# LLEMamba: Low-Light Enhancement via Relighting-Guided Mamba with Deep
Unfolding Network

Xuanqi Zhang  Harbin Institute of Technology, Shenzhen  Haijin Zeng  IMEC-
UGent  Jinwang Pan  Harbin Institute of Technology  Qiangqiang Shen  Harbin
Institute of Technology, Shenzhen  Yongyong Chen  Harbin Institute of
Technology, Shenzhen

###### Abstract

Transformer-based low-light enhancement methods have yielded promising
performance by effectively capturing long-range dependencies in a global
context. However, their elevated computational demand limits the scalability
of multiple iterations in deep unfolding networks, and hence they have
difficulty in flexibly balancing interpretability and distortion. To address
this issue, we propose a novel Low-Light Enhancement method via relighting-
guided Mamba with a deep unfolding network (_LLEMamba_), whose theoretical
interpretability and fidelity are guaranteed by Retinex optimization and Mamba
deep priors, respectively. Specifically, our LLEMamba first constructs a
Retinex model with deep priors, embedding the iterative optimization process
based on the Alternating Direction Method of Multipliers (ADMM) within a deep
unfolding network. Unlike Transformer, to assist the deep unfolding framework
with multiple iterations, the proposed LLEMamba introduces a novel Mamba
architecture with lower computational complexity, which not only achieves
light-dependent global visual context for dark images during reflectance
relight but also optimizes to obtain more stable closed-form solutions.
Experiments on the benchmarks show that LLEMamba achieves superior
quantitative evaluations and lower distortion visual results compared to
existing state-of-the-art methods.

##  1 Introduction

Low-light image enhancement is an essential function within the domains of
computer vision and image processing, which not only aids in better visual
perception but also boosts the efficacy of downstream applications such as
autonomous vehicles, object recognition, and semantic segmentation li2021low ;
hou2024global . Historically, various methodologies have been employed to
address the challenge of enhancing images captured under low-light conditions,
including histogram equalization pizer1987adaptive , Retinex-based model
jobson1997multiscale , and learning-based strategy guo2020zero  to manipulate
the luminance and contrast of such images.

Deep learning models that utilize end-to-end convolutional neural networks
(CNNs) to relight low-light images have been actively developed zhang2022deep
; wang2022low ; xu2023low . However, the performance of these learning-based
methods is limited due to the lack of large-scale training data to uncover the
diversity and complex mappings from low-light to normal-light conditions
ren2019low . In the meantime, model-based algorithms such as Retinex-based
models, formulate an input image as pixel-wise multiplication of illumination
and reflectance, and attempt to estimate ideal illumination and reflectance by
deriving their optimal closed-form solutions with theoretical guarantee
park2017low ; li2018structure ; lin2022low . However, on the one hand, these
model-based Retinex methods reveal limitations in denoising and restoring the
reflectance parts in the low-light images, due to the lack of well-designed
priors. On the other hand, these methods show slow convergence, due to the
inevitable hundreds of iterations and hand-crafted constraints that are
difficult to optimize.

Accordingly, Retinex-based unfolding networks are proposed to deal with the
above defects of both deep learning and Retinex methods while retaining their
benefits zheng2021adaptive ; wu2022uretinex ; liu2023low , which have shown
promising performance and explainability in different benchmarks. Among them,
Zheng et al. zheng2021adaptive  proposed to incorporate total variation
regularization into the unfolding process, and could recover more details by
learning a noise level map. Beyond their proposed UTVNet zheng2021adaptive ,
Wu et al. wu2022uretinex  replaced the traditional prior of total variation by
two deep priors, while Li et al. liu2023low  integrated both implicit priors
learned from data and explicit priors inherited from traditional methods into
algorithm unrolling networks and could capture both global and local
brightness. However, these Retinex-based unfolding techniques just rely on
simple convolutional neural networks as the deep priors, and hence fail to
acquire the long-range dependencies and non-local self-similarity in both
light and dark areas for low-light images. One clear example is shown in Fig.
1. For the Retinex-based unfolding model URetinex-Net wu2022uretinex , the
exposure to the lighting causes distant objects to appear excessively white
and bright, losing their original color information.

Recently, to compensate for the aforementioned deficiencies, some advanced
architectures, such as vision Transformers, have been employed for better
reflectance restoration xu2022snr ; cai2023retinexformer ; wang2023low ;
ye2024codedbgt . For example, to maintain the ability of ong-range
dependencies, Cai et al. cai2023retinexformer  and Wang et al. wang2023low
presented Retinexformer and IAGC models, respectively. The former emphasized
developing an Illumination-Guided Transformer after a Retinex decomposition to
manage the non-local interactions across regions with varying lighting
conditions, while the latter designed a new Transformer block that fully
modeled pixel dependencies through a local-to-global hierarchical attention
approach, enabling dark areas to leverage information from distant,
informative regions effectively. However, these Transformer-based models are
often encountered with overexposure in lighting areas, as shown in Fig. 1. Not
only that, they generally bear a tedious training process and higher
computational complexity that significantly hinder the expansion of Retinex-
based unfolding networks into the Transformer framework, and hence face
challenges in adeptly managing the trade-off between interpretability and
image distortion.

To this end, this paper, motivated by the efficient Mamba architecture
zhu2024vision , designs a Mamba-driven deep Retinex unfolding network for low-
light enhancement (LLEMamba) that implements Mamba to relight the reflectance
and illumination parts for visual guarantee and sticks to the Retinex theory
to optimize the closed-form solution of each subproblem for interpretability
maintenance. Firstly, the proposed LLEMamba performs deep unfolding on the
iteration optimization process of the Retinex model to obtain reflectance and
illumination images with mathematical meaning as shown in Fig. 2. Secondly,
LLEMamba introduces Relighting-Guided Mamba to relight the reflectance, which
adopts a novel Illumination-Fused Bidirectional Mamba (IFBM). Thirdly, the
Mamba-driven network utilizes the linear complexity of State Space Model to
enhance the Retinex unfolding network efficiently. Additionally, further
experiments demonstrate the effectiveness and efficiency of our LLEMamba.

Figure 1: Example of (b) URetinex-Net wu2022uretinex , (c) Retinexformer
cai2023retinexformer , and the proposed (d) LLEMamba for reconstruction error
(i.e., color distortion, noise, artifact) comparison in the light area. In
contrast to existing state-of-the-art low-light enhancement methods URetinex-
Net, Retinexformer, our LLEManba not only restores the bright areas without
overexposure but also relights the dark areas without noise and color
distortion. This benefits from the stability of Retinex optimization and the
sustainability of long-range dependencies.

Our main contributions are summarized as follows.

  1. 1.

We propose the relighting-guided Mambda with deep unfolding network
(LLEMamba), building the first Mamba-based method for low-light enhancement to
our knowledge, which could achieve a double win across theoretical
interpretability and reconstruction quality.

  2. 2.

We fuse Mamba into the iterative optimization process of Retinex model with
lower computational complexity, which could boost the multiple iterations of
deep unfolding networks for stable closed-form solutions.

  3. 3.

We design a more accurate alternating iterative solution method based on ADMM.
Numerous experiments show that our proposed models outperform the state-of-
the-art methods on various benchmark datasets.

Figure 2: Overview of our proposed Relighting-guided Mamba with Deep Unfolding
Network. (a) In the Deep Unfolding Network for Relight, the input is first
decomposed by convolutional layers. Then decomposed images are optimized by
deep unfolding layers in $k$ iterations to output the enhanced images. (b) The
reflectance in $\mathbf{P}^{(k)}$ is processed by Relighting-Guided Mamba. The
Relighting-Guided Mamba is a U-shaped network with Illumination-Fused
Bidirectional Mamba (IFBMamba) as the backbone. (c) Then, the reflectance is
processed by IFBMamba. The input is flattened and input into bidirectional
Mamba after fused with Illumination.

##  2 Related work

Retinex-based low-light image enhancement:  Retinex theory, recognized for its
role in achieving lightness and color constancy in computer vision
jobson1997properties , is instrumental in low-light image enhancement. It
enables the decomposition of an image into its reflectance and illumination
components li2018structure ; lin2022low . By enhancing the illumination
component, Retinex-based models aim to simulate brighter lighting conditions,
thereby improving visibility and image quality guo2016lime ; wei2018deep . To
address the challenges (i.e., inevitable noise and poor visibility) in low-
light image enhancement, sophisticated neural networks have been developed to
tackle the illumination and reflectance components separately. These networks
are designed to adjust the light levels and remove degradations caused by poor
lighting conditions zhang2021beyond . Furthermore, there has been progress in
creating simple CNN-based networks that allow for user-specific illumination
adjustment zhang2019kindling ; wu2022uretinex . Despite these advancements,
current models still face limitations, particularly in accurately recovering
the reflectance component. They often struggle with noise and color distortion
issues. Consequently, there is a pressing demand for the development of more
efficient networks that can effectively enhance illumination and recover
reflectance.

Vision Mamba: The Mamba architecture, initially introduced for its efficiency
in training and inference compared to Transformers and Recurrent Neural
Networks gu2023mamba , has been increasingly adopted in various vision
applications, such as image dehazing zheng2024u , video understanding
li2024videomamba , and biomedical image segmentation ma2024u . Particularly, a
pivotal component of the Mamba framework, the scanning mechanism, is not only
instrumental in enhancing efficiency but also in providing essential
contextual information for visual tasks zhang2024survey . In order to adeptly
handle 2D or 3D data, innovative designs of the scanning mechanism and the
architecture of Mamba blocks are critical for effectively managing multi-
dimensional inputs. For example, bidirectional scanning has been effectively
employed in applications such as image classification and semantic
segmentation wang2024large ; zhu2024vision . Additionally, a multi-path
scanning strategy has been proposed within the frequency domain
zhen2024freqmamba , with the Frequency Band Scanning Mamba offering a new
perspective on 2D modeling. Beyond the pure Mamba architectures, hybrid models
combining Mamba with other architectural paradigms, such as CNNs chen2024res
and Transformers zubic2024state , are currently being developed. Despite these
advances, the potential of Mamba architectures in addressing low-light image
enhancement problem, remains largely uncharted and presents an opportunity for
further research.

##  3 Method

In this section, we introduce the proposed LLEMamba that consists of three
parts, i.e., Retinex-based deep unfolding network, relighting-guided Mamba,
and illumination-fused Bidirectional Mamba, as shown in Fig. 2.

###  3.1 Retinex-based deep unfolding network

Following the Retinex theory, images can be decomposed into reflectance with
physical color information and Illumination with the degree of lighting. Then,
given an input image $\mathbf{I}\in\mathbb{R}^{H\times W\times 3}$, it can be
formulated as the multiplication of Reflectance
$\mathbf{R}\in\mathbb{R}^{H\times W\times 3}$ and Illumination
$\mathbf{L}\in\mathbb{R}^{H\times W\times 3}$:

$\begin{array}[]{lr}\mathbf{I}=\mathbf{R}\circ\mathbf{L},\end{array}$ (1)

where $\circ$ represents the pixel-wise multiplication. $H$ and $W$ denote the
spatial dimensions of the original low-light image.

It is known that separating $\mathbf{R}$ and $\mathbf{L}$ from $\mathbf{I}$ is
an ill-posed problem. To address the above ill-posedness issue, several hand-
crafted priors have been designed, such as low-rankness for noise suppression
ren2020lr3m , total variation for noise level map learning zheng2021adaptive .
Although these hand-crafted priors have clear mathematical meanings, they have
limited reconstruction performance and require manual adjustment for different
scenarios. To relight the two decomposed components, we add deep priors for
both the reflectance layer and illumination layer as $f(\cdot)$ and
$g(\cdot)$. Unlike URetinex-Net wu2022uretinex , we design Mamba networks to
replace $f(\cdot)$ and $g(\cdot)$. The objective function of minimization of
the Eq. (1) can be formulated as:

$\begin{array}[]{lr}\mathop{\min}\limits_{\mathbf{R},\mathbf{L}}\|\mathbf{R}\circ\mathbf{L}-\mathbf{I}\|_{F}^{2}+\lambda
f(\mathbf{R})+\gamma g(\mathbf{L}).\end{array}$ (2)

By introducing two auxiliary variables, i.e., $\mathbf{R}=\mathbf{P}$ and
$\mathbf{L}=\mathbf{Q}$, the corresponding Lagrangian function of Eq. (2) can
be written as:

$\begin{array}[]{lr}\mathcal{L}=\|\mathbf{R}\circ\mathbf{L}-\mathbf{I}\|_{F}^{2}\par+\lambda
f(\mathbf{P})+\gamma
g(\mathbf{Q})\par+\frac{\mu}{2}\|\mathbf{R}-\mathbf{P}+\frac{\mathbf{Y_{1}}}{\mu}\|_{F}^{2}+\frac{\mu}{2}\|\mathbf{L}-\mathbf{Q}+\frac{\mathbf{Y_{2}}}{\mu}\|_{F}^{2},\end{array}$
(3)

where $\mathbf{Y_{2}}$ and $\mathbf{Y_{1}}$ represent the Lagrangian
Multipliers. We employ the Alternative Directional Method of Multipliers
(ADMM) to decompose the optimization problem into subproblems with respect to
$\mathbf{R}$, $\mathbf{L}$, $\mathbf{P}$, and $\mathbf{Q}$.

$\mathbf{R}$-subproblem:  We update $\mathbf{R}$ by fixing other variables as

$\begin{array}[]{lr}\mathbf{R}^{(k+1)}=\mathop{\arg\min}\limits_{\mathbf{R}}\|\mathbf{R}\circ\mathbf{L}^{(k)}-\mathbf{I}\|_{F}^{2}\par+\frac{\mu^{(k)}}{2}\|\mathbf{R}-\mathbf{P}^{(k)}+\frac{\mathbf{Y_{1}}^{(k)}}{\mu^{(k)}}\|_{F}^{2}.\end{array}$
(4)

We take the derivative with respect to $\mathbf{R}$ and take it to zero. The
closed-form solution of Eq. (4) is:

$\begin{array}[]{lr}\mathbf{R}^{(k+1)}=(2(\mathbf{I}\circ\mathbf{L}^{(k)})+\mu^{(k)}\mathbf{P}^{(k)}-\mathbf{Y}_{1}^{(k)})(2(\mathbf{L}^{(k)}\circ\mathbf{L}^{(k)})+\mu^{(k)}\mathbf{D})^{-1}.\end{array}$
(5)

where $\mathbf{D}\in\mathbb{R}^{H\times W\times 3}$ is concatenated by three
identity matrices along the mode 3.

$\mathbf{L}$-subproblem:  We update $\mathbf{L}$ by fixing other variables as

$\begin{array}[]{lr}\mathbf{L}^{(k+1)}=\mathop{\arg\min}\limits_{\mathbf{L}}\|\mathbf{R}^{(k+1)}\circ\mathbf{L}-\mathbf{I}\|_{F}^{2}+\frac{\mu^{(k)}}{2}\|\mathbf{L}-\mathbf{Q}^{(k)}+\frac{\mathbf{Y}_{2}^{(k)}}{\mu^{(k)}}\|_{F}^{2}.\end{array}$
(6)

The closed-form solution of Eq. (6) is given by

$\begin{array}[]{lr}\mathbf{L}^{(k+1)}=(2(\mathbf{I}\circ\mathbf{R}^{(k+1)})+\mu^{(k)}\mathbf{Q}^{(k)}-\mathbf{Y}_{2}^{(k)})(2(\mathbf{R}^{(k+1)}\circ\mathbf{R}^{(k+1)})+\mu^{(k)}\mathbf{D})^{-1}.\end{array}$
(7)

$\mathbf{P}$-subproblem:  We update $\mathbf{P}$ by fixing other variables as

$\begin{array}[]{lr}\mathbf{P}^{(k+1)}=\mathop{\arg\min}\limits_{\mathbf{P}}\lambda
f(\mathbf{P})+\frac{\mu^{(k)}}{2}\|\mathbf{R}^{(k+1)}-\mathbf{P}+\frac{\mathbf{Y_{1}}^{(k)}}{\mu^{(k)}}\|_{F}^{2}.\end{array}$
(8)

By simple algebra, we can obtain

$\begin{array}[]{lr}\mathbf{P}^{(k+1)}=\mathop{\arg\min}\limits_{\mathbf{P}}f(\mathbf{P})+\frac{1}{(2\sqrt{\lambda/\mu^{(k)}})^{2}}\|\mathbf{P}-\mathbf{M}^{(k+1)}\|_{F}^{2},\end{array}$
(9)

where
$\mathbf{M}^{(k+1)}=\mathbf{R}^{(k+1)}+\frac{\mathbf{Y_{1}}^{(k)}}{\mu^{(k)}}$
could be viewed as the noisy image. Thus, the clean image $\mathbf{P}^{(k+1)}$
could be perceived from the noisy image $\mathbf{M}^{(k+1)}$ referring to
noise $\alpha$, where $\alpha=\sqrt{\lambda/\mu^{(k)}}$. According to
zhu2023denoising , we can also derive Eq. (9) as

$\begin{array}[]{lr}\mathbf{P}^{(k+1)}=\mathbf{M}^{(k+1)}+\alpha^{2}f_{\Theta}(\mathbf{M}^{(k+1)}),\end{array}$
(10)

where $f_{\Theta}$ represents the relighting-guided Mamba network and $\Theta$
denotes its network parameter. Compared with URetinex-Net wu2022uretinex , we
obtain a more accurate $\mathbf{P}$ by embedding the parameters $\lambda$ and
$\mu$ into the closed-form solution.

$\mathbf{Q}$-subproblem:  We update $\mathbf{Q}$ by fixing other variables as

$\begin{array}[]{lr}\mathbf{Q}^{(k+1)}=\mathop{\arg\min}\limits_{\mathbf{Q}}\gamma
g(\mathbf{Q}^{(k+1)})+\frac{\mu^{(k)}}{2}\|\mathbf{L}^{(k+1)}-\mathbf{Q}^{(k+1)}+\frac{\mathbf{Y_{2}}^{(k)}}{\mu^{(k)}}\|_{F}^{2}.\end{array}$
(11)

We can simply improve Eq. (11) as

$\begin{array}[]{lr}\mathbf{Q}^{(k+1)}=\mathop{\arg\min}\limits_{\mathbf{Q}}f(\mathbf{Q}^{(k+1)})+\frac{1}{(2\sqrt{\gamma/\mu^{(k)}})^{2}}\|\mathbf{Q}^{(k+1)}-\mathbf{N}^{(k+1)}\|_{F}^{2}.\end{array}$
(12)

Similarly,
$\mathbf{N}^{(k+1)}=\mathbf{L}^{(k+1)}+\frac{\mathbf{Y_{2}}^{(k)}}{\mu^{(k)}}$
is treated as the noisy image, while the clean image $\mathbf{Q}^{(k+1)}$ can
be recovered from the noisy image $\mathbf{N}^{(k+1)}$ with noise $\delta$.
Let $\delta=\sqrt{\lambda/\mu^{(k)}}$ zhu2023denoising , Eq. (12) can be
reformulated as

$\begin{array}[]{lr}\mathbf{Q}^{(k+1)}=\mathbf{N}^{(k+1)}+\delta^{2}g_{\Theta}(\mathbf{N}^{(k+1)}),\end{array}$
(13)

where $g_{\Theta}$ represents a Mamba block in Fig. 2 (a).

Multipliers:  We update $\mathbf{Y}_{1}$ and $\mathbf{Y}_{2}$ as

$\begin{array}[]{lr}\mathbf{Y}_{1}^{(k+1)}=\mathbf{Y}_{1}^{(k)}+\mu^{(k)}(\mathbf{R}^{(k+1)}-\mathbf{P}^{(k+1)}).\end{array}$
(14)
$\begin{array}[]{lr}\mathbf{Y}_{2}^{(k+1)}=\mathbf{Y}_{2}^{(k)}+\mu^{(k)}(\mathbf{L}^{(k+1)}-\mathbf{Q}^{(k+1)}).\end{array}$
(15)

Finally, the above iteration optimization process can be embedded into an
unfolding network, as shown in Fig. 2 (a). Based on the Retinex unfolding
algorithm, our model carries out decomposition through 4 convolution layers
and obtains the initial illumination $\mathbf{L}$ and reflectance
$\mathbf{R}$. Then, our model conducts deep unfolding optimization on
illumination layer $\mathbf{L}$ and reflectance layer $\mathbf{R}$
iteratively.

###  3.2 Relighting-guided Mamba

After the decomposition from the last section, the decomposed input image is
usually corrupted with color distortion, noise, and over-exposure. In this
paper, we define the process of enhancing and restoring the decomposed layers
as Relight, which attempts to restore the physical and illumination details of
the overall image after the first decomposition phase.

The existing deep unfolding model on Retinex wu2022uretinex  utilized the CNNs
as backbone networks, which has limitations for global visual context learning
ability. Although the Transformer-based Retinex network is proposed with
promising performance cai2023retinexformer , the GPU memory limit obstructs
the iteration of a deep unfolding network. Therefore, we utilize the pure
Mamba as our backbone network to achieve a trade-off memory efficiency and
relight effect as shown in Fig. 2 (b).

We adopt a U-shaped network cai2023retinexformer  with pure Mamba as our
backbone network to restore the reflectance $\mathbf{R}$ and utilize a vanilla
mamba to extract illumination feature in $\mathbf{L}$. With noise and color
distortion, reflectance $\mathbf{R}$ plays a critical role in Relighting.
Given the input decomposed reflectance $\mathbf{R}$, in the encoder of the
U-shape network, $\mathbf{R}$ is passed through a $3\times 3$ convolution
layer, an illumination-fused bidirectional Mamba block, a $4\times 4$
convolution layer which generates features
$\mathbf{F}_{i}\in\mathbb{R}^{{\frac{H}{2^{i}}}\times{{\frac{W}{2^{i}}}\times{2^{i}C}}}$,
and then another illumination-fused bidirectional Mamba blocks. After the
downsampling branch, the $2\times 2$ deconvolution layer is employed to
upscale the features. Additionally, skip connections are exploited to reduce
the loss during downsampling. In the end, the network outputs a $H\times
W\times 3$ image with restoration.

###  3.3 Illumination-fused Bidirectional Mamba

According to Eq. 10, both illumination $\mathbf{L}$ and reflectance
$\mathbf{R}$ are needed for the solution of $\mathbf{R}$. In addition, the
color distortion in a dark area is highly correlated with the illumination
condition. Thus, We take the illumination features into consideration for the
Mamba model design as shown in Fig 2 (c). We fuse the flattened illumination
$\mathbf{L}$ and reflectance $\mathbf{R}$ firstly in the illumination-fused
bidirectional Mamba (IFBMamba). The input reflectance
$\mathbf{R}\in\mathbb{R}^{H\times W\times C}$ is reshaped into tokens of
$\mathbf{R}_{p}\in\mathbb{R}^{J\times(P^{2}\dot{C})}$, where $H,W$ is the size
of input, $C$ is the number of channels, and $P$ is the size of patches.
$\mathbf{R}_{p}$ is linearly projected into vectors as follows:

$\begin{array}[]{lr}\mathbf{T}_{0}=[\mathbf{t}_{cls};\mathbf{t}_{p}^{1}\mathbf{W};\mathbf{t}_{p}^{2}\mathbf{W};...;;\mathbf{t}_{p}^{J}\mathbf{W}],\end{array}$
(16)

where $\mathbf{t}_{p}^{J}$ is the $j$-th patch of $\mathbf{t}$, $\mathbf{W}$
is the learnable projection matrix. To efficiently learn the global color
information of these vectors, we adopt a bidirectional Mamba to extract the
feature of reflectance instead of a vanilla Mamba. In the right part of Fig.
3, the sequence of patches goes through a forward-scanning Mamba and a
backward-scanning Mamba. Vanilla Mamba will forget previous information when
the scanned length grows longer while bidirectional Mamba can prevent
excessive focus on local patches and model the global patches via forward and
backwared scanning.

Figure 3: Scanning order of Mamba and Bidirectional Mamba. A bidirectional
scan mechanism gathers global color context more accurately.

##  4 Experiments

###  4.1 Experiment Settings

Datasets. LOL-v1 wei2018deep  is captured in real scenes with different
exposure conditions and ISO, which contains 485 low-light and normal image
pairs as the training set and 15 low-light and normal image pairs as the test
set. LOL-v2-Real yang2021sparse  is the second version of the LOL dataset,
with 689:100 training sets and test sets. LOL-v2-Syn yang2021sparse  contains
900 low-light and normal-light image pairs, which are synthesized from
captured images by analyzing the distribution of luminance channels of dark
and normal images. SID chen2019seeing  is captured by the Sony $\alpha$7S II
camera. It contains 2697 short-exposure and long-exposure RAW image pairs,
which are taken in sufficient wide dynamic low-light scenes.

Evaluation Metrics. PSNR wang2013naturalness  is utilized to measure the
quality of images. SSIM wang2013naturalness  is a method used to measure the
similarity between two images. LPIPS zhang2018unreasonable  calculates the
distance between two images in high-level features.

Compared Methods. Traditional models: LIME guo2016lime , MF fu2016fusion , NPE
wang2013naturalness , SRIE fu2016weighted  and learning-based models:
RetinexNet wei2018deep , DeepUPE wang2019underexposed , DRBN yang2021band ,
Restormer zamir2022restormer , MIRNet zamir2020learning , Kind
zhang2019kindling , Kind++ zhang2021beyond , SGM yang2021sparse , RUAS
liu2021retinex , SNR-Aware xu2022snr , Bread guo2023low , URetinex-Net
wu2022uretinex , FourLLIE wang2023fourllie , GSAD hou2024global ,
Retinexformer cai2023retinexformer .

Figure 4: Visual comparison on LOL-v2wei2018deep  dataset. The brightness
contrast between objects is well preserved in LLEMamba.

Implementation Details. The Initialization and Relight are trained separately,
where the batch sizes are set to 4. Adam optimizer is utilized kingma2014adam
with $\beta_{1}$ = 0.9 and $\beta_{2}$=0.999. In the relight module, it is
trained for $1.5\times 10^{5}$ iterations with initial learning rate =
$2\times 10^{-4}$ and decreased to $1\times 10^{-6}$. The initial penalty
parameters $\lambda$ and $\gamma$ are set 0.1 and 0.05 respectively Eq. (3).
All the experiments are conducted on the NVIDIA GeForce RTX 4090 GPU with
PyTorch framework.

Table 1: Quantitative Comparison on the LOL-v1, LOL-v2-Real, and LOL-v2-Syn Dataset. The highest result is in red and the second highest result is in blue. Methods | Venue | LOL-v1 | LOL-v2-Real | LOL-v2-Syn
---|---|---|---|---
PSNR | SSIM | LPIPS | PSNR | SSIM | LPIPS | PSNR | SSIM | LPIPS
NPE wang2013naturalness  | TIP2013 | 16.97 | 0.589 | 0.416 | 17.33 | 0.464 | 0.236 | 16.60 | 0.778 | 0.187
LIME guo2016lime  | TIP2016 | 16.76 | 0.578 | 0.418 | 15.24 | 0.419 | 0.220 | 16.88 | 0.758 | 0.204
MF fu2016fusion  | Signal Processing | 18.79 | 0.642 | 0.407 | 18.72 | 0.509 | 0.240 | 17.50 | 0.774 | 0.208
SRIE fu2016weighted  | CVPR2016 | 11.86 | 0.498 | 0.423 | 14.45 | 0.524 | 0.216 | 14.50 | 0.664 | 0.248
RetinexNet wei2018deep  | BMVC2018 | 13.10 | 0.429 | 0.325 | 16.08 | 0.656 | 0.236 | 18.28 | 0.774 | 0.234
Kind zhang2019kindling  | MM2019 | 20.87 | 0.802 | 0.240 | 20.01 | 0.641 | 0.081 | 22.01 | 0.904 | 0.273
Kind++ zhang2021beyond  | IJCV2021 | 21.30 | 0.823 | 0.262 | 20.59 | 0.829 | 0.088 | 21.07 | 0.881 | 0.267
SGM yang2021sparse  | TIP2021 | 20.06 | 0.816 | 0.215 | 20.06 | 0.816 | 0.073 | 22.05 | 0.909 | 0.484
RUAS liu2021retinex  | CVPR2021 | 18.23 | 0.717 | 0.270 | 18.37 | 0.723 | 0.181 | 16.55 | 0.652 | 0.579
SNR-Aware xu2022snr  | CVPR2022 | 23.61 | 0.842 | 0.262 | 21.48 | 0.848 | 0.074 | 24.13 | 0.927 | 0.342
URetinex-Net wu2022uretinex  | CVPR2022 | 21.33 | 0.835 | 0.050 | 21.54 | 0.801 | 0.044 | 24.23 | 0.897 | 0.128
Bread guo2023low  | IJCV2023 | 22.92 | 0.836 | 0.160 | 20.83 | 0.822 | 0.095 | 17.63 | 0.838 | 0.168
FourLLIE wang2023fourllie  | MM2023 | 19.34 | 0.757 | 0.338 | 19.09 | 0.770 | 0.380 | 16.85 | 0.852 | 0.423
NerRCo yang2023implicit  | ICCV2023 | 22.95 | 0.815 | 0.338 | 24.17 | 0.813 | 0.311 | 19.07 | 0.714 | 0.463
LLEMamba | Ours | 23.71 | 0.901 | 0.046 | 22.20 | 0.901 | 0.054 | 24.27 | 0.914 | 0.142

###  4.2 Experimental Results

Quantitative Analysis. In the quantitative comparison shown in Table 1, our
proposed LLEMamba achieves the highest results on average with evaluation
metrics of PSNR, SSIM, and LPIPS. In the LOL-v1 dataset, we first make
comparison with SOTA Retinex-based methods, i.e. RetinexNet wei2018deep , Kind
zhang2019kindling , Kind++ zhang2021beyond , RUAS liu2021retinex , URetinex-
Net wu2022uretinex , with 10.61, 2.84, 2.41, 5.48, and 2.38dB improvements in
PSNR respectively. Especially for the deep unfolding based network URetinex-
Net, our proposed LLEMamba has shown superior image quality with higher PSNR,
which shows the relight effect of the proposed LLEMamba. In the LOL-v2-Real
dataset, LLEMamba achieves the highest in PSNR, SSIM, and LPIPS.

LLEMamba also outperforms other methods on average metrics in the LOL-v2-Syn
dataset. Meanwhile, URetinex-Netwu2022uretinex  has the highest result in a
few metrics, which comes from its overfitting on the LOL-v2 dataset.
Specifically, the deep unfolding network preserves the physical information in
both the illumination and reflectance layers, and the proposed IFBMamba boosts
the long-range sequence learning with superb denoising and restoration
effects. Generally, the superb performance on PSNR has shown the denoising
effect of LLEMamba, and the excellent scores on SSIM and LPIPS prove its
excellent global visual context modeling.

In Table 2, our proposed LLEMamba has surpassed the existing SOTA methods in
all metrics. Compared with advanced Retinexformercai2023retinexformer ,
LLEMamba achieves higher PSNR and SSIM in the SID dataset which involves both
indoor and outdoor real-scene low-light images with stable long-range
dependency learning. As for the model parameters, our LLEMamba has decreased
6.25% parameters compared with transformer-based Retinexformer
cai2023retinexformer , which could support deep unfolding networks in low-
level vision tasks. The SID chen2019seeing  dataset involves dark images
indoors and outdoors with different noise levels, thus LLEMamba proves robust
learning ability in different low-light scenes.

Qualitative Analysis. To facilitate an intuitive comparison, we make visual
results comparison with classic Retinex-based methods: Kind zhang2019kindling
, URetinex-Net wu2022uretinex , FourLLIE wang2023fourllie , and Retinexformer
cai2023retinexformer . Compared with Kind zhang2019kindling  and FourLLIE
wang2023fourllie , the proposed LLEMamba can capture color information more
precisely. Additionally, LLEMamba prevents over-exposure in the light area
compared with URetinex wu2022uretinex  in the background of Fig. 5.

In the SID dataset which contains more noise in the input image, traditional
LIME has a severe over-exposure problem and Retinexformer may fail to learn
the precise color in reflectance of the bicycles in Fig. 6. The 1-D RGB plots
depict the pixel values in the images, from which we can obtain the following
information: the max value in the curve and the sharp changes in the curve.
Unlike the curves of other methods with mismatched max values, our proposed
LLEMamba prevent over-exposure at the peak of the curves. Moreover, the sharp
change tendency of LLEMamba is fitted with the curves of GT precisely. Thus,
LLEMamba outperforms other SOTA algorithms in multiple dark scenes.

Table 2: Quantitative Comparison with Different Methods on SID dataset. The highest result is in red and the second highest result is in blue. | DeepUPE | DRBN | KinD | SGM | Restormer | MIRNet | SNR-Aware | Retinexformer | Ours
---|---|---|---|---|---|---|---|---|---
SID | PSNR | 17.01 | 19.02 | 18.02 | 18.68 | 22.27 | 20.84 | 22.87 | 24.44 | 24.55
SSIM | 0.604 | 0.577 | 0.583 | 0.606 | 0.649 | 0.605 | 0.625 | 0.680 | 0.682
Complexity | FLOPS(G) | 5.86 | 48.61 | 34.99 | 53.26 | 144.25 | 785 | 26.35 | 15.57 | 13.96
Parameters(M) | 1.77 | 5.27 | 0.583 | 0.606 | 26.13 | 31.76 | 4.01 | 1.6 | 1.5
Figure 5: Visual comparison on LOL-v2wei2018deep  dataset. LLEMamba accurately
captures the texture details of objects. Figure 6: Visual comparison on SID
dataset. The 1-D RGB signals in each image at the red line markers in (a) are
represented separately in red, green, and blue. The horizontal axis represents
the pixel index, while the vertical axis represents the corresponding pixel
value.

###  4.3 Ablation Study

Figure 7: Ablation study of the deep unfolding iterations.

Effect of Deep Unfolding Network. To explore the relationship between visual
performance and deep unfolding iterations, we conduct experiments on the
LOL-v2 dataset with iterations = 1, 2, 3. The enhanced images are taken at
their corresponding highest PSNR model weight. As shown in Fig. 7, for most
images, deeper iteration models better illumination and color information. To
achieve a trade-off between training cost and enhancement effect, we suggest
selecting iteration = 3 on the LOL-v2 dataset. In large-scale datasets such as
SID with limited GPU memory, deeper unfolding results in a decrease in batch
size, which deteriorates model convergence.

Effect of Low-Light Enhancement Mamba. We analyze the quantitative results of
our proposed illumination-fused bidirectional mamba by comparing them with
convolutional networks and transformer-based model cai2023retinexformer . The
proposed illumination-fused bidirectional mamba in the reflectance
$\mathbf{P}$ optimization module is replaced with other networks. The
implementation is as follows: DnCNN along with SENet in the reflectance
enhancement in URetinex-Net wu2022uretinex ,

Table 3: Comparison with different backbones in deep unfolding network on the
LOL-v1 and LOL-v2-Real Dataset. The best results are boldfaced.

Backbone | LOL-v1 | LOL-v2
---|---|---
PSNR | SSIM | PSNR | SSIM
DnCNN + SENet | 21.20 | 0.810 | 20.52 | 0.804
IGMA | 21.70 | 0.822 | 21.29 | 0.829
Vanilla Mamba | 20.14 | 0.704 | 19.97 | 0.789
IFBMamba | 23.71 | 0.901 | 21.80 | 0.901

Illumination-guided Multi-attention (IGMA) in Retinexformer
cai2023retinexformer , and vanilla Mamba block. The quantitative results on
the LOL-v2 dataset suggest the design of our IFBMamba fused with iterative
illumination $\mathbf{L}$ is effective with its long-range dependency capture
ability.

##  5 Conclusion

Based on Retinex theory, this paper introduces the concept of Relight, which
aims to denoise and restore degraded reflectance. To address the relight
problem, we present a relighting-guided Mamba embedding within a Retinex
unfolding network with mathematical meaning. Through experiments conducted on
four widely used low-light benchmarks, we demonstrate the effectiveness of the
proposed model from both quantitative and qualitative perspectives.

There are several promising avenues for future research. One option is to
develop a more lightweight Mamba block in the backbone network, enabling the
use of large-scale datasets for deep unfolding architectures. Additionally,
exploring other computer vision tasks with the Mamba-driven deep unfolding
framework holds great potential for advancing these fields. By adapting and
extending our framework to these problems, we can leverage the inherent
strengths of deep unfolding Mamba in tasks such as semantic segmentation,
object detection, and hyperspectral imaging.

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