$ $\displaystyle=s_{B}(\textbf{x}(t)),$
(10) $\displaystyle{\overline{\textbf{C}}}$
$\displaystyle=s_{C}(\textbf{x}(t)),$ $\displaystyle{\Delta}$
$\displaystyle=\tau_{A}(\text{Parameter}+s_{A}(\textbf{x}(t)))$

where $\overline{\textbf{B}}\in\mathbb{R}^{B\times L\times N}$,
$\overline{\textbf{C}}\in\mathbb{R}^{B\times L\times N}$, and
$\Delta\in\mathbb{R}^{B\times L\times D}$. $s_{B}(\textbf{x}$ and
$s_{C}(\textbf{x}(t))$ are linear functions that project the input x into an
$N$-dimensional space, while $s_{A}(x)$ projects the hidden state dimension
$D$ linearly into the desired dimension, connected to the RNN gating
mechanism. Through these computations, the parameters $\Delta$, B, C become
input functions with length $L$, transforming the time-invariant model into a
time-varying model, thus achieving selectivity.

The parameter A does not directly depend on the input data, but after the
discretization process of the SSM, its relevance to the input can be
established through the data dependency of $\Delta$. Given that A is of
dimension $N$, it plays distinct roles in each dimension of the SSM. This
differentiation enables precise generalization of all preceding information
rather than merely compressing it.

The Mamba architecture further includes a Hardware-aware Algorithm designed to
optimize computational processes by utilizing parallel scanning, kernel
fusion, and strategic recalculation. These features are part of an expanded
architecture that includes model dimension expansion by a factor $E$,
normalization, and residual connections. Activation functions such as SiLU or
Swish improve the gating mechanisms in MLP configurations, with optional Layer
Normalization to stabilize training (Figure 4).

This innovative framework significantly enhances the adaptability and
computational efficiency of SSMs, making them suitable for complex dynamic
modeling tasks such as language modeling, CV, and medical image analysis.

##  3 Architecture Redesign

Scope of this section

Following the introduction of Mamba, several researchers have explored
modifications to this architecture, aiming to enhance its performance and
extend its applications [62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74,
39, 75]. This section reviews recent papers proposing various Mamba model
architectural adaptations. Specifically, we delve into visual Mambas, which
introduce diverse types of scanning mechanisms to understand and traverse
direction-sensitive visual information. Figure 5 presents a comprehensive
overview of the landscape of scanning mechanisms within visual Mambas.

Architecture Types

Jamba [76] introduces a hybrid architecture that interleaves blocks of
transformer and Mamba layers, integrating the strengths of both models. The
use of a mixture-of-experts (MoE) approach within this framework allows Jamba
to scale effectively while maintaining a manageable memory footprint. This
model achieves SOTA performance on language benchmarks and long-context
evaluations, handling up to 256K tokens in context length. Jamba’s hybrid
design showcases the potential of combining Mamba with other architectures to
leverage their respective advantages.

Building on the concept of integrating MoE with mamba, MoE-Mamba [77]
significantly enhances the scalability and efficiency of SSMs. This
architecture outperforms both the original Mamba and Transformer-MoE models,
achieving the same performance as Mamba in 2.35× fewer training steps. MoE-
Mamba’s selective state space modelling and expert selection underscores the
potential for efficient large-scale modelling in sequential tasks.

Blackmamba [78] takes the integration of MoE with Mamba a step further,
combining the linear-complexity benefits of SSMs with the efficient inference
capabilities of MoE. The model demonstrates competitive performance against
both Mamba and transformer baselines, excelling in inference and training
FLOPs. By open-sourcing its weights and inference code, Blackmamba encourages
further exploration and application of this hybrid architecture in various
domains.

Vision Mamba (Vim) [79] addresses the challenge of visual representation
learning by proposing a bidirectional Mamba block design. This architecture
marks image sequences with position embeddings and compresses visual
representation using bidirectional SSMs to effectively scan visual data
(5(a)). Vim performs superior to established Vision Transformers (ViTs), such
as DeiT [80], while significantly improving computation and memory efficiency.
This positions Vim as a promising next-generation backbone for vision
foundation models.

Visual Mamba (VMamba) introduces [81] a novel approach to visual
representation learning by combining the strengths of CNNs and ViTs with the
computational efficiency of SSMs. The architecture includes a Cross-Scan
Module (CSM) to address direction-sensitive issues and traverse the spatial
domain effectively, as illustrated in 5(b). Vmamba exhibits promising
capabilities across various visual perception tasks, outperforming established
benchmarks, particularly as image resolution increases.

ZigMa [82] leverages Mamba’s long sequence modelling capabilities for visual
data generation, addressing scalability and complexity issues in diffusion
models. The model introduces a Zigzag Mamba scan (5(f)) and method that
improves speed and memory utilization, outperforming Mamba-based and
transformer-based baselines. ZigMa demonstrates its scalability on large-
resolution visual datasets, showcasing its potential for efficient visual data
generation.

Mamba-ND [83] extends the Mamba architecture to handle multi-dimensional data,
such as images and videos. The model unravels input data across different
dimensions in a row-major order, providing a systematic comparison with other
multi-dimensional extensions. Mamba-ND shows competitive performance on
benchmarks like ImageNet-1K [84] classification and action recognition,
demonstrating its versatility and efficiency in handling complex multi-
dimensional data.

LocalMamba [85] addresses the limitations of Vim in capturing local
dependencies within visual data by introducing a novel local scanning strategy
(as shown in 5(d)). This approach divides images into distinct windows,
effectively capturing local dependencies while maintaining a global
perspective. Additionally, it employs a dynamic method to independently search
for optimal scan choices for each layer, significantly improving performance.
Extensive experiments demonstrate LocalMamba’s ability to effectively capture
image representations, outperforming Vim-Ti by 3.1% on ImageNet [84] with the
same 1.5G FLOPs.

PlainMamba [86] presents a simple non-hierarchical SSM designed for general
visual recognition. This model enhances the selective scanning process of
Mamba for visual data by employing a continuous 2D scanning process (5(c))
that improves spatial continuity and a direction-aware updating mechanism.
These innovations enable PlainMamba to learn features from two-dimensional
images more effectively. The architecture is easy to use and scale, formed by
stacking identical PlainMamba blocks with constant width throughout all
layers. PlainMamba achieves performance gains over previous non-hierarchical
models and is competitive with hierarchical alternatives, particularly
excelling in tasks requiring high-resolution inputs while maintaining high
performance with reduced computing requirements.

(a) Bidrectional Scan [79]

(b) Cross-Scan [81]

(c) Continuous 2D Scan [86]

(d) Local Scan [85]

(e) Efficient 2D Scanning [67]

(f) Zigzag Scan [82]

(g) Omnidirectional Selective Scan [74]

(h) 3D BiDirectional Scan [39]

(i) Hierarchical Scan [75]

(j) Spatiotemporal Selective Scan [87]

(k) Multi-Path Scan [38]

Figure 5: Comparison of various 2D scanning and selective scan orders in Vim,
VMamba, PlainMamba, LocalMamba, Efficient VMamba, Zigzag, VMambaIR,
VideoMamba, Motion Mamba, Vivim, and RSMamba. From [42]

These papers represent diverse modifications and extensions to the Mamba
architecture, each addressing specific challenges and applications. From
hybrid models and visual representation learning to medical image segmentation
and multi-dimensional data processing, the evolving landscape of Mamba-based
models highlights the architecture’s flexibility and potential for innovation.
As researchers continue to explore and refine these models, the Mamba
architecture is poised to play a crucial role in the future of deep learning.

Clinical Importance

The adoption of Mamba models in medical imaging marks a transformative
advancement in clinical practice and research. These models bring several
critical enhancements to traditional imaging techniques, aligning with the
pivotal needs of modern medical diagnostics and therapeutic strategies.

Enhanced Computational Efficiency: One of the fundamental challenges in
medical imaging is managing the extensive computational resources required for
processing complex imaging data. With their linear complexity and hardware-
aware algorithms, Mamba models facilitate rapid processing of large imaging
datasets, such as full-body scans, which are common in routine clinical
evaluations. This efficiency is crucial for real-time diagnostic applications,
such as in emergency radiology, where quick decision-making can significantly
impact patient outcomes.

Extended Contextual Understanding: Unlike conventional deep learning models
that often require segmentation or region-specific annotations, Mamba models
inherently understand and process extensive imaging data sequences. This
ability is invaluable in medical imaging, where contiguous sections of a scan
need to be evaluated in context to diagnose conditions such as cancers or
vascular diseases accurately. For instance, the ability of Mamba to handle
long data sequences can be leveraged to understand tumour progression over
large areas or across multiple scans, enhancing both the diagnosis and
monitoring phases.

Reduced Radiation Exposure: The efficient data processing capabilities of
Mamba models allow for high-quality imaging results from lower-quality inputs
[42]. This feature can be particularly beneficial in reducing the radiation
doses required in imaging techniques like CT scans. By needing fewer passes to
produce diagnostic-quality images, Mamba models minimize the patient’s
exposure to potentially harmful radiation and reduce the operational costs
associated with these procedures.

Multi-modal Data Integration: In clinical settings, the integration of various
types of medical data (e.g., MRI, CT, PET) provides a more comprehensive view
of a patient’s health status [88, 89]. Mamba models excel in processing and
integrating diverse data types, offering a holistic view of the patient’s
medical images. This capability ensures more accurate diagnoses and tailored
treatment plans, improving patient care quality.

Scalability to Advanced Applications: Mamba models are designed to be
scalable, a critical feature in medical research and clinical trials where
voluminous data is processed. They can be adapted for advanced applications
like genetic sequencing and biometric analyses, which are becoming
increasingly relevant in personalized medicine and advanced diagnostics.

In summary, the Mamba model’s ability to efficiently process extensive
sequences, integrate multimodal data, and provide scalable solutions marks a
significant advancement in the clinical application of medical imaging
technologies. Its introduction into the medical field promises to enhance
diagnostic accuracy, reduce operational inefficiencies, and pave the way for
innovative therapeutic strategies, ultimately leading to improved patient care
and health outcomes.

##  4 State Space Models in Action

Figure 6: The proposed taxonomy for Mamba-based medical imaging research
encompasses ten sub-fields: 1) Multi-Task Learning, 2) Multi-Modal
Understanding, 3) Medical Image Classification, 4) Medical Image Synthesis, 5)
Medical Image Registration, 6) Medical Image Reconstruction, 7) Medical
Language Processing, and Medical Image Segmentation, which is subsequently
divided into 8) Pure, 9) Hybrid and 10) Multi-disciplinary learning methods,
referred to as other learning types. For conciseness, we use ascending prefix
numbers in the paper’s title and denote the reference for each study
accordingly: 1.[90], 2.[91], 3.[92], 4.[93], 5.[94], 6.[95], 7.[96], 8.[97],
9\. [98], 10\. [99], 11.[100], 12.[101], 13.[102], 14.[103], 15.[104],
16.[105], 17.[106], 18.[107], 19.[108], 20.[87], 21.[109], 22.[33], 23.[28],
24.[110], 25.[111], 26.[112], 27.[113], 28.[114], 29.[115], 30.[116],
31.[117], 32.[118], 33.[119] 34.[120], 35.[121], 36.[122].

###  4.1 Medical Image Segmentation

Medical image segmentation is pivotal in various clinical applications,
including disease diagnosis, treatment planning, and patient monitoring [123].
Accurate segmentation of anatomical structures and pathological regions from
medical images is essential for extracting quantitative measurements,
identifying abnormalities, and facilitating automated analysis. Selective SSMs
offer a promising approach for medical image segmentation due to their ability
to model temporal dependencies, handle long sequences of data, and capture
complex spatial relationships within images while maintaining linear
computational complexity compared to the quadratic burden of transformers and
the small receptive fields of CNNs. Leveraging Mamba with selective state
space mechanisms and efficient hardware-aware designs, Mamba-based models
effectively model the complex structures and variations present in medical
images. Integrating Mamba in medical image segmentation tasks enhances
segmentation accuracy and reduces the need for large-scale datasets and
massive computational resources, making it a valuable tool in resource-
constrained environments.

In this context, we categorize Mamba-based segmentation networks into three
groups based on their initial structure and training methodology. The taxonomy
includes: "Pure SSM and Mamba-based Models (Denoted as Pure)" which mainly
utilize visual SSM modules for segmentation tasks, exploiting their ability to
model long-range dependencies and capture complex spatial relationships within
medical images. Additionally, "Hybrid Architectures Involving Mamba (Denoted
as Hybrid))" approaches incorporate convolutional layers alongside SSM modules
to enhance feature capture and improve local representation, combining the
strengths of both techniques for more effective segmentation results. Finally,
"Other Learning Types" approaches use alternative learning techniques such as
self-supervised, semi-supervised, and weakly supervised learning to boost
segmentation performance.

####  4.1.1 Pure SSM and Mamba-based Models

Wang et al. [64] introduced Mamba-UNet, a novel architecture that combines the
UNet in medical image segmentation with Mamba’s capabilities. Mamba-UNet
adopts a VMamba-based encoder-decoder structure, incorporating skip
connections to retain spatial information across different network scales.
This design facilitates comprehensive feature learning, capturing intricate
details and broader semantic contexts within medical images. A novel
integration mechanism within the VMamba blocks ensures seamless connectivity
and information flow between the encoder and decoder paths, enhancing
segmentation performance. TM-UNet [106] is introduced to address the challenge
that visual SSMs feature extraction methods often retain redundant structures,
leaving room for parameter reduction. Featuring Residual VSS Blocks and a
Triplet SSM Module, TM-UNet improves information transfer, mitigates network
degradation, and effectively combines spatial and channel features through the
Triplet SSM, avoiding the extra parameters of conventional attention
mechanisms. Mamba-HUNet [107] is another architecture that captures localized
fine-grained features and long-range dependencies while ensuring linear
feature size scaling, avoiding the quadratic complexity often seen in
transformers in purely SSM-based U-shaped networks. Another UNet structure in
cooperate with VMamba is VM-UNet [108] which presents a pure SSM-based model
developed to demonstrate its potential in medical image segmentation tasks. In
this model, the Visual State Space (VSS) block is designed to effectively
capture extensive contextual information by utilizing an asymmetrical encoder-
decoder structure, making it a foundational component in the system. Moreover,
ViM-UNet [109] is proposed as a model for microscopy instance segmentation
based on visual Mamba.

One of the pioneering efforts to integrate SSMs into medical video object
segmentation, resulting in enhanced speed and performance, is Vivim [87]. This
is a framework that integrates Mamba into a multi-level transformer
architecture for medical video object segmentation. The authors have designed
a novel Temporal Mamba Block and incorporated a structured state-space
sequence model with a spatiotemporal selective scan, ST-Mamba, to enhance
video visual representation learning. Additionally, they have employed a
boundary-aware constraint and collected a thyroid segmentation dataset VTUS
for benchmarking. Their experiments validate the effectiveness of Vivim. The
Vivim system consists of a hierarchical encoder with stacked Temporal Mamba
Blocks to extract feature sequences and a lightweight CNN-based decoder head
to make predictions for segmentation masks.

####  4.1.2 Hybrid Architectures Involving Mamba

U-Mamba [33] combines CNNs and SSMs to form a hybrid framework. This blend
capitalizes on CNNs’ proficiency in extracting local features and SSMs’
ability to grasp extensive relationships within images. Structured with an
encoder-decoder setup, as illustrated in Figure 7, the architecture boosts its
effectiveness in handling long-range data and adapts well to diverse
segmentation assignments. Through the fusion of these elements, U-Mamba
surpasses conventional CNN and Transformer-based models in medical image
segmentation tasks, showcasing enhanced performance.

Figure 7: Overview of the U-Mamba architecture: a) Each U-Mamba block has two
Residual blocks followed by an SSM-based Mamba block for long-range dependency
modelling. b) The encoder-decoder framework includes U-Mamba blocks in the
encoder, Residual blocks in the decoder, and skip connections. From [33].

In an exploration of the potency of pretraining, which has demonstrated
significant efficacy in data-efficient medical image analysis, Swin-UMamba
[116] is designed specifically for medical image segmentation tasks,
harnessing the benefits of ImageNet-based pretraining.

To improve the Mamba model, Vision Mamba UNetV2 (VM-UNetV2) [112] reintegrates
both low-level and high-level features. It infuses semantic information into
the low-level features and refines the high-level features using more detailed
information. SegMamba [117] also is an architecture designed for 3D medical
image segmentation, combining a U-shaped structure with Mamba to capture
global features across entire volumes at multiple scales. To optimize Mamba
for high-dimensional medical images, the architecture includes a tri-
orientated Mamba (ToM) module that enhances the sequential modelling of 3D
features from three different directions. A gated spatial convolution (GSC)
module is incorporated to improve spatial feature representation before each
ToM module. In another work, High-order Vision Mamba UNet (H-VMUnet) [111]
proposes a High-order 2D-selective-scan (HSS2D) to guarantee an outstanding
global sensory field within SS2D, while also reducing redundant information.
Wang et al. [113] introduce the LMa-UNet, a pioneering solution for segmenting
2D and 3D medical images. Its innovation lies in the use of large windows,
transforming local spatial modelling compared to traditional methods.
Remarkably efficient in global modelling, it outperforms self-attention
mechanisms. Additionally, a novel hierarchical and bidirectional Mamba block
enhances both global modelling capabilities and proficiency in capturing
intricate spatial relationships. Introducing the polyp segmentation model,
Prompt-Mamba [110] integrates Vision-Mamba as its backbone while implementing
prompt assistance, showcasing superior generalization performance on
downstream datasets. Also, Ye et al. [115] introduce P-Mamba for efficient
pediatric echocardiographic left ventricular segmentation. P-Mamba comprises
three key parts: the Vim encoder branch, the DWT-based PMD encoder branch, and
decoders. Each branch generates four feature maps, starting from higher
resolutions and gradually decreasing while also augmenting the channels. The
Vim branch is responsible for ensuring the model’s efficiency and capturing
overarching dependencies, while the DWT-based PMD branch focuses on
eliminating noise interference and preserving the integrity of target edges to
capture localized features. During the decoding process, the outputs from both
branches are merged and processed through Segmentation Head (SegHead) and
Fully Convolutional Network Head (FCNHead) decoders, which generate
segmentation masks by increasing resolution. Each decoder is guided by a
specific loss function to enhance the overall performance of the network.
Moreover, T-Mamba [118] presents a novel approach by integrating shared
positional encoding and frequency-based features into Vim, effectively
addressing concerns regarding spatial position preservation and feature
enhancement within the frequency domain. Additionally, it incorporates a gate
selection unit that dynamically combines two spatial domain features with one
frequency domain feature. T-Mamba marks the pioneering integration of
frequency-based features into Vim.

Various approaches have been proposed to reduce computational complexity, such
as Light M-UNet [114] and UltraLight VM-UNet [28]. UltraLight VM-UNet [28]
utilizes a Parallel Vision Mamba (PVM) layer, an approach within Vision Mamba,
which processes features in parallel. This method attains outstanding
performance with minimal computational complexity while maintaining a
consistent number of processing channels. UltraLight VM-UNet has a total of
6-layer structure consisting of a U-shaped structure. From layers 4 to 6, each
layer incorporates a PVM Layer. The decoder section also replicates the
encoder’s configuration. The skip-connection pathway employs both the Channel
Attention Bridge (CAB) module and the Spatial Attention Bridge (SAB) module to
fuse multi-level and multi-scale information. In another approach, the HC-
Mamba [119] model introduces dilated convolution to capture a wider range of
contextual details without increasing computational expenses. Furthermore, HC-
Mamba employs depthwise separable convolutions, decreasing parameters and
computational demands. This fusion of methods enables HC-Mamba to efficiently
handle extensive medical image datasets with reduced computational overhead
while upholding excellent performance.

####  4.1.3 Other Learning Types

The current paradigm of training deep learning models necessitates vast
amounts of labelled training data. This process is not only time-intensive but
also costly, particularly when it comes to gathering medical images, prompting
the path for methods based on limited supervision [124, 125]. These challenges
have inspired Mamba-based research efforts on learning medical image
segmentation with limited supervision. In this regard, Vim4Path [122] adopts a
modified version of the Vim [79] architecture with positional encoding [7]
within the seminal DINO [126] network to sequentially process on patch level
from the Gigapixel Whole Slide Image (WSI). Specifically, Vim4Path exploits a
self-distillation setup, where two Vim networks are considered teacher-
student, guiding the student’s training without labelled data. To compensate
for the mismatch of the dimensions of the input image, bicubic interpolation
is employed to modify the patch embeddings based on the target grid size,
which is determined from the input dimensions and patch size. This method
simulates the way cancer cells are realistically represented, transitioning
from close-up to a broader view on a slide, similar to how pathologists
navigate slides under a microscope to diagnose cancer cells. Two related
studies [120, 121] adopt the Mamba architecture to enhance model efficacy with
sparse annotations with distinct supervisory methods. In particular, The Weak-
Mamba-UNet [120] integrates CNN, ViT, and Mamba architectures for scribble-
based medical image segmentation. This method employs a collaborative cross-
supervisory mechanism that uses pseudo-labels to enhance learning and
refinement across the three architectures. Similarly, Semi-Mamba-UNet [121]
merges a conventional CNN-based UNet with a Mamba-based U-shaped encoder-
decoder within a semi-supervised learning framework. It introduces a pixel-
level contrastive learning strategy that maximizes feature extraction from
labelled and unlabeled data. Both methods demonstrate superior performance on
the ACDC MRI cardiac segmentation dataset [127] by effectively leveraging
sparse annotations through an integrated approach, demonstrating the range of
limited-supervised learning contexts that benefit from the unique features of
the visual Mamba.

###  4.2 Medical Image Classification

Medical image classification is a fundamental and essential task in the field
of CV. MedMamba architecture [96], inspired by the success of VMamba in
natural image classification, incorporates the SS-Conv-SSM module to enhance
feature extraction capabilities. This module uniquely combines convolutional
layers, which capture local features, with SSMs for long-range modelling, as
illustrated in Figure 8. This integration enables MedMamba to classify medical
images across various datasets effectively. The SS-Conv-SSM Block, a central
component of MedMamba, adopts a dual-branch approach using a 2D-selective-scan
(SS2D) to ensure robust integration of both fine-grained and coarse-grained
features, thus maximizing classification efficacy.

Figure 8: MedMamba architecture and illustration of SS-Conv-SSM block. From
[104]

Yang et al. [95] introduce the Contrastive Masked Vim Autoencoder (CMViM), a
novel representation learning method designed for 3D multi-modal data. This
approach incorporates the Vim into the masked autoencoder framework,
effectively reconstructing and modelling long-range dependencies in 3D medical
data for Alzheimer’s disease (AD) classification. The method consists of two
key steps: firstly, leveraging Vim within the masked autoencoder to enhance
the modelling of 3D masked multi-modal data, and secondly, applying
contrastive learning mechanisms to align multi-modal representations from both
intra-modal and inter-modal perspectives. This dual strategy enhances the
discriminative capabilities of image representations and ensures effective
alignment of multi-modal data, integrating intra-modal learning from the same
modality and inter-modal learning across different modalities to optimize
representation learning for AD classification.

Furthermore, MamMIL [97] integrates Mamba into multiple instance learning
(MIL), achieving efficient WSI classification. The model features a
bidirectional SSM and a 2D content-aware block using pyramid-structured
convolutions to learn bidirectional instance dependencies and 2D spatial
relations. MamMIL demonstrates advanced classification performance and uses
less GPU memory than transformer-based methods.

###  4.3 Medical Image Synthesis

In advancing smart healthcare, researchers are improving the scale and
diversity of medical datasets through medical image synthesis. Existing
methods face limitations due to CNN’s local perception and the quadratic
complexity of transformers, complicating the balance of structural texture
consistency. To address these challenges, the Vision Mamba DDPM (VM-DDPM) [99]
has been proposed. VM-DDPM is based on a SSM that integrates CNN’s local
perception with SSM’s global modeling capabilities(as illustrated in Figure
9), maintaining linear computational complexity. The design includes a multi-
level feature extraction module, the Multi-level State Space Block (MSSBlock),
and an encoder-decoder structure’s basic unit, the State Space Layer
(SSLayer), specifically for medical pathological images. Additionally, a
Sequence Regeneration strategy enhances the Cross-Scan Module (CSM), enabling
the S6 module to fully perceive 2D image spatial features and stimulate model
generalization. This innovative approach marks the first application of the
SSM-CNN hybrid architecture in medical image synthesis, demonstrating
competitive performance on various datasets, along with qualitative
assessments by radiologists.

Figure 9: (a) The general structure of VM-DDPM. (b) The primary building layer
of VM-DDPM is the SSLayer. (c) The central element of SSLayer is the MSSBlock
incorporates time embedding and CSM operations. From [99]

In a related effort, MD-Dose [98] introduces an innovative diffusion model
based on the Mamba architecture for predicting radiation therapy dose
distribution in thoracic cancer patients. MD-Dose adds Gaussian noise to dose
distribution maps in the forward process to create pure noise images and uses
a Mamba-based noise predictor to reconstruct the dose distribution maps in the
backward process. A Mamba encoder extracts structural information integrated
into the noise predictor to localize dose regions within the planning target
volume (PTV) and organs at risk (OARs). Experiments on a dataset of 300
thoracic tumour patients demonstrate MD-Dose’s superior performance across
various metrics and in terms of time efficiency.

###  4.4 Medial Image Registration

Capturing voxel-wise spatial correspondence across distinct modalities is
essential for medical image registration [128], yet current registration
methods often lack accuracy and clinical practicality. MambaMorph [101], an
innovative multi-modality deformable registration framework, leverages a
Mamba-based module for efficient long-range spatial modelling and a fine-
grained UNet-inspired feature extractor for high-dimensional learning.
Featuring well-aligned MR-CT volume pairs, MambaMorph excels in both
registration accuracy and speed, outperforming existing methods and
highlighting its significant potential for practical medical applications.

VMambaMorph [100], a groundbreaking hybrid VMamba-CNN network, is designed for
3D image registration. VMambaMorph computes the deformation field based on
target and source volumes using a U-shaped network architecture. The VMamba-
based block, redesigned with a 2D cross-scan module for 3D volumetric feature
processing and a fine-grained feature extraction module, is proposed for high-
dimensional feature learning. VMambaMorph incorporates a fine-grained feature
extractor to achieve high-level spatial features more effectively.

###  4.5 Medial Image Reconstruction

In endoscopic imaging, maintaining high-quality images is crucial for
assisting healthcare professionals in decision-making, as recorded images are
prone to exposure abnormalities [129]. To address this issue, motivated by the
success of Mamba in visual resotoration [103], FDVision Mamba (FDVM-Net)
[102], a frequency-domain based network, has been designed to achieve high-
quality image exposure correction by reconstructing the frequency domain of
endoscopic images. Inspired by SSMs, FDVM-Net incorporates a C-SSM block that
combines convolutional layers’ local feature extraction ability with the SSM’s
capability to capture long-range dependencies. The network features a dual-
path design, where each path processes the phase and amplitude information of
the image separately. Additionally, a novel frequency-domain cross-attention
mechanism enhances model performance by determining which information values
to preserve or overlook, thereby improving image quality and supporting better
clinical decision-making.

Similarly, MambaMIR [103], a Mamba-based model for medical image
reconstruction, and its Generative Adversarial Network-based variant,
MambaMIR-GAN, are introduced. MambaMIR inherits several advantages from the
original Mamba model, such as linear complexity, global receptive fields, and
dynamic weights. These features are particularly well-suited for medical image
reconstruction tasks, which require processing long sequences (large spatial
resolutions) to preserve detailed information and ensure global sensitivity
through long-range dependency. A novel arbitrary-mask mechanism is introduced
to adapt Mamba to this task, providing randomness for subsequent Monte Carlo-
based uncertainty estimation by randomly masking out redundant image scan
sequences. This mechanism enhances the model’s ability to handle variability
in medical imaging data, making MambaMIR and MambaMIR-GAN powerful tools for
both image reconstruction and uncertainty estimation.

###  4.6 Medical Language Processing

NLP systems have enormous potential in healthcare due to their ability to
comprehend complex clinical notes. The paper, [104], introduces a language
model designed to analyze longitudinal clinical notes with unmatched
precision, understand clinical context, and predict future patient outcomes.
ClinicalMamba harnesses the power of deep learning architecture trained on a
vast dataset of electronic health records, generating coherent and relevant
clinical text that has significant implications in healthcare. The proposed
model captures temporal relationships and context within patient records.

Figure 10: Prompt-based fine-tuning [104]

The provided text outlines a three-step methodology for training and fine-
tuning a language model tailored for clinical NLP tasks with limited labelled
data. The methodology involves pre-training on MIMIC-III clinical notes [130],
prompt-based fine-tuning (illustrated in Figure 10, and fine-tuning for two
specific clinical tasks: cohort selection for clinical trials and ICD coding.
The researchers also leveraged previous discharge summaries and incorporated
ICD code descriptions from prior visits to enhance the quality and
effectiveness of their approach.

###  4.7 Multi-Modal Understanding

Multi-modal learning, which combines pathological images with genomic data,
has significantly enhanced the accuracy of survival prediction in cancer
patients. This approach leverages the advantages of both data types;
pathological images detail the tumour microenvironment, capturing the
diversity of cancer cells and immune interactions [131], while genomic
profiles provide critical insights into cancer cell states and immune system
factors that affect dynamic prognostic outcomes [132]. By integrating these
complementary sources of information, multi-modal learning holds considerable
promise for improving the precision of cancer survival predictions.

SurvMamba [92] leverages state space modelling and multi-grained multi-modal
interactions to enhance its predictive performance, addressing the limitations
of traditional models. The paper introduces the Mamba model for multi-modal
survival prediction. It efficiently processes high-dimensional WSIs and
transcriptomic data, outperforming various SOTA methods with lower
computational cost. The proposed Hierarchical Interaction Mamba (HIM) module
encodes comprehensive intra-modal representations at fine-grained and coarse-
grained levels from WSI and transcriptomic data. An Interaction Fusion Mamba
(IFM) module also integrates histological and genomic features across various
levels, capturing multi-modal features from diverse perspectives. The system
creates a "bag" of each WSI and transcriptomics data, extracting features of
small instances and using a bidirectional Mamba in a dual-level Multiple
Instance Learning (MIL) framework to combine the small instances into larger
ones. The IFM module enables interactions between histological and genomic
features to derive representations at both small and large scales. Finally,
these multi-scale representations are fused to predict a hazard function and
obtain precise survival risk scores with confidence.

The MambaDFuse model, presented in [93], is designed for multi-modality image
fusion (MMIF). It operates in three phases: feature extraction, fusion, and
reconstruction. The model preserves essential information from different
modalities, such as MRI and CT scans, to produce high-quality fused images for
medical imaging applications. Each modality’s image is processed separately to
extract relevant features in the feature extraction phase. In the fusion
phase, the extracted features are combined using a fusion mechanism to
generate a fused representation that preserves essential information from both
modalities. In the final step, the fused image reconstruction module applies
the inverse transformation of the feature extraction process to produce a
high-quality fused image. The proposed model effectively preserves details and
enhances the quality of fused images, making it valuable for various medical
imaging applications, including diagnosis and treatment planning.

Figure 11: The architecture of MambaDFuse [93]. The system comprises three
stages: dual-level feature extraction, dual-phase feature fusion, and fused
image reconstruction.

The research focuses on enhancing image fusion techniques with MambaDFuse
(Figure 11), a more effective method than traditional CNNs and transformers.
The proposed dual-level feature extractor and dual-phase feature fusion module
achieve SOTA image fusion performance for both Infrared-visible image fusion
(IVF) and Multi-modality image fusion (MIF). The method’s fusion images
effectively facilitate downstream object detection, indicating potential for
future advancements in the field of image fusion.

A prediction model for acuity in the Intensive Care Unit (ICU) named
Stability, Transitions, and Life-Sustaining Therapies Prediction Model is
presented in [94]. The model, developed and validated in the paper, aims to
forecast the clinical condition of patients in the ICU, focusing on stability,
transitions, and necessary life-sustaining therapies. Leveraging the Mamba
framework, the model utilizes a combination of deep learning techniques and
clinical data to make accurate predictions regarding patient outcomes. Through
rigorous development and validation processes, Acuity Prediction in Intensive
Care Unit-Mamba (APRICOT-Mamba) demonstrates promising performance in
predicting ICU patient acuity, offering potential benefits for clinical
decision-making and patient care management in critical care settings.
APRICOT-M is an algorithm that accurately predicts the probability of a
patient being stable or unstable, along with the probability of mortality or
discharge. It also predicts transitions between acuity states and the need for
life-sustaining therapies, such as mechanical ventilation (MV), vasopressors
(VP), and continuous renal replacement therapy (CRRT).

###  4.8 Multi Task Learning

Multi-task learning offers significant advantages and is essential for
efficiently leveraging shared representations and improving the generalization
capabilities of models across various tasks. By learning multiple related
tasks simultaneously, models can capture commonalities and differences between
tasks, leading to better performance and reduced risk of overfitting. This
approach is particularly beneficial in complex domains such as 3D medical
imaging, where tasks like segmentation, classification, and landmark detection
are interrelated.

Integrating Mamba blocks in CNNs exemplifies an innovative approach in 3D
medical imaging, as demonstrated by nnMamba [91]. This led to the creation of
nnMamba, a versatile architecture that sets a new standard for segmentation,
classification, and landmark detection. The authors implemented a UNet
architecture, strategically incorporating the Mamba layer early to empower
features with global context from the start.

The paper introduces Mamba as a parallel module to further enhance the CNNs’
capability for modelling long-range dependencies. Additionally, the paper
proposes the mamba-In-Convolution (MIC) block, which combines SSM with
Convolutional layers, including a 1 × 1 convolution, batch normalization, and
ReLU activation. The paper introduces the Channel-Spatial Siamese (CSS) input
module, which fully harnesses the representational capabilities of SSMs,
inspired by Siamese Networks [133, 134]. It also emphasizes the effectiveness
of the Mamba-In-Convolution with Channel-Spatial Siamese input (MICCSS) module
for long-range relationship modelling. The authors improved performance in
dense prediction tasks by using an encoder with the MICCSS module and skip
scaling. Additionally, they enhanced the stem layer with the MICCSS module for
classification tasks, leading to significant improvements in accuracy and
performance.

In [90], a new MambaMIL model is proposed to address challenges in Multiple
Instance Learning (MIL). It includes the Reordering Mamba (SR-Mamba)
component, which captures long-range dependencies among positive instances.
This model has shown promising results in computational pathology tasks, such
as cancer diagnosis and tissue classification, highlighting the effectiveness
of sequence reordering for image analysis. With MambaMIL, each instance can
interact with any previously scanned instances through a compressed hidden
state, making it easier to model long sequences while mitigating computational
complexity. The authors partition the tissue regions of a WSI into patches and
map them into instance features using a feature extractor. The features are
then passed through linear projection and a series of stacked SR-Mamba modules
to model long sequences. Finally, an aggregation module obtains bag-level
representations for downstream tasks, capturing comprehensive contextual
information with minimal computational complexity.

##  5 Discussion

Table 1: Overview of the assessed Mamba-based models in medical applications,
emphasizing their core ideas and notable highlights.

Application |  Paper Names |  Core Idea |  Highlights
---|---|---|---
Multi-Task Learning |  MambaMIL [90] |  |
nnMamba [91] |  Utilizing shared representations enhances generalization and reduces overfitting, improving segmentation, classification, and landmark detection in 3D medical imaging. Mamba-CNN blocks effectively capture long-range dependencies and sequence relationships for vital medical tasks such as cancer diagnosis. |  $\bullet$ Enhancing dense prediction versatility across multiple tasks [91]
$\bullet$ Using Channel-Spatial Siamese modules for improved accuracy [91]
$\bullet$ Maintains minimal computational complexity for efficiency [91, 90]
$\bullet$ Employs shared representation to optimize learning [90] |
Multi-Modal Understanding |  SurvMamba [92] |  |
MambaDFuse [93] |  |  |
APRICOT-Mamba [94] |  Combining pathological images and genomic data improves survival prediction by leveraging their strengths. This method uses state space modeling and multi-modal interactions for efficient processing and high-quality image fusion. Deep learning with clinical data predicts ICU patient acuity, stability, transitions, and life-sustaining therapies |  $\bullet$ Producing high-quality fused images from multiple sources [93]
$\bullet$ Enhances understanding through multi-modal interactions and achieving effective multi-modality image fusion techniques [92, 93] |
Medial Image Classification |  CMViM [95] |  |
MedMamba [96] |  |  |
MamMIL [97] |  Combining convolutional layers with SSMs improves classification accuracy. Strategies like masked autoencoders and contrastive learning enhance 3D medical data classification. Multiple instance learning with bidirectional SSMs and pyramid-structured convolutions efficiently classifies whole slide images while reducing memory usage. |  $\bullet$ Utilizing contrastive learning for improved feature differentiation [95];
$\bullet$ Employs multiple instance learning for robust classification [97]
$\bullet$ Ensures efficient GPU usage for faster processing [97] |
Medial Image Synthesis |  MD-Dose [98] |  |
VM-DDPM [99] |  Combining CNN’s local perception with SSM’s global modeling, this approach maintains linear computational complexity. The diffusion process refines image details through noise addition and removal. Mamba and diffusion models together enhance radiation therapy dose prediction and medical image synthesis by managing noise and extracting structural information effectively |  $\bullet$ Leveraging sequence regeneration, enhance spatial feature perception and model generalization [99]
$\bullet$ Using a Mamba-based diffusion model, efficiently reconstruct dose
distribution maps and image synthesis with high accuracy [99, 98]
$\bullet$ Maintaining time efficiency by ensuring fast processing times while delivering high-quality data synthesis [98, 99] |
Medial Image Registration |  VMambaMorph [100] |  |
MambaMorph [101] |  Enhancing medical image registration involves capturing voxel-wise spatial correspondence through efficient long-range spatial modeling and high-dimensional feature learning. Using Mamba-based modules and a UNet-inspired feature extractor, these frameworks achieve superior registration accuracy and speed, making them practical for medical applications. |  $\bullet$ Excelling in aligning MR-CT volume pairs with high accuracy [101]
$\bullet$ Providing high registration speed through high-dimensional feature
learning [101]
$\bullet$ Efficient long-range spatial modeling enhances registration
performance and multi-modality deformable registration capabilities [100]
$\bullet$ Capturing voxel-wise spatial correspondence for better accuracy [101]. |
Medial Image Reconstruction |  FD-Vision Mamba [102] |  |
MambaMIR [103] |  Utilizing a dual-path design with frequency-domain cross-attention to improve image quality. Linear complexity, global receptive fields, and dynamic weights preserve detailed information, while an arbitrary-mask mechanism handles variability and provides uncertainty estimation. |  $\bullet$ Enhancing image quality via frequency-spatial dual-path reconstruction [102]
$\bullet$ Cross-attention with linear complexity preserves detailed
information [102]
$\bullet$ Monte Carlo-based uncertainty estimation handles variability effectively [103] |
Medical Language Processing |  ClinicalMamba [104] |  Leveraging a pre-trained Mamba language model, precisely analyzes longitudinal clinical notes, capturing temporal relationships and context within patient records. It employs a three-step methodology |  $\bullet$ Enhances context understanding for better medical insights by utilizing prompt-based fine-tuning [104]
$\bullet$ Facilitates accurate cohort selection in studies and efficiently
handles ICD coding tasks [104]
Medial Image Segmentation - Pure |  Mamba-UNet [105] |  |
TM-UNet [106] |  |  |
Mamba-HUNet [107] |  |  |
VM-UNet [108] |  |  |
Vivim (Video) [87] |  |  |
ViM-UNet [109] |  Excel at capturing long-range dependencies and intricate spatial relationships within medical images by utilizing visual SSM modules |  $\bullet$ Discerning long-range dependencies and modeling complex spatial relations for accurate segmentation [105, 106, 108, 109]
$\bullet$ Achieves efficient segmentation with linear time complexity [105, 87, 107] |
Medial Image Segmentation - Hybrid |  U-Mamba [33] |  |
UltraLight VM-UNet [28] |  |  |
ProMamba [110] |  |  |
H-vmunet [111] |  |  |
VM-UNET-V2 [112] |  |  |
LMa-UNet [113] |  |  |
LightM-UNet [114] |  |  |
P-Mamba [115] |  |  |
Swin-UMamba [116] |  |  |
SegMamba [117] |  |  |
T-Mamba [118] |  |  |
HC-Mamba [119] |  Hybrid models are proposed to combine the strengths of convolutional blocks and SSMs, enhancing local representation and feature capturing. |  $\bullet$ Balances local and global representation effectively by introducing convolutional blocks [33, 116, 112, 115]
$\bullet$ Integrating low and high-level features seamlessly [118, 115, 112]
$\bullet$ Reducing computational complexity for faster processing [28, 114, 117, 112] |
Medial Image Segmentation - Other Learning Types |  |  |
Weakly-Supervised Semi-Supervised |  |  |
Self-Supervised |  Weak-Mamba-UNet [120] |  |
Semi-Mamba-UNet [121] |  |  |
ViM4Path [122] |  Alternative learning methods, including self-supervised, semi-supervised, and weakly supervised techniques, aim to improve segmentation performance with limited supervision beside utilizing visual SSM modules. |  $\bullet$ Effectively handles segmentation tasks with limited annotated data [120, 121, 122]
$\bullet$ Leveraging self-supervised and semi-supervised learning to improve
segmentation performance [122, 121]
$\bullet$ Applying weakly supervised learning for better feature utilization and improving segmentation accuracy [120] |

Section 5 highlights the key concepts and objectives of the reviewed Mamba-
based models according to each category, representing the core ideas and
important features that can be investigated and utilized in future research.

Mamba-based models demonstrate significant advancements across various medical
imaging tasks by leveraging shared representations and advanced techniques. In
multi-task learning, models like MambaMIL [90] and nnMamba [91] enhance
generalization and reduce overfitting, proving effective in segmentation,
classification, and landmark detection. Multi-modal models such as SurvMamba
[92] and MambaDFuse [93] integrate pathological images with genomic data,
improving survival predictions and clinical outcomes through high-quality
image fusion. Medical image Synthesis models, including MD-Dose [98] and VM-
DDPM [99], combine local and global modelling to manage noise and extract
structural information efficiently, enhancing dose prediction and image
synthesis. Registration models like VMambaMorph [100] and MambaMorph [101]
utilize high-dimensional feature learning for accurate and fast alignment of
medical images. Reconstruction models, such as FD-Vision Mamba [102] and
MambaMIR [103], employ dual-path designs to enhance image quality and handle
variability. ClinicalMamba [104] uses a pre-trained language model in medical
language processing to analyze clinical notes, capturing temporal
relationships and context, thereby improving cohort selection and ICD coding
tasks. These models collectively contribute to improved accuracy, efficiency,
and clinical insights in medical image analysis.

Much of the research has focused on medical image segmentation (particularly
in proposing hybrid networks), where inputs often entail high-resolution data.
These segmentation frameworks leverage novel convolutional blocks to
efficiently capture local representations while utilizing SSM blocks to
capture long-range dependencies seamlessly. For example, U-Mamba [33] employs
Mamba blocks followed by residual convolutional blocks to understand local and
global information sequentially. Similarly, for segmenting 2D and 3D medical
images, LMa-UNet [113] uses large windows, transforming local spatial
modelling compared to traditional methods. This method is remarkably efficient
in global modelling, surpassing self-attention but with linear computational
complexity. It introduces a novel hierarchical and bidirectional Mamba block
that enhances global modelling capabilities and proficiency in capturing
intricate spatial relationships while using a convolutional decoder to
reconstruct the exact spatial relationships. Two approaches have been proposed
to reduce computational complexity significantly [28, 114]. Notably,
UltraLight VM-UNet [28], another hybrid approach, presents a lightweight
parallel SSM module alongside convolutional blocks to enhance local and global
segmentation accuracy. It is worth noting that pure models attempt to leverage
different visual Mamba blocks as an alternative to transformer blocks and
self-attention mechanisms, which suffer from the quadratic computational
burden. In both segmentation categories, SSM blocks capture long-range
dependencies across various datasets in different modalities. However, they
have not been effectively modified to act as versatile modules capturing both
types of information efficiently or to serve as a trade-off. In recent
developments, the "Other Learning Approaches" category has tried to apply
Mamba-based networks with novel learning types to reduce the need for vast
amounts of labelled training data and maximize feature extraction from
labelled and unlabeled data.

Like medical image segmentation, Mamba is also used in medical image
classification across different modalities to capture global dependencies and
utilize novel learning methodologies. Classification models like CMViM [95],
and MedMamba [96] improve accuracy by integrating convolutional layers with
SSMs. Techniques such as contrastive learning and multiple instance learning
(MIL) enhance the robustness of 3D medical data classification. These models
are designed for efficient GPU usage, making them suitable for processing
large-scale medical datasets while maintaining high accuracy.

Despite the advancements in various Mamba-based models, there remains a need
to investigate why these models have gained popularity in medical imaging and
why some tasks have more successfully adopted them. SSM-based models,
particularly in tasks like segmentation, have become increasingly favoured due
to significantly reducing the model’s theoretical complexity and its modelling
capability on high-resolution data. In medical imaging, efficiently processing
high-resolution images that provide accurate local information for disease
detection is crucial, and these models excel in this area. While SSMs have the
potential to be applied to different tasks, they may require further
modifications to be adapted to other specific tasks. For example, while being
applied to classification, the main contributions in this task still lie under
the broader ideas of leveraging these methodologies rather than modifying the
core SSM structures to achieve SOTA results [135]. Based on Figure 6, there is
still room for studies concerning other medical tasks in particular
categories, such as anomaly detection and image denoising. Lastly, it is worth
underscoring the necessity for trailblazing efforts in this dynamic and
swiftly advancing field, with numerous papers currently emerging alongside our
survey [136, 137, 138, 139, 140]. We are committed to continuously updating
our survey to reflect these ongoing developments.

##  6 Future Direction and Open Challenges

Throughout this survey, we have thoroughly analysed several Mamba models,
exploring their architectural designs, motivations, objectives, and
applications, all focused on addressing real-world challenges. In this
section, we delve into the challenges linked to Mamba’s unexplored potential
in the medical domain. Our goal is to pinpoint critical areas where Mamba’s
capabilities can be enhanced and expanded, thereby contributing to the
continuous advancement of medical Mamba.

$\bullet$ Generalization:

The power of generalization is key in developing smart healthcare, enabling a
wide range of research and clinical diagnosis applications. However, the Mamba
structure can be improved to enhance its ability to generalize. By effectively
managing domain-specific information that may accumulate or even amplify
within hidden states, we can significantly improve the generalization
performance of the SSM model in medical image analysis.

$\bullet$ Scanning Mechanism:

The selective scanning mechanism is a fundamental aspect of the Mamba model,
originally optimized for 1D causal sequential data. While effective for
autoregressive tasks, this mechanism is less suitable for understanding visual
domains [135]. Many existing approaches utilize bi-directional scanning and
extend scanning directions to capture the spatial information inherent in 2D
or higher-dimensional medical visual data to address the non-causal nature of
visual data. Despite these adaptations, Mamba-based models have shown a
performance drop in mainstream CV tasks and face a performance gap compared to
SOTA CNN-based and ViT models in high-level vision tasks. Therefore, there is
a potential need for more innovative scanning schemes to fully harness the
potential of higher-dimensional non-causal visual data, especially in medical
imaging applications.

$\bullet$ Explainability:

Studies have experimentally elucidated the mechanisms underlying the Mamba
model and its SSM counterparts in NLP, focusing on their in-context learning
capabilities [141]. Additionally, other works have established theoretical
foundations for Mamba’s applications in NLP [60], analyzing the Mamba model
and other pioneering SSMs from a control theoretic perspective to unravel the
decision-making processes within these models [61]. Despite these
advancements, understanding why Mamba excels in visual tasks, particularly in
medical imaging, remains challenging. This underscores the need for further
research to enhance the interpretability of Mamba networks in the field of
medical image analysis, aiming to unravel the nuances of exploitability in
visual Mamba networks.

$\bullet$ Inferior Performace on Some Tasks:

Recent studies suggest that SSMs are potentially beneficial for tasks that
follow the long-sequence and autoregressive characteristics such as object
detection & segmentation [135], while performing inferior in image
classification, which does not benefit from either feature. Given the
significance of models pre-trained on extensive datasets like ImageNet [84]
for various downstream applications, releasing the base, large, and huge
versions of Mamba could be extremely beneficial and represent a promising
future direction. Recently, the authors of Mamba have introduced the Mamba-2
architecture [142], which combines SSMs with attention mechanisms. This new
design leverages a theoretical framework that effectively bridges the gap
between SSMs and attention, significantly enhancing Mamba’s performance.

$\bullet$ Adaptation of Mamba to Medical Foundation Models:

Large-scale pre-trained models, namely foundation models [143], are crucial in
the field of medical imaging and considered an important step towards
artificial general intelligence (AGI) [144]. Although there are efforts to
incorporate Mamba as a foundation model, such as the Jamba framework [76] for
language modelling, there is still significant potential for developing
foundational models based on Mamba specifically for medical imaging. This area
remains largely unexplored, presenting a vast opportunity for innovation and
improvement in medical imaging analysis.

$\bullet$ Multi-modal Mamba:

Medicine is inherently a multi-modal field containing various sources of
information, such as clinical notes, laboratory tests, medical images, and
more, to deliver patient care [145]. Despite significant advancements in
biomedical AI, most existing models, including those based on mamba, are still
unimodal and focused on single tasks. Consequently, there is a need to
investigate further the development of new SSM-based backbones for the multi-
modal learning paradigm.

##  7 Conclusion

This survey reviews state space models (SSMs) in the medical domain, focusing
on the Mamba architecture. Specifically, the applications of Mamba models in
image segmentation, reconstruction, registration, classification, language
processing, multi-modal understanding, and other medically related works were
taxonomized and fully explored from multiple perspectives. We provide
systematic categorization of the literature incorporating additional facets
such as imaging modalities, organs of interest, and the computational
complexity of these methods. Furthermore, we consolidate the potential future
direction and the existing challenges, which should be carefully considered in
practice, can inspire more innovative works within the field of medical image
analysis. It is worth mentioning that some of the papers referenced in this
survey are pre-prints, particularly relevant because much of the work in this
field is happening simultaneously. Nevertheless, we have diligently ensured
the inclusion of high-quality research from respected sources in this fast-
moving area. We aspire this endeavour to offer a roadmap for researchers in
medical imaging, harnessing the potential of Mamba while also addressing its
shortcomings.

## References

  * [1] S Kevin Zhou, Hayit Greenspan, and Dinggang Shen.  Deep learning for medical image analysis.  Academic Press, 2023.
  * [2] Pawan Kumar Mall, Pradeep Kumar Singh, Swapnita Srivastav, Vipul Narayan, Marcin Paprzycki, Tatiana Jaworska, and Maria Ganzha.  A comprehensive review of deep neural networks for medical image processing: Recent developments and future opportunities.  Healthcare Analytics, page 100216, 2023.
  * [3] Reza Azad, Amirhossein Kazerouni, Moein Heidari, Ehsan Khodapanah Aghdam, Amirali Molaei, Yiwei Jia, Abin Jose, Rijo Roy, and Dorit Merhof.  Advances in medical image analysis with vision transformers: a comprehensive review.  Medical Image Analysis, page 103000, 2023.
  * [4] Olaf Ronneberger, Philipp Fischer, and Thomas Brox.  U-net: Convolutional networks for biomedical image segmentation.  In Medical image computing and computer-assisted intervention–MICCAI 2015: 18th international conference, Munich, Germany, October 5-9, 2015, proceedings, part III 18, pages 234–241. Springer, 2015.
  * [5] Dulari Bhatt, Chirag Patel, Hardik Talsania, Jigar Patel, Rasmika Vaghela, Sharnil Pandya, Kirit Modi, and Hemant Ghayvat.  Cnn variants for computer vision: History, architecture, application, challenges and future scope.  Electronics, 10(20):2470, 2021.
  * [6] DR Sarvamangala and Raghavendra V Kulkarni.  Convolutional neural networks in medical image understanding: a survey.  Evolutionary intelligence, 15(1):1–22, 2022.
  * [7] Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al.  An image is worth 16x16 words: Transformers for image recognition at scale.  arXiv preprint arXiv:2010.11929, 2020.
  * [8] Yang Liu, Yao Zhang, Yixin Wang, Feng Hou, Jin Yuan, Jiang Tian, Yang Zhang, Zhongchao Shi, Jianping Fan, and Zhiqiang He.  A survey of visual transformers.  IEEE Transactions on Neural Networks and Learning Systems, 2023.
  * [9] Salman Khan, Muzammal Naseer, Munawar Hayat, Syed Waqas Zamir, Fahad Shahbaz Khan, and Mubarak Shah.  Transformers in vision: A survey.  ACM computing surveys (CSUR), 54(10s):1–41, 2022.
  * [10] Jieneng Chen, Yongyi Lu, Qihang Yu, Xiangde Luo, Ehsan Adeli, Yan Wang, Le Lu, Alan L Yuille, and Yuyin Zhou.  Transunet: Transformers make strong encoders for medical image segmentation.  arXiv preprint arXiv:2102.04306, 2021.
  * [11] Pedro Celard, Eva Lorenzo Iglesias, José Manuel Sorribes-Fdez, Rubén Romero, A Seara Vieira, and Lourdes Borrajo.  A survey on deep learning applied to medical images: from simple artificial neural networks to generative models.  Neural Computing and Applications, 35(3):2291–2323, 2023.
  * [12] Sunil Kumar, Renu Dhir, and Nisha Chaurasia.  Brain tumor detection analysis using cnn: a review.  In 2021 international conference on artificial intelligence and smart systems (ICAIS), pages 1061–1067. IEEE, 2021.
  * [13] Vatsala Anand, Sheifali Gupta, Deepika Koundal, and Karamjeet Singh.  Fusion of u-net and cnn model for segmentation and classification of skin lesion from dermoscopy images.  Expert Systems with Applications, 213:119230, 2023.
  * [14] T Balamurugan and E Gnanamanoharan.  Brain tumor segmentation and classification using hybrid deep cnn with lunetclassifier.  Neural Computing and Applications, 35(6):4739–4753, 2023.
  * [15] Haval I Hussein, Abdulhakeem O Mohammed, Masoud M Hassan, and Ramadhan J Mstafa.  Lightweight deep cnn-based models for early detection of covid-19 patients from chest x-ray images.  Expert Systems with Applications, 223:119900, 2023.
  * [16] N Jagan Mohan and DN Kiran Pandiri.  Gil-cnn: A novel multipath features for covid-19 detection using ct-scan images.  IETE Journal of Research, 69(12):8804–8815, 2023.
  * [17] Osman Özkaraca, Okan İhsan Bağrıaçık, Hüseyin Gürüler, Faheem Khan, Jamil Hussain, Jawad Khan, and Umm e Laila.  Multiple brain tumor classification with dense cnn architecture using brain mri images.  Life, 13(2):349, 2023.
  * [18] Adyasha Sahu, Pradeep Kumar Das, and Sukadev Meher.  High accuracy hybrid cnn classifiers for breast cancer detection using mammogram and ultrasound datasets.  Biomedical Signal Processing and Control, 80:104292, 2023.
  * [19] André LS Meirelles, Tahsin Kurc, Jun Kong, Renato Ferreira, Joel H Saltz, and George Teodoro.  Building efficient cnn architectures for histopathology images analysis: A case-study in tumor-infiltrating lymphocytes classification.  Frontiers in Medicine, 9:894430, 2022.
  * [20] Fangyun Li, Lingxiao Zhou, Yunpeng Wang, Chuan Chen, Shuyi Yang, Fei Shan, and Lei Liu.  Modeling long-range dependencies for weakly supervised disease classification and localization on chest x-ray.  Quantitative Imaging in Medicine and Surgery, 12(6):3364, 2022.
  * [21] Fahad Shamshad, Salman Khan, Syed Waqas Zamir, Muhammad Haris Khan, Munawar Hayat, Fahad Shahbaz Khan, and Huazhu Fu.  Transformers in medical imaging: A survey.  Medical Image Analysis, page 102802, 2023.
  * [22] Kelei He, Chen Gan, Zhuoyuan Li, Islem Rekik, Zihao Yin, Wen Ji, Yang Gao, Qian Wang, Junfeng Zhang, and Dinggang Shen.  Transformers in medical image analysis.  Intelligent Medicine, 3(1):59–78, 2023.
  * [23] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin.  Attention is all you need.  Advances in neural information processing systems, 30, 2017.
  * [24] Yi Tay, Mostafa Dehghani, Dara Bahri, and Donald Metzler.  Efficient transformers: A survey.  ACM Computing Surveys, 55(6):1–28, 2022.
  * [25] Yi Xin, Siqi Luo, Haodi Zhou, Junlong Du, Xiaohong Liu, Yue Fan, Qing Li, and Yuntao Du.  Parameter-efficient fine-tuning for pre-trained vision models: A survey.  arXiv preprint arXiv:2402.02242, 2024.
  * [26] Josh Beal, Hao-Yu Wu, Dong Huk Park, Andrew Zhai, and Dmitry Kislyuk.  Billion-scale pretraining with vision transformers for multi-task visual representations.  In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 564–573, 2022.
  * [27] Moein Heidari, Amirhossein Kazerouni, Milad Soltany, Reza Azad, Ehsan Khodapanah Aghdam, Julien Cohen-Adad, and Dorit Merhof.  Hiformer: Hierarchical multi-scale representations using transformers for medical image segmentation.  In Proceedings of the IEEE/CVF winter conference on applications of computer vision, pages 6202–6212, 2023.
  * [28] Renkai Wu, Yinghao Liu, Pengchen Liang, and Qing Chang.  Ultralight vm-unet: Parallel vision mamba significantly reduces parameters for skin lesion segmentation, 2024.
  * [29] Sepp Hochreiter and Jürgen Schmidhuber.  Long short-term memory.  Neural computation, 9(8):1735–1780, 1997.
  * [30] Kyunghyun Cho, Bart Van Merriënboer, Caglar Gulcehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio.  Learning phrase representations using rnn encoder-decoder for statistical machine translation.  arXiv preprint arXiv:1406.1078, 2014.
  * [31] Nicolas Zucchet and Antonio Orvieto.  Recurrent neural networks: vanishing and exploding gradients are not the end of the story, 2024.
  * [32] Albert Gu and Tri Dao.  Mamba: Linear-time sequence modeling with selective state spaces, 2023.
  * [33] Jun Ma, Feifei Li, and Bo Wang.  U-mamba: Enhancing long-range dependency for biomedical image segmentation, 2024.
  * [34] Badri Narayana Patro and Vijay Srinivas Agneeswaran.  Mamba-360: Survey of state space models as transformer alternative for long sequence modelling: Methods, applications, and challenges.  arXiv preprint arXiv:2404.16112, 2024.
  * [35] Qinfeng Zhu, Yuanzhi Cai, Yuan Fang, Yihan Yang, Cheng Chen, Lei Fan, and Anh Nguyen.  Samba: Semantic segmentation of remotely sensed images with state space model.  arXiv preprint arXiv:2404.01705, 2024.
  * [36] Hang Guo, Jinmin Li, Tao Dai, Zhihao Ouyang, Xudong Ren, and Shu-Tao Xia.  Mambair: A simple baseline for image restoration with state-space model.  arXiv preprint arXiv:2402.15648, 2024.
  * [37] Qiuhong Shen, Xuanyu Yi, Zike Wu, Pan Zhou, Hanwang Zhang, Shuicheng Yan, and Xinchao Wang.  Gamba: Marry gaussian splatting with mamba for single view 3d reconstruction.  arXiv preprint arXiv:2403.18795, 2024.
  * [38] Keyan Chen, Bowen Chen, Chenyang Liu, Wenyuan Li, Zhengxia Zou, and Zhenwei Shi.  Rsmamba: Remote sensing image classification with state space model.  arXiv preprint arXiv:2403.19654, 2024.
  * [39] Kunchang Li, Xinhao Li, Yi Wang, Yinan He, Yali Wang, Limin Wang, and Yu Qiao.  Videomamba: State space model for efficient video understanding.  arXiv preprint arXiv:2403.06977, 2024.
  * [40] Jiuming Liu, Ruiji Yu, Yian Wang, Yu Zheng, Tianchen Deng, Weicai Ye, and Hesheng Wang.  Point mamba: A novel point cloud backbone based on state space model with octree-based ordering strategy.  arXiv preprint arXiv:2403.06467, 2024.
  * [41] Xiao Liu, Chenxu Zhang, and Lei Zhang.  Vision mamba: A comprehensive survey and taxonomy.  arXiv preprint arXiv:2405.04404, 2024.
  * [42] Hanwei Zhang, Ying Zhu, Dan Wang, Lijun Zhang, Tianxiang Chen, and Zi Ye.  A survey on visual mamba.  arXiv preprint arXiv:2404.15956, 2024.
  * [43] Xiao Wang, Shiao Wang, Yuhe Ding, Yuehang Li, Wentao Wu, Yao Rong, Weizhe Kong, Ju Huang, Shihao Li, Haoxiang Yang, et al.  State space model for new-generation network alternative to transformers: A survey.  arXiv preprint arXiv:2404.09516, 2024.
  * [44] Albert Gu, Karan Goel, and Christopher Ré.  Efficiently modeling long sequences with structured state spaces, 2022.
  * [45] Rudolph Emil Kalman.  A new approach to linear filtering and prediction problems.  1960\.
  * [46] Albert Gu, Isys Johnson, Karan Goel, Khaled Saab, Tri Dao, Atri Rudra, and Christopher Ré.  Combining recurrent, convolutional, and continuous-time models with linear state-space layers, 2021.
  * [47] Albert Gu, Tri Dao, Stefano Ermon, Atri Rudra, and Christopher Re.  Hippo: Recurrent memory with optimal polynomial projections, 2020.
  * [48] Daniel Y. Fu, Tri Dao, Khaled K. Saab, Armin W. Thomas, Atri Rudra, and Christopher Ré.  Hungry hungry hippos: Towards language modeling with state space models, 2023.
  * [49] Albert Gu, Ankit Gupta, Karan Goel, and Christopher Ré.  On the parameterization and initialization of diagonal state space models, 2022.
  * [50] Ankit Gupta, Albert Gu, and Jonathan Berant.  Diagonal state spaces are as effective as structured state spaces, 2022.
  * [51] Jimmy T. H. Smith, Andrew Warrington, and Scott W. Linderman.  Simplified state space layers for sequence modeling, 2023.
  * [52] Daniel Y. Fu, Elliot L. Epstein, Eric Nguyen, Armin W. Thomas, Michael Zhang, Tri Dao, Atri Rudra, and Christopher Ré.  Simple hardware-efficient long convolutions for sequence modeling, 2023.
  * [53] Yuhong Li, Tianle Cai, Yi Zhang, Deming Chen, and Debadeepta Dey.  What makes convolutional models great on long sequence modeling?, 2022.
  * [54] Michael Poli, Stefano Massaroli, Eric Nguyen, Daniel Y. Fu, Tri Dao, Stephen Baccus, Yoshua Bengio, Stefano Ermon, and Christopher Ré.  Hyena hierarchy: Towards larger convolutional language models, 2023.
  * [55] Bo Peng, Eric Alcaide, Quentin Anthony, Alon Albalak, Samuel Arcadinho, Stella Biderman, Huanqi Cao, Xin Cheng, Michael Chung, Matteo Grella, Kranthi Kiran GV, Xuzheng He, Haowen Hou, Jiaju Lin, Przemyslaw Kazienko, Jan Kocon, Jiaming Kong, Bartlomiej Koptyra, Hayden Lau, Krishna Sri Ipsit Mantri, Ferdinand Mom, Atsushi Saito, Guangyu Song, Xiangru Tang, Bolun Wang, Johan S. Wind, Stanislaw Wozniak, Ruichong Zhang, Zhenyuan Zhang, Qihang Zhao, Peng Zhou, Qinghua Zhou, Jian Zhu, and Rui-Jie Zhu.  Rwkv: Reinventing rnns for the transformer era, 2023.
  * [56] Yuchen Duan, Weiyun Wang, Zhe Chen, Xizhou Zhu, Lewei Lu, Tong Lu, Yu Qiao, Hongsheng Li, Jifeng Dai, and Wenhai Wang.  Vision-rwkv: Efficient and scalable visual perception with rwkv-like architectures, 2024.
  * [57] Xuezhe Ma, Chunting Zhou, Xiang Kong, Junxian He, Liangke Gui, Graham Neubig, Jonathan May, and Luke Zettlemoyer.  Mega: Moving average equipped gated attention, 2023.
  * [58] Harsh Mehta, Ankit Gupta, Ashok Cutkosky, and Behnam Neyshabur.  Long range language modeling via gated state spaces, 2022.
  * [59] Yutao Sun, Li Dong, Shaohan Huang, Shuming Ma, Yuqing Xia, Jilong Xue, Jianyong Wang, and Furu Wei.  Retentive network: A successor to transformer for large language models, 2023.
  * [60] Nicola Muca Cirone, Antonio Orvieto, Benjamin Walker, Cristopher Salvi, and Terry Lyons.  Theoretical foundations of deep selective state-space models, 2024.
  * [61] Carmen Amo Alonso, Jerome Sieber, and Melanie N. Zeilinger.  State space models as foundation models: A control theoretic overview, 2024.
  * [62] Ali Behrouz, Michele Santacatterina, and Ramin Zabih.  Mambamixer: Efficient selective state space models with dual token and channel selection.  arXiv preprint arXiv:2403.19888, 2024.
  * [63] Arnab Sen Sharma, David Atkinson, and David Bau.  Locating and editing factual associations in mamba.  arXiv preprint arXiv:2404.03646, 2024.
  * [64] Ziyang Wang, Jian-Qing Zheng, Yichi Zhang, Ge Cui, and Lei Li.  Mamba-unet: Unet-like pure visual mamba for medical image segmentation.  arXiv preprint arXiv:2402.05079, 2024.
  * [65] Jiqun Chu and Zuoquan Lin.  Incorporating exponential smoothing into mlp: A simple but effective sequence model.  arXiv preprint arXiv:2403.17445, 2024.
  * [66] Chengbin Du, Yanxi Li, and Chang Xu.  Understanding robustness of visual state space models for image classification.  arXiv preprint arXiv:2403.10935, 2024.
  * [67] Xiaohuan Pei, Tao Huang, and Chang Xu.  Efficientvmamba: Atrous selective scan for light weight visual mamba.  arXiv preprint arXiv:2403.09977, 2024.
  * [68] Chengkai Liu, Jianghao Lin, Jianling Wang, Hanzhou Liu, and James Caverlee.  Mamba4rec: Towards efficient sequential recommendation with selective state space models.  arXiv preprint arXiv:2403.03900, 2024.
  * [69] Ameen Ali, Itamar Zimerman, and Lior Wolf.  The hidden attention of mamba models.  arXiv preprint arXiv:2403.01590, 2024.
  * [70] Haruka Ezoe and Kazuhiro Sato.  Learning method for s4 with diagonal state space layers using balanced truncation.  arXiv preprint arXiv:2402.15993, 2024.
  * [71] Zhengcong Fei, Mingyuan Fan, Changqian Yu, and Junshi Huang.  Scalable diffusion models with state space backbone.  arXiv preprint arXiv:2402.05608, 2024.
  * [72] Naman Agarwal, Daniel Suo, Xinyi Chen, and Elad Hazan.  Spectral state space models.  arXiv preprint arXiv:2312.06837, 2023.
  * [73] Junxiong Wang, Tushaar Gangavarapu, Jing Nathan Yan, and Alexander M Rush.  Mambabyte: Token-free selective state space model.  arXiv preprint arXiv:2401.13660, 2024.
  * [74] Yuan Shi, Bin Xia, Xiaoyu Jin, Xing Wang, Tianyu Zhao, Xin Xia, Xuefeng Xiao, and Wenming Yang.  Vmambair: Visual state space model for image restoration, 2024.
  * [75] Zeyu Zhang, Akide Liu, Ian Reid, Richard Hartley, Bohan Zhuang, and Hao Tang.  Motion mamba: Efficient and long sequence motion generation with hierarchical and bidirectional selective ssm, 2024.
  * [76] Opher Lieber, Barak Lenz, Hofit Bata, Gal Cohen, Jhonathan Osin, Itay Dalmedigos, Erez Safahi, Shaked Meirom, Yonatan Belinkov, Shai Shalev-Shwartz, et al.  Jamba: A hybrid transformer-mamba language model.  arXiv preprint arXiv:2403.19887, 2024.
  * [77] Maciej Pióro, Kamil Ciebiera, Krystian Król, Jan Ludziejewski, and Sebastian Jaszczur.  Moe-mamba: Efficient selective state space models with mixture of experts.  arXiv preprint arXiv:2401.04081, 2024.
  * [78] Quentin Anthony, Yury Tokpanov, Paolo Glorioso, and Beren Millidge.  Blackmamba: Mixture of experts for state-space models.  arXiv preprint arXiv:2402.01771, 2024.
  * [79] Lianghui Zhu, Bencheng Liao, Qian Zhang, Xinlong Wang, Wenyu Liu, and Xinggang Wang.  Vision mamba: Efficient visual representation learning with bidirectional state space model.  arXiv preprint arXiv:2401.09417, 2024.
  * [80] Hugo Touvron, Matthieu Cord, Matthijs Douze, Francisco Massa, Alexandre Sablayrolles, and Hervé Jégou.  Training data-efficient image transformers & distillation through attention.  In International Conference on Machine Learning, pages 10347–10357. PMLR, 2021.
  * [81] Yue Liu, Yunjie Tian, Yuzhong Zhao, Hongtian Yu, Lingxi Xie, Yaowei Wang, Qixiang Ye, and Yunfan Liu.  Vmamba: Visual state space model.  arXiv preprint arXiv:2401.10166, 2024.
  * [82] Vincent Tao Hu, Stefan Andreas Baumann, Ming Gui, Olga Grebenkova, Pingchuan Ma, Johannes Fischer, and Bjorn Ommer.  Zigma: Zigzag mamba diffusion model.  arXiv preprint arXiv:2403.13802, 2024.
  * [83] Shufan Li, Harkanwar Singh, and Aditya Grover.  Mamba-nd: Selective state space modeling for multi-dimensional data.  arXiv preprint arXiv:2402.05892, 2024.
  * [84] Jia Deng, Wei Dong, Richard Socher, Li-Jia Li, Kai Li, and Li Fei-Fei.  Imagenet: A large-scale hierarchical image database.  In 2009 IEEE conference on computer vision and pattern recognition, pages 248–255. Ieee, 2009.
  * [85] Tao Huang, Xiaohuan Pei, Shan You, Fei Wang, Chen Qian, and Chang Xu.  Localmamba: Visual state space model with windowed selective scan.  arXiv preprint arXiv:2403.09338, 2024.
  * [86] Chenhongyi Yang, Zehui Chen, Miguel Espinosa, Linus Ericsson, Zhenyu Wang, Jiaming Liu, and Elliot J Crowley.  Plainmamba: Improving non-hierarchical mamba in visual recognition.  arXiv preprint arXiv:2403.17695, 2024.
  * [87] Yijun Yang, Zhaohu Xing, Chunwang Huang, and Lei Zhu.  Vivim: a video vision mamba for medical video object segmentation, 2024.
  * [88] Alessia Artesani, Alessandro Bruno, Fabrizia Gelardi, and Arturo Chiti.  Empowering pet: harnessing deep learning for improved clinical insight.  European Radiology Experimental, 8(1):17, 2024.
  * [89] Reza Azad, Nika Khosravi, Mohammad Dehghanmanshadi, Julien Cohen-Adad, and Dorit Merhof.  Medical image segmentation on mri images with missing modalities: A review.  arXiv preprint arXiv:2203.06217, 2022.
  * [90] Shu Yang, Yihui Wang, and Hao Chen.  Mambamil: Enhancing long sequence modeling with sequence reordering in computational pathology, 2024.
  * [91] Haifan Gong, Luoyao Kang, Yitao Wang, Xiang Wan, and Haofeng Li.  nnmamba: 3d biomedical image segmentation, classification and landmark detection with state space model, 2024.
  * [92] Ying Chen, Jiajing Xie, Yuxiang Lin, Yuhang Song, Wenxian Yang, and Rongshan Yu.  Survmamba: State space model with multi-grained multi-modal interaction for survival prediction, 2024.
  * [93] Zhe Li, Haiwei Pan, Kejia Zhang, Yuhua Wang, and Fengming Yu.  Mambadfuse: A mamba-based dual-phase model for multi-modality image fusion, 2024.
  * [94] Miguel Contreras, Brandon Silva, Benjamin Shickel, Tezcan Ozrazgat-Baslanti, Yuanfang Ren, Ziyuan Guan, Jeremy Balch, Jiaqing Zhang, Sabyasachi Bandyopadhyay, Kia Khezeli, Azra Bihorac, and Parisa Rashidi.  Apricot-mamba: Acuity prediction in intensive care unit (icu): Development and validation of a stability, transitions, and life-sustaining therapies prediction model, 2024.
  * [95] Guangqian Yang, Kangrui Du, Zhihan Yang, Ye Du, Yongping Zheng, and Shujun Wang.  Cmvim: Contrastive masked vim autoencoder for 3d multi-modal representation learning for ad classification, 2024.
  * [96] Yubiao Yue and Zhenzhang Li.  Medmamba: Vision mamba for medical image classification, 2024.
  * [97] Zijie Fang, Yifeng Wang, Zhi Wang, Jian Zhang, Xiangyang Ji, and Yongbing Zhang.  Mammil: Multiple instance learning for whole slide images with state space models, 2024.
  * [98] Linjie Fu, Xia Li, Xiuding Cai, Yingkai Wang, Xueyao Wang, Yali Shen, and Yu Yao.  Md-dose: A diffusion model based on the mamba for radiotherapy dose prediction, 2024.
  * [99] Zhihan Ju and Wanting Zhou.  Vm-ddpm: Vision mamba diffusion for medical image synthesis, 2024.
  * [100] Ziyang Wang, Jian-Qing Zheng, Chao Ma, and Tao Guo.  Vmambamorph: a multi-modality deformable image registration framework based on visual state space model with cross-scan module, 2024.
  * [101] Tao Guo, Yinuo Wang, Shihao Shu, Diansheng Chen, Zhouping Tang, Cai Meng, and Xiangzhi Bai.  Mambamorph: a mamba-based framework for medical mr-ct deformable registration, 2024.
  * [102] Zhuoran Zheng and Jun Zhang.  Fd-vision mamba for endoscopic exposure correction, 2024.
  * [103] Jiahao Huang, Liutao Yang, Fanwen Wang, Yinzhe Wu, Yang Nan, Angelica I. Aviles-Rivero, Carola-Bibiane Schönlieb, Daoqiang Zhang, and Guang Yang.  Mambamir: An arbitrary-masked mamba for joint medical image reconstruction and uncertainty estimation, 2024.
  * [104] Zhichao Yang, Avijit Mitra, Sunjae Kwon, and Hong Yu.  Clinicalmamba: A generative clinical language model on longitudinal clinical notes, 2024.
  * [105] Ziyang Wang, Jian-Qing Zheng, Yichi Zhang, Ge Cui, and Lei Li.  Mamba-unet: Unet-like pure visual mamba for medical image segmentation, 2024.
  * [106] Hao Tang, Lianglun Cheng, Guoheng Huang, Zhengguang Tan, Junhao Lu, and Kaihong Wu.  Rotate to scan: Unet-like mamba with triplet ssm module for medical image segmentation, 2024.
  * [107] Kazi Shahriar Sanjid, Md. Tanzim Hossain, Md. Shakib Shahariar Junayed, and Dr. Mohammad Monir Uddin.  Integrating mamba sequence model and hierarchical upsampling network for accurate semantic segmentation of multiple sclerosis legion, 2024.
  * [108] Jiacheng Ruan and Suncheng Xiang.  Vm-unet: Vision mamba unet for medical image segmentation, 2024.
  * [109] Anwai Archit and Constantin Pape.  Vim-unet: Vision mamba for biomedical segmentation, 2024.
  * [110] Jianhao Xie, Ruofan Liao, Ziang Zhang, Sida Yi, Yuesheng Zhu, and Guibo Luo.  Promamba: Prompt-mamba for polyp segmentation, 2024.
  * [111] Renkai Wu, Yinghao Liu, Pengchen Liang, and Qing Chang.  H-vmunet: High-order vision mamba unet for medical image segmentation, 2024.
  * [112] Mingya Zhang, Yue Yu, Limei Gu, Tingsheng Lin, and Xianping Tao.  Vm-unet-v2 rethinking vision mamba unet for medical image segmentation, 2024.
  * [113] Jinhong Wang, Jintai Chen, Danny Chen, and Jian Wu.  Large window-based mamba unet for medical image segmentation: Beyond convolution and self-attention, 2024.
  * [114] Weibin Liao, Yinghao Zhu, Xinyuan Wang, Chengwei Pan, Yasha Wang, and Liantao Ma.  Lightm-unet: Mamba assists in lightweight unet for medical image segmentation, 2024.
  * [115] Zi Ye, Tianxiang Chen, Fangyijie Wang, Hanwei Zhang, Guanxi Li, and Lijun Zhang.  P-mamba: Marrying perona malik diffusion with mamba for efficient pediatric echocardiographic left ventricular segmentation, 2024.
  * [116] Jiarun Liu, Hao Yang, Hong-Yu Zhou, Yan Xi, Lequan Yu, Yizhou Yu, Yong Liang, Guangming Shi, Shaoting Zhang, Hairong Zheng, and Shanshan Wang.  Swin-umamba: Mamba-based unet with imagenet-based pretraining, 2024.
  * [117] Zhaohu Xing, Tian Ye, Yijun Yang, Guang Liu, and Lei Zhu.  Segmamba: Long-range sequential modeling mamba for 3d medical image segmentation, 2024.
  * [118] Jing Hao, Lei He, and Kuo Feng Hung.  T-mamba: Frequency-enhanced gated long-range dependency for tooth 3d cbct segmentation, 2024.
  * [119] Jiashu Xu.  Hc-mamba: Vision mamba with hybrid convolutional techniques for medical image segmentation, 2024.
  * [120] Ziyang Wang and Chao Ma.  Weak-mamba-unet: Visual mamba makes cnn and vit work better for scribble-based medical image segmentation, 2024.
  * [121] Chao Ma and Ziyang Wang.  Semi-mamba-unet: Pixel-level contrastive and pixel-level cross-supervised visual mamba-based unet for semi-supervised medical image segmentation, 2024.
  * [122] Ali Nasiri-Sarvi, Vincent Quoc-Huy Trinh, Hassan Rivaz, and Mahdi S. Hosseini.  Vim4path: Self-supervised vision mamba for histopathology images, 2024.
  * [123] Reza Azad, Moein Heidary, Kadir Yilmaz, Michael Hüttemann, Sanaz Karimijafarbigloo, Yuli Wu, Anke Schmeink, and Dorit Merhof.  Loss functions in the era of semantic segmentation: A survey and outlook.  arXiv preprint arXiv:2312.05391, 2023.
  * [124] Shih-Cheng Huang, Anuj Pareek, Malte Jensen, Matthew P Lungren, Serena Yeung, and Akshay S Chaudhari.  Self-supervised learning for medical image classification: a systematic review and implementation guidelines.  NPJ Digital Medicine, 6(1):74, 2023.
  * [125] Jialin Peng and Ye Wang.  Medical image segmentation with limited supervision: a review of deep network models.  IEEE Access, 9:36827–36851, 2021.
  * [126] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jégou, Julien Mairal, Piotr Bojanowski, and Armand Joulin.  Emerging properties in self-supervised vision transformers.  In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 9650–9660, 2021.
  * [127] Olivier Bernard, Alain Lalande, Clement Zotti, Frederick Cervenansky, Xin Yang, Pheng-Ann Heng, Irem Cetin, Karim Lekadir, Oscar Camara, Miguel Angel Gonzalez Ballester, et al.  Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: is the problem solved?  IEEE transactions on medical imaging, 37(11):2514–2525, 2018.
  * [128] Mark Nowell, Roman Rodionov, Beate Diehl, Tim Wehner, Gergely Zombori, Jane Kinghorn, Sebastien Ourselin, John Duncan, Anna Miserocchi, and Andrew McEvoy.  A novel method for implementation of frameless stereoeeg in epilepsy surgery.  Neurosurgery, 10, 08 2014.
  * [129] Lu Sang, Bjoern Haefner, and Daniel Cremers.  Inferring super-resolution depth from a moving light-source enhanced rgb-d sensor: a variational approach.  In Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision, pages 1–10, 2020.
  * [130] Alistair E W Johnson, Tom J Pollard, Lu Shen, Li-wei H Lehman, Mengling Feng, Mohammad Ghassemi, Benjamin Moody, Peter Szolovits, Leo Anthony Celi, and Roger G Mark.  Mimic-iii, a freely accessible critical care database.  Scientific Data, 2016.
  * [131] Cheng-Peng Gui, Yu-Hang Chen, Hong-Wei Zhao, Jia-Zheng Cao, Tian-Jie Liu, Sheng-Wei Xiong, Yan-Fei Yu, Bing Liao, Yun Cao, Jia-Ying Li, Kang-Bo Huang, Hui Han, Zhi-Ling Zhang, Wen-Fang Chen, Ze-Ying Jiang, Ye Gao, Guan-Peng Han, Qi Tang, Kui Ouyang, Gui-Mei Qu, Ji-Tao Wu, Jian-Ping Guo, Cai-Xia Li, Pei-Xing Li, Zhi-Ping Liu, Jer-Tsong Hsieh, Mu-Yan Cai, Xue-Song Li, Jin-Huan Wei, and Jun-Hang Luo.  Multimodal recurrence scoring system for prediction of clear cell renal cell carcinoma outcome: a discovery and validation study.  The Lancet Digital Health, 5(8):e515–e524, 2023.
  * [132] Mengsha Tong, Yuxiang Lin, Wenxian Yang, Jinsheng Song, Zheyang Zhang, Jiajing Xie, Jingyi Tian, Shijie Luo, Chenyu Liang, Jialiang Huang, et al.  Prioritizing prognostic-associated subpopulations and individualized recurrence risk signatures from single-cell transcriptomes of colorectal cancer.  Briefings in Bioinformatics, 24(3):bbad078, 2023.
  * [133] Luca Bertinetto, Jack Valmadre, Joao F. Henriques, Andrea Vedaldi, and Philip H. S. Torr.  Fully-convolutional siamese networks for object tracking.  In Computer Vision – ECCV 2016 Workshops, pages 850–865, 2016.
  * [134] Haifan Gong, Yumeng Zhang, Chenhe Dong, Yue Wang, Guanqi Chen, Bilin Liang, Haofeng Li, Lanxuan Liu, Jie Xu, and Guanbin Li.  Unbiased curriculum learning enhanced global-local graph neural network for protein thermodynamic stability prediction.  Bioinformatics, 2023.
  * [135] Weihao Yu and Xinchao Wang.  Mambaout: Do we really need mamba for vision?  arXiv preprint arXiv:2405.07992, 2024.
  * [136] Omer F Atli, Bilal Kabas, Fuat Arslan, Mahmut Yurt, Onat Dalmaz, and Tolga Çukur.  I2i-mamba: Multi-modal medical image synthesis via selective state space modeling.  arXiv preprint arXiv:2405.14022, 2024.
  * [137] Adibvafa Fallahpour, Mahshid Alinoori, Arash Afkanpour, and Amrit Krishnan.  Ehrmamba: Towards generalizable and scalable foundation models for electronic health records.  arXiv preprint arXiv:2405.14567, 2024.
  * [138] Jiashu Xu.  Hc-mamba: Vision mamba with hybrid convolutional techniques for medical image segmentation.  arXiv preprint arXiv:2405.05007, 2024.
  * [139] Viet-Thanh Nguyen, Van-Truong Pham, and Thi-Thao Tran.  Ac-mambaseg: An adaptive convolution and mamba-based architecture for enhanced skin lesion segmentation.  arXiv preprint arXiv:2405.03011, 2024.
  * [140] Kazi Shahriar Sanjid, Md Tanzim Hossain, Md Shakib Shahariar Junayed, and M Monir Uddin.  Optimizing universal lesion segmentation: State space model-guided hierarchical networks with feature importance adjustment.  arXiv preprint arXiv:2404.17235, 2024.
  * [141] Riccardo Grazzi, Julien Siems, Simon Schrodi, Thomas Brox, and Frank Hutter.  Is mamba capable of in-context learning?, 2024.
  * [142] Tri Dao and Albert Gu.  Transformers are ssms: Generalized models and efficient algorithms through structured state space duality, 2024.
  * [143] Bobby Azad, Reza Azad, Sania Eskandari, Afshin Bozorgpour, Amirhossein Kazerouni, Islem Rekik, and Dorit Merhof.  Foundational models in medical imaging: A comprehensive survey and future vision.  arXiv preprint arXiv:2310.18689, 2023.
  * [144] Muhammad Awais, Muzammal Naseer, Salman Khan, Rao Muhammad Anwer, Hisham Cholakkal, Mubarak Shah, Ming-Hsuan Yang, and Fahad Shahbaz Khan.  Foundational models defining a new era in vision: A survey and outlook.  arXiv preprint arXiv:2307.13721, 2023.
  * [145] Tao Tu, Shekoofeh Azizi, Danny Driess, Mike Schaekermann, Mohamed Amin, Pi-Chuan Chang, Andrew Carroll, Charles Lau, Ryutaro Tanno, Ira Ktena, et al.  Towards generalist biomedical ai.  NEJM AI, 1(3):AIoa2300138, 2024.