# Enhancing Super-Resolution Networks through Realistic Thick-Slice CT
Simulation

Zeyu Tang1,2, Xiaodan Xing1, Guang Yang1,3 This study was supported in part by
the ERC IMI (101005122), the H2020 (952172), the MRC (MC/PC/21013), the Royal
Society (IEC/NSFC/211235), the Imperial College UROP, the NVIDIA Academic
Hardware Grant Program, the SABER project supported by Boehringer Ingelheim
Ltd, NIHR Imperial Biomedical Research Centre (RDA01), and the UKRI Future
Leaders Fellowship (MR/V023799/1).
1\. National Heart and Lung Institute, Imperial College London, SW7 2BX
London, U.K.
2\. Department of Bioengineering, Imperial College London, SW7 2AZ London,
U.K.
3\. Royal Brompton Hospital, SW3 6NP London, U.K.

###### Abstract

This study aims to develop and evaluate an innovative simulation algorithm for
generating thick-slice CT images that closely resemble actual images in the
AAPM-Mayo’s 2016 Low Dose CT Grand Challenge dataset. The proposed method was
evaluated using Peak Signal-to-Noise Ratio (PSNR) and Root Mean Square Error
(RMSE) metrics, with the hypothesis that our simulation would produce images
more congruent with their real counterparts. Our proposed method demonstrated
substantial enhancements in terms of both PSNR and RMSE over other simulation
methods. The highest PSNR values were obtained with the proposed method,
yielding 49.7369 $\pm$ 2.5223 and 48.5801 $\pm$ 7.3271 for D45 and B30
reconstruction kernels, respectively. The proposed method also registered the
lowest RMSE with values of 0.0068 $\pm$ 0.0020 and 0.0108 $\pm$ 0.0099 for D45
and B30, respectively, indicating a distribution more closely aligned with the
authentic thick-slice image. Further validation of the proposed simulation
algorithm was conducted using the TCIA LDCT-and-Projection-data dataset. The
generated images were then leveraged to train four distinct super-resolution
(SR) models, which were subsequently evaluated using the real thick-slice
images from the 2016 Low Dose CT Grand Challenge dataset. When trained with
data produced by our novel algorithm, all four SR models exhibited enhanced
performance.

###### Index Terms:

Thick-slice CT, Super-Resolution, Synthetic Data

##  I Introduction

Around late 1980s, the concept of helical or spiral Computed Tomography (CT)
emerged [1, 2, 3, 4]. This technique involves gathering data without
interruption as the patient is moved at a consistent pace through the gantry.
The distance the patient travels per gantry rotation during the helical scan
is known as the table speed. Since there are no breaks in data collection, the
duty cycle of the helical scan is significantly enhanced, reaching close to
100%. Nevertheless, a significant problem became evident: helical CT posed
considerable strain on x-ray tubes. To address this problem of overheating, a
potential solution was to optimize the utilization of the x-ray beam. By
widening the x-ray beam in the z-direction (slice thickness) and employing
multiple rows of detectors, it became possible to gather data for multiple
slices simultaneously. Implementing this method would reduce the overall
number of rotations required to cover the desired anatomy, consequently
minimizing the x-ray tube usage. This concept forms the foundation of multi-
slice helical CT [5, 6, 7].

###  I-A Clinical Application

Multi-slice helical CT has been extensively utilized as a non-intrusive
imaging technique since then and has proven especially valuable in the
examination of lung diseases like lung cancer [8, 9, 10], Chronic Obstructive
Pulmonary Disease (COPD) [11, 12, 13], and Idiopathic Pulmonary Fibrosis (IPF)
[14, 15, 16]. Moreover, the application of CT scans is not restricted to
pulmonary investigations alone; it is greatly employed to examine other
anatomical regions, including the head-neck [17, 18, 19], heart [20, 21, 22],
kidney [23, 24, 25], and liver [26, 27, 28]. CT has indeed become the
preferred method in medical practice for imaging and identifying these
conditions, thanks to its remarkable sensitivity and specificity. The
effective execution of a lung disease screening protocol is deeply contingent
upon the precise identification and evaluation of biomarkers, including
pulmonary nodules, thickening of the airway walls, and traction
bronchiectasis. However, such elusive radiomics features (RF) are highly
affected by he acquisition thickness of CT images shown in Figure 1. Previous
research showed that RFs derived from thin-slice (1.25 mm) CT scans performed
considerably better in differentiating benign from malignant solitary
pulmonary nodules than those from thick-slice CT scans (5 mm). This indicates
that thin-slice CT scans provide a richer source of information for radiomics
analyses [29, 30, 31]. Nevertheless, it is essential to acknowledge that the
acquiring of thin-slice CT images augments not only the requisites for data
storage, but also escalates the radiation dose. To reduce the radiation
exposure thereby diminishing the lifelong risk of secondary malignancies [32,
33] \- notably among pediatric patients - thick slice CT images are
customarily obtained across various anatomical sites of interest in clinical
practice. Such practice further mitigates the complexity associated with
contouring on an extensive series of slices. In summary, thin-slice CT scans
provide richer information for identifying diseases but require more storage
and increase radiation exposure, while thick-slice scans are safer and simpler
but less detailed.

Figure 1: Examples of lesions in liver, lung and lymph nodes on 1.25, 2.5 and
5 mm slice interval images adopt from [31]. The left panel shows a close-up of
(a) liver metastasis on a 1.25 mm slice interval image, (b) lung lesion on a
2.5 mm image, and (c) lymph node metastasis on a 5 mm image. The right panel
shows the computer-aided contour, 2 maximal perpendicular diameters and three-
dimensional views of each lesion on (from left to right, respectively) 1.25,
2.5 and 5 mm slice intervals.

###  I-B Super-Resolution

To get the best from both worlds, one potential strategy is the use of post-
processing super-resolution (SR) algorithms. These algorithms are capable of
generating high-resolution (HR) thin-slice CT images from low-resolution (LR)
thick-slice CT images. Image SR is a sub-field of image processing that aims
to generate a HR image from its corresponding LR counterpart. It is typically
formulated as an inverse problem. The relationship between a LR image $Y$ and
its corresponding HR image $X$ is often described using the following
equation:

${I_{LR}}=D\cdot S\cdot{I_{HR}}+N$ (1)

Where $S$ is the downsampling operator, $D$ is the blurring operator (which
represents the real-world degradation that often occurs when an image is
captured), and $N$ is the noise. The aim of SR is to reverse this process,
effectively trying to find the inverse of ${D}({S}(\cdot)+{N})$ to generate a
super-resolved image ${I^{\prime}_{HR}}$ that is an approximation of the
original ${I_{HR}}$. Ideally, we want ${I^{\prime}_{HR}}$ to minimize some
loss function $L$ over inverse function parameters $\theta$ with respect to
${I_{HR}}$:

${\hat{\theta}}=\arg\min_{{\theta}}L({I^{\prime}_{HR}},{I_{HR}})$ (2)

In practice, ${I_{HR}}$ is unknown during the inference phase, and the model
is trained on pairs of HR and LR images to learn the mapping from ${I_{LR}}$
to ${I_{HR}}$. A myriad of machine learning and deep learning models have been
put forth to tackle the challenge of axial-plane SR. However, the lack of
publicly available paired LR-HR training data forces researchers to create
their own thick-slice CT images derived from thin-slice CT datasets.
Regrettably, their simulation methods often overlook the crucial parameters of
slice thickness and interval, leading to an inability to accurately capture
the distribution of thick-slice images. This results in underperformance of
the trained models when processing true thick-slice images.

###  I-C Aims and Objectives

The objective of this research is to present an innovative simulation
algorithm that generates images closely resemble the actual thick-slice CT
images found in the AAPM-Mayo’s 2016 Low Dose CT Grand Challenge (LDCT)
dataset [34]. According to our current understanding, the AAPM-Mayo’s LDCT
dataset stands as the sole public resource providing thin-thick slice pairs.
We intend to utilise metrics such as the Peak Signal-to-Noise Ratio (PSNR) and
the Root Mean Square Error (RMSE) to evaluate the quality of thick-slice
images generated by different algorithms. The initial hypothesis posits that
our proposed simulation method will yield thick-slice images more congruent
with their real counterparts. Furthermore, a secondary hypothesis suggests
that Super Resolution (SR) models trained on our dataset will demonstrate
enhanced efficacy when applied to actual thick-slice images, in contrast to
models trained on alternative simulated data. The evaluation of the SR model’s
performance will also leverage PSNR and RMSE metrics.

##  II Related Works

Deep learning [35] has revolutionized the field of medical imaging super-
resolution by enabling models to learn complex mappings from low to high-
resolution images. Convolutional Neural Networks (CNNs) [36] and Generative
Adversarial Networks (GANs) [37] are commonly used architectures in these
tasks. These models are typically trained on pairs of low and high-resolution
medical images, learning a function that can effectively upscale the low-
resolution images. Their capacity to learn hierarchical features allows for
the reconstruction of fine details in high-resolution images. Mansoor et al.
[38] applied a 3D Gaussian smoothing filter on slices with 1mm thickness
followed by downsampling to create slices with 4mm thickness on their in-house
chest CT dataset. Subsequently, they utilized a VGG-like GAN model for the
reconstruction of HR thin-slice images. Park et al. [39] employed a method for
thick-slice image simulation that involved averaging five slices with a 3mm
thickness to create a single slice with a 15mm slice thickness on their in-
house Brain CT dataset. In this approach, the middle slice was selected as the
ground truth high-resolution image. To reconstruct the HR thin-slice image
from the LR thick-slice images, they employed a 2-D U-Net model. Wang et al.
[40] generated thick slices by downsampling directly on the 1mm thin-slice
images. They trained a CycleGAN in a self-supervised manner to recover the HR
image. Xie et al. [41] employed a method for simulating thick-slice images by
averaging three or seven slices with a 1mm thickness from their in-house brain
CT dataset. This averaging process resulted in the creation of a single slice
with a thickness of 3mm or 7mm, respectively. Additionally, they implemented a
self-supervised CycleGAN model to synthesize HR thin-slice images. Park et al.
[42] utilized a direct reconstruction approach from the sinogram in their in-
house dataset to generate CT images with slice thicknesses of 1mm, 3mm, and
5mm. Their findings highlighted a significant variability in radiomic features
across different CT slice thicknesses, particularly in the context of lung
cancer. To address this variability, they proposed the use of a residual CNN-
based SR algorithm. Wu et al. [43] simulated thick slices by downsampling
directly on the 2.5mm thin-slice images. They proposed a parallel U-net
architecture for CT slice reconstruction along the z-axis. Kudo et al. [44]
simulated various combinations of slice thickness and slice interval by
reducing the number of slices to either 1/4 or 1/8. They applied spline
interpolation and random Gaussian noise to the reduced slices and utilized a
3D GAN model to convert the thick-slice images back to thin-slice images. In
summary, prior simulation methodologies predominantly fall into three
categories: Simple Averaging, Gaussian Averaging, and Direct Downsampling.
Furthermore, the super-resolution models employed in these studies typically
rely on CNN-based and GAN-based frameworks.

##  III Methods

###  III-A Dataset

This study principally utilized two data sets: the TCIA LDCT-and-Projection-
data [45] and the 2016 Low Dose CT Grand Challenge [34]. We simulated thick-
slice data based on the TCIA LDCT-and-Projection-data, employing it for the
training phase. The 2016 Low Dose CT Grand Challenge was then deployed for
testing purposes. Important features of these two datasets have been compiled
and are presented in Table I and Table II for reference.

####  III-A1 TCIA LDCT-and-Projection-data

This compilation includes 99 neuro scans (denoted by N), 100 chest scans
(denoted by C), and 100 liver scans (denoted by L). Half of each scan category
comes from a SOMATOM Definition Flash CT scanner, a product of Siemens
Healthcare from Forchheim, Germany. The remaining scans, consisting of 49 for
the head, 50 for the chest, and 50 for the liver, were captured with a
Lightspeed Volume Computed Tomography (VCT) CT scanner from GE Healthcare,
based in Waukesha, WI. Some data in this collection might be utilized to
reconstruct a human face. In order to protect the privacy of individuals
involved, those accessing the data are required to sign and submit a TCIA
Restricted License Agreement upon usage.

TABLE I: Key data acquisition parameters for each exam type in TCIA LDCT-and-Projection-data Scanner | Parameters |  Head CT (N) |  Chest CT (C) |  Abdomen CT (L)
---|---|---|---|---
GE Healthcare (Discovery CT750i) | Tube Potential (kV) |  120 |  80-120 |  80-120
| Contrast Enhanced |  No |  No |  Yes
| Field of View |  200-260 |  282-423 |  315-500
| Reconstruction Algorithm |  Standard |  Standard |  Standard
| Thickness/Increment (mm) |  5/5 |  1.25/1 |  5/3
Siemens Healthineers (SOMATOM Definition AS+, SOMATOM Definition Flash) | Tube Potential (kV) |  120 |  120 |  100-120
| Contrast Enhanced |  No |  No |  Yes
| Field of View |  250 |  300-350 |  300-350
| Reconstruction Kernel |  H40 |  B50 |  B30
| Thickness/Increment (mm) |  5/5 |  1.5/1 |  5/3

####  III-A2 2016 Low Dose CT Grand Challenge

The dataset consists of 30 deidentified contrast-enhanced abdominal CT patient
scans, which were obtained using a Siemens SOMATOM Flash scanner in the portal
venous phase. The data comprises two types: Full Dose (FD) data and Quarter
Dose (QD) data. Full Dose data corresponds to scans acquired at 120 kV and 200
quality reference mAs (QRM), while Quarter Dose data refers to simulated scans
acquired at 120 kV and 50 QRM. The provided dataset includes various
components: 1) Projection data for all 30 patient scans, including 10 cases
for training purposes (both FD and QD) and 20 cases for testing (QD only). 2)
DICOM images for the 10 training cases, encompassing FD and QD data, with
reconstructions using 1 mm thick B30 and D45 kernels, as well as 3 mm thick
B30 and D45 kernels. 3) DICOM images for the 20 testing cases, consisting of
QD data only, with the same reconstruction configurations as the training
cases (1 mm thick B30 and D45 kernels, and 3 mm thick B30 and D45 kernels).

TABLE II: Key data acquisition parameters for each exam type in 2016 Low Dose CT Grand Challenge Reconstruction Kernel | Parameters |  Full Dosage (FD) |  Quarter Dosage (QD)
---|---|---|---
D45 | Tube Potential (kV) |  100-120 |  100-120
| Tube Current (mAs) |  200 |  50
| Contrast Enhanced |  Yes |  Yes
| Thickness/Increment (mm) |  1/0.8 and 3/2 |  1/0.8 and 3/2
B30 | Tube Potential (kV) |  100-120 |  100-120
| Tube Current (mAs) |  200 |  50
| Contrast Enhanced |  Yes |  Yes
| Thickness/Increment (mm) |  1/0.8 and 3/2 |  1/0.8 and 3/2

###  III-B Evaluation Metrics

The Peak Signal-to-Noise Ratio (PSNR) and the Root Mean Square Error (RMSE)
are two popular metrics used to measure the quality of image, particularly for
comparing the differences between the original and reconstructed data. PSNR is
defined as the ratio between the maximum possible power of a signal and the
power of corrupting noise that affects the fidelity of its representation.
Mathematically, PSNR is calculated using the following formula:

$PSNR=20\cdot\log_{10}\left(\frac{MAX_{I}}{\sqrt{MSE}}\right)$ (3)

Where $MAX_{I}$ is the maximum possible pixel value of the image. $MSE$ stands
for Mean Squared Error, which is the mean of the squared differences between
the original and the reconstructed image. The mathematical expression is as
follows:

$MSE=\frac{1}{mn}\sum_{i=0}^{m}\sum_{j=0}^{n}(I(i,j)-\hat{I}(i,j))^{2}$ (4)

where, $I(i,j)$ is the original value, $\hat{I}(i,j)$ is the predicted value,
and $m\times n$ is the image dimension (i.e. total number of pixels in an
image). RMSE is a quadratic scoring rule that measures the average magnitude
of the error, and it is defined as the square root of the average of squared
differences between prediction and actual observation. The RMSE gives a
relatively high weight to large errors, so it is especially useful when large
errors are particularly undesirable. It can be calculated using equation 4:

$RMSE=\sqrt{MSE}$ (5)

Both PSNR and RMSE are higher-is-better metrics, with higher values indicating
better match between the original and reconstructed data.

###  III-C Thick-slice Simulation

Drawing inspiration from the Weighted Filter Backprojection (wFBP) [46], we
have crafted a weighted sum algorithm designed to simulate thick-slice images
from thin-slice counterparts. Our initial step involves determining the new
positions of the simulated-thick slices, which is based on the slice
increment, $d$. This process is concisely delineated in Algorithm 1.

Algorithm 1 Slice location algorithm

1:start $s$, end $e$, slice increment $d$

2:slice locations $L_{\text{thick}}$

3:direction $D\leftarrow\frac{e-s}{|e-s|}$

4:Initialize $L_{\text{thick}}=[]$

5:$p\leftarrow s$

6:if $s=e$ then

7: Append $s$ to $L_{\text{thick}}$

8:else

9: while $(D=1\land s\leq p\leq e)\lor(D=-1\land e\leq p\leq s)$ do

10: Append $p$ to $L_{\text{thick}}$

11: $p\leftarrow p+D\cdot d$

12: end while

13:end if

Subsequently, our focus shifts to estimating the extent to which contiguous
thin-slice images at location $l\in L_{\text{thin}}$ contribute to the
reconstruction of the thick-slice image at location $p\in L_{\text{thick}}$.
To this end, we define a triangular weight function $g(s)$, where $s$
represents the slice thickness:

$g(s)=\max\left(0,1-\frac{{\left|p-l\right|}}{s}\right)$ (6)

The generated thick slices are weighted sums of the thin slices, normalized by
the total weight of the slices used. The detailed steps for the generation of
thick-slice images is illustrated in Algorithm 2. We applied our simulation
algorithm to the 2016 Low Dose CT Grand Challenge dataset, thereby
establishing the superior efficacy of our method compared to existing
alternatives. Subsequently, we produced thick-slice data for the chest CT
images from the TCIA LDCT-and-Projection-data dataset using Simple Averaging
and our proposed method. These synthesized thick-thin image pairs served as
the training set for the super-resolution models.

Algorithm 2 Weighted Sum of Images

1:$L_{\text{thick}}$ (thick-slice locations),
$\bm{I}_{\text{thin}}\in\mathbb{R}^{512\times 512\times\text{depth}}$ (thin-
slice images), $s$ (slice thickness)

2:$\bm{I}_{\text{thick}}\in\mathbb{R}^{512\times
512\times\text{depth}}\leftarrow$ Initialize With Zeros(depth of $L_{thick}$)

3:for each $l$ in $L_{\text{thick}}$ do

4: $w_{\text{total}}\leftarrow$ 0

5: for each $\bm{i}\in\mathbb{R}^{512\times 512}$ in $\bm{I}_{\text{thin}}$ do

6: $w\leftarrow$ $g(s)$

7: if $w=0$ then

8: continue

9: end if

10: $\tilde{i}\leftarrow\tilde{i}+i\cdot w$

11: $w_{\text{total}}\leftarrow$ $w_{\text{total}}+w$

12: end for

13: $\tilde{i}\leftarrow$ $\frac{1}{w_{\text{total}}}\cdot\tilde{i}$

14: Append $\tilde{i}$ to $\bm{I}_{\text{thick}}$ along the depth dimension

15:end for

16:return $\bm{I}_{\text{thick}}$

###  III-D Super-Resolution Models

To fairly evaluate the quality of our simulated dataset in model training, We
selected four SR models to benchmark our simulated thick-slice data.

####  III-D1 Convolutional Neural Network

Convolutional Neural Networks (CNNs), a class of artificial neural networks,
have been instrumental in the evolution of deep learning, particularly in
image analysis tasks. The basic underlying principle of CNNs is the
application of a convolution operation, which uses a kernel or filter that
passes over the input data. This kernel convolves with the input layer to
compute the dot product of their entries, thereby preserving the spatial
relationships in the image. Layers of these convolutional operations are often
interspersed with other layers such as pooling (downsampling) and
normalization layers. Over time, the CNN learns the optimal values for this
kernel, allowing it to detect complex patterns in the input data. CNN-based
Super-Resolution models revolutionized this field, with the most famous being
the Super-Resolution Convolutional Neural Network (SRCNN) introduced by Dong
et al. in 2014 [47]. This model uses a three-layer CNN to learn an end-to-end
mapping of low-resolution images to their high-resolution counterparts. It
applies a patch extraction and representation layer, a non-linear mapping
layer, and a reconstruction layer. The learning objective of SRCNN is to
minimize the Mean Squared Error (MSE) between the original high-resolution
image and the super-resolved output. Since then, newer models like the very
Deep Super-Resolution (VDSR) [48] have further improved super-resolution
performance. We have re-engineered the VDSR architecture to better suit our
needs, transforming all 2-D operations into 3-D. Further, we streamlined the
structure by reducing the convolutional layer count to twelve and integrated a
global residual connection. This refined model will serve as our first SR
model for benchmarking our simulated dataset.

####  III-D2 U-Net

U-Net [49], a type of CNN that was first developed for biomedical image
segmentation, has also been utilized in super-resolution tasks due to its
unique architecture that excels in capturing both local features and global
context. The U-Net architecture consists of a contracting (downsampling) path
and an expansive (upsampling) path with skip connections between layers of the
same level, which help in localizing the high resolution features. One example
of a U-Net-based super-resolution model is the Enhanced Deep Residual Networks
for Single Image Super-Resolution (EDSR) model [50] that’s been adapted into a
U-Net-like structure. In this model, the downsampling path captures context
information, while the upsampling path allows the model to make precise
localization decisions to super-resolve the image. We have adapted the
original U-Net architecture to better suit the 3-D medical image super-
resolution task. Our modifications include transforming all 2-D operations
into 3-D and introducing two additional residual blocks. This revised model
now serves as our second benchmark SR model.

####  III-D3 Residual Neural Nerwork

ResNet, short for Residual Network, was introduced by He et al. in their 2015
paper [51]. This deep learning model, distinguished by its ”skip” or
”shortcut” connections, was developed to address the problem of vanishing
gradients that plagued training of very deep neural networks. These shortcut
connections allow the model to learn identity functions that effectively
prevent the higher layers from destroying the learned information of lower
layers, thereby enabling the successful training of networks that are
significantly deeper than those previously possible. ResNet has had a
significant impact on the field of computer vision, including the domain of
super-resolution. SRResNet, or Super-Resolution Residual Network, is a direct
adaptation of the principles of ResNet to super-resolution tasks. SRResNet was
proposed by Ledig et al. in the SRGAN (Super-Resolution Generative Adversarial
Networks) paper and serves as the backbone for the generator network in SRGAN
[52]. SRResNet incorporates residual blocks to learn the residual mapping
between the low-resolution and high-resolution images. It is designed with a
shallow network at the beginning and end (for feature extraction and
reconstruction) while having a deeper body composed of residual blocks.
Building upon the success of SRResNet, researchers proposed an enhanced
version known as Enhanced SRResNet (ESRResNet) [53]. The enhanced version
incorporates several advancements in deep learning, like the use of dense
connections (as seen in DenseNet [54]) and parameter-efficient convolutions to
improve the network’s learning capacity while keeping the computational load
manageable. In addition, one key feature of the ESRResNet is the use of
Residual-in-Residual Dense Blocks (RRDBs) instead of the simple residual
blocks in the original SRResNet. The RRDB is essentially a stack of residual
blocks where the output of each residual block is added to its input (forming
a local skip connection), and the output of the last residual block in the
stack is also added to the input of the stack (forming a long skip
connection). This architecture allows for better propagation of features and
gradients through the network, making it easier for the network to learn the
mapping from low-resolution to high-resolution images. The ESRResNet has
proven to be highly effective in super-resolution tasks, leading to
significant improvements over the original SRResNet in terms of both
quantitative metrics and perceptual quality of the super-resolved images.
Consequently, we selected the ESRResNet architecture, modifying all its 2-D
operations to 3-D. This adaptation makes it more suitable for the specific
demands of the medical imaging super-resolution task. This adaptation now
constitutes our third super-resolution model for benchmarking purposes.

####  III-D4 Generative Adversarial Network

Generative Adversarial Networks (GANs) are a type of neural network
architecture introduced by Ian Goodfellow et al. in 2014 [37]. GANs consist of
two parts: a generator network, which produces synthetic data, and a
discriminator network, which tries to distinguish between real and synthetic
data. The two networks are trained together, with the generator network
attempting to produce data that the discriminator network cannot distinguish
from real data, and the discriminator network attempting to get better at
distinguishing real data from the data generated by the generator. This
adversarial process leads to the generator network producing high-quality
synthetic data. In the context of image super-resolution, GANs have shown
great potential. Ledig et al. introduced the Super-Resolution Generative
Adversarial Network (SRGAN) in 2016 [52], which uses a GAN in combination with
a super-resolution network (SRResNet, described in section III-D3). In this
architecture, the generator is a super-resolution model that transforms a low-
resolution input into a high-resolution output, and the discriminator is
trained to distinguish the super-resolved images from real high-resolution
images. The result is super-resolved images that are perceptually more similar
to real high-resolution images compared to those produced by traditional
super-resolution methods. ESRGAN [53], or Enhanced Super-Resolution Generative
Adversarial Networks, is a direct and substantial improvement of SRGAN. It
keeps the GAN structure of the original SRGAN model, with a generator and
discriminator, but upgrades the generator with RRDB (desribed in section
III-D3). RRDB allows the model to effectively capture more complex texture and
detail information by encouraging both short and long skip connections. The
discriminator in these networks is typically constructed as a deep CNN, with
several layers of convolution, batch normalization, and activation function
such as LeakyReLU, culminating in a final decision layer that outputs a
probability indicating how likely it is that the input image is real. There
are more advanced architectures such as PatchGAN [55]. Unlike traditional
discriminators that try to classify the entire image as real or fake, a
PatchGAN discriminator employs the concept of Markov Random Field and
classifies individual patches of an image. The underlying assumption is that
natural images are locally coherent, meaning that the authenticity of an image
can be determined by examining its subregions or patches. In this study, we
included the PatchGAN discriminator during the training of ESRResNet, adding
it as our fourth SR model for benchmarking.

###  III-E Implementation Details

The scripts used in this study were developed in Python3 and the PyTorch
framework, executed on Imperial College’s HPC Clusters. Computations were run
on an NVIDIA RTX 6000 GPU with 24 GB of memory. Four distinct Super Resolution
(SR) models: VDSR, U-Net, ESRResNet and ESRGAN (ESRResNet+PatchGAN
Discriminator), were trained over 1000 epochs using the Adam solver (learning
rate = 1e-4) and augmented with random horizontal flips during training. The
source code can be accessed at: https://github.com/Feanor007/Thick2Thin.

##  IV Results

The results from all conducted experiments, represented as mean $\pm$ standard
deviation, are tabulated in this section. We assessed the performance of our
proposed simulation method against Simple Averaging, Gaussian Averaging, and
Direct Downsampling. This was accomplished by simulating images with a
thickness of 3mm from those with a thickness of 1mm, utilizing the 2016 Low
Dose CT Grand Challenge dataset. The results outlined in Table III provide a
comparative analysis of different thick-slice simulation methods used in two
datasets from the 2016 Low Dose CT Grand Challenge. Both the PSNR and the RMSE
were used as key performance indicators for these methods. The data clearly
demonstrate that the proposed method significantly outperformed Simple
Averaging, Gaussian Averaging, and Direct Downsampling in both datasets (D45
and B30). The highest PSNR values were obtained with the proposed method,
yielding 49.7369 $\pm$ 2.5223 and 48.5801 $\pm$ 7.3271 for D45 and B30
datasets, respectively. The proposed method also registered the lowest RMSE
with values of 0.0068 $\pm$ 0.0020 and 0.0108 $\pm$ 0.0099 for D45 and B30,
respectively. These results indicate a superior level of accuracy and
reliability in the proposed method. The statistically significant differences
were confirmed by a Wilcoxon signed-rank test with p-value ¡ 0.05, implying
that the improvements from the proposed method were not due to random chance.
These findings support our first hypothesis that the proposed simulation
method provides a more efficient and precise approach to thick-slice
simulations compared to traditional methods. To provide a more comprehensive
evaluation, visual comparisons from axial, coronal and sagittal plane were
also undertaken, as depicted in Figures 2 to 4. In summary, Our proposed
method demonstrated substantial enhancements in terms of both PSNR and RMSE,
indicating a distribution more closely aligned with the authentic thick-slice
image.

(a) True Thick-slice image

(b) Simple Averaging
RMSE: 0.0329, PSNR: 35.6776

(c) Gaussian Averaging
RMSE: 0.0955, PSNR: 26.4221

(d) Direct Downsampling
RMSE: 0.0454, PSNR: 32.8776

(e) Proposed Simulation
RMSE: 0.0010, PSNR: 46.4076

Figure 2: Axial-plane thick-slice image quality comparison across four
simulation methods.

(a) True Thick-slice image

(b) Simple Averaging
RMSE: 0.0250, PSNR: 38.0530

(c) Gaussian Averaging
RMSE: 0.1758, PSNR: 21.1182

(d) Direct Downsampling
RMSE: 0.0348, PSNR: 35.1697

(e) Proposed Simulation
RMSE: 0.0051, PSNR: 51.8504

Figure 3: Coronal-plane thick-slice image quality comparison across four
simulation methods.

(a) True Thick-slice image

(b) Simple Averaging
RMSE: 0.0357, PSNR: 34.9781

(c) Gaussian Averaging
RMSE: 0.0454, PSNR: 32.8866

(d) Direct Downsampling
RMSE: 0.0486, PSNR: 32.2861

(e) Proposed Simulation
RMSE: 0.0070, PSNR: 49.1774

Figure 4: Sagittal-plane thick-slice image quality comparison across four
simulation methods. TABLE III: Comparison experiments on different thick-slice
simulation methods

Dataset | Simulation Methods | PSNR | RMSE
---|---|---|---
2016 Low Dose CT Grand Challenge (D45) | Simple Averaging |  38.5023 $\pm$ 2.5851$\dagger$ |  0.0249 $\pm$ 0.0081$\dagger$
| Gaussian Averaging |  30.0969 $\pm$ 5.0047$\dagger$ |  0.0746 $\pm$ 0.0484$\dagger$
| Direct Downsampling |  36.0757 $\pm$ 2.9024$\dagger$ |  0.0334 $\pm$ 0.0131$\dagger$
| Proposed | 49.7369 $\pm$ 2.5223 | 0.0068 $\pm$ 0.0020
2016 Low Dose CT Grand Challenge (B30) | Simple Averaging |  39.6945 $\pm$ 2.8208$\dagger$ |  0.0219 $\pm$ 0.0072$\dagger$
| Gaussian Averaging |  33.4242 $\pm$ 4.9641$\dagger$ |  0.0521 $\pm$ 0.0412$\dagger$
| Direct Downsampling |  36.2342 $\pm$ 3.3025$\dagger$ |  0.0334 $\pm$ 0.0150$\dagger$
| Proposed | 48.5801 $\pm$ 7.3271 | 0.0108 $\pm$ 0.0099

  * $\dagger$

represents statistical significance (with Wilcoxon signed-rank test p-value ¡
0.05) compared with the proposed method.

We investigated our second hypothesis by training four different SR models
using the data generated by top two simulation methods, as referenced in III,
which are our proposed method and Simple Averaging. The results in Table IV
highlight the comparison of various super-resolution (SR) models trained by
different simulation methods on two distinct datasets: 2016 Low Dose CT Grand
Challenge (D45 and B30). In each case, the performance of the SR model trained
by proposed simulation method outperforms itself trained by the Simple
Averaging simulation method in terms of both PSNR and RMSE, indicating
improved image quality and lower error rates, respectively. The differences
observed were statistically significant as determined by the Wilcoxon signed-
rank test (p-value ¡ 0.05). For the D45 dataset, the PSNR and RMSE of the
proposed method ranged from 37.2176 $\pm$ 3.0876 and 0.0296 $\pm$ 0.0128 (for
VDSR) to 37.9786 $\pm$ 2.4597 and 0.0264 $\pm$ 0.0089 (for ESRGAN). Similarly,
for the B30 dataset, the proposed method’s PSNR and RMSE varied between
38.5657 $\pm$ 4.6613 and 0.0280 $\pm$ 0.0196 (for VDSR) and 40.5083 $\pm$
3.8736 and 0.0215 $\pm$ 0.0144 (for ESRGAN). The SR model that demonstrated
the best performance using the proposed method on the B30 dataset was the
ESRGAN model, yielding the highest PSNR (40.5083 $\pm$ 3.8736) and the lowest
RMSE (0.0215 $\pm$ 0.0144). In contrast, the lowest performance in the
proposed method was observed in the VDSR model for the D45 dataset, exhibiting
the lowest PSNR (37.2176 $\pm$ 3.0876) and the highest RMSE (0.0296 $\pm$
0.0128). Regardless of the dataset and the SR model, the proposed simulation
method consistently outperformed the simple averaging method, signifying its
effectiveness in training super-resolution models in the task of thick-to-thin
CT image transformation.

TABLE IV: Comparison experiments on models trained by different simulated
thick-slice images

Dataset | Super-Resolution Model | Simulation Methods | PSNR | RMSE
---|---|---|---|---
2016 Low Dose CT | VDSR | Simple Averaging |  36.4722 $\pm$ 2.9112$\dagger$ |  0.0320 $\pm$ 0.0131$\dagger$
Grand Challenge (D45) |  | Proposed | 37.2176 $\pm$ 3.0876 | 0.0296 $\pm$ 0.0128
| U-Net | Simple Averaging |  36.5079 $\pm$ 2.9129$\dagger$ |  0.0319 $\pm$ 0.0133$\dagger$
|  | Proposed | 37.9405 $\pm$ 2.1842 | 0.0262 $\pm$ 0.0071
| ESRResNet | Simple Averaging |  36.6322 $\pm$ 2.7383$\dagger$ |  0.0312 $\pm$ 0.0120$\dagger$
|  | Proposed | 37.8946 $\pm$ 2.5350 | 0.0267 $\pm$ 0.0094
| ESRGAN | Simple Averaging |  36.8371 $\pm$ 2.4522$\dagger$ |  0.0301 $\pm$ 0.0098$\dagger$
|  | Proposed | 37.9786 $\pm$ 2.4597 | 0.0264 $\pm$ 0.0089
2016 Low Dose CT | VDSR | Simple Averaging |  37.2458 $\pm$ 4.6983$\dagger$ |  0.0323 $\pm$ 0.0209$\dagger$
Grand Challenge (B30) |  | Proposed | 38.5657 $\pm$ 4.6613 | 0.0280 $\pm$ 0.0196
| U-Net | Simple Averaging |  37.4172 $\pm$ 4.4380$\dagger$ |  0.0311 $\pm$ 0.0185$\dagger$
|  | Proposed | 39.7475 $\pm$ 3.5318 | 0.0226 $\pm$ 0.0112
| ESRResNet | Simple Averaging |  37.9217 $\pm$ 4.1180$\dagger$ |  0.0289 $\pm$ 0.0171$\dagger$
|  | Proposed | 40.2103 $\pm$ 3.9283 | 0.0223 $\pm$ 0.0150
| ESRGAN | Simple Averaging |  38.2401 $\pm$ 3.6225$\dagger$ |  0.0270 $\pm$ 0.0136$\dagger$
|  | Proposed | 40.5083 $\pm$ 3.8736 | 0.0215 $\pm$ 0.0144

  * $\dagger$

represents statistical significance (with Wilcoxon signed-rank test p-value ¡
0.05) compared with the proposed method.

##  V Discussion and Conclusion

The findings from our study underscore the potential effectiveness of our
proposed simulation algorithm in generating images that closely resemble
authentic thick-slice CT images from the AAPM-Mayo’s 2016 Low Dose CT Grand
Challenge dataset. According to the comparison metrics used, specifically PSNR
and RMSE, our proposed method presented a significant improvement over
previous simulation methods, implying an image distribution more closely
aligned with the actual thick-slice images. This superior performance over the
other methods (Simple Averaging, Gaussian Averaging and Direct Downsampling)
demonstrates its potential as a reliable tool for training super-resolution
(SR) models for the task of thick-to-thin CT image transformation. The
positive results reaffirm our initial hypothesis and add to the growing body
of evidence that highlights the importance of using high-fidelity simulated
data in training deep learning models, especially in the realm of medical
imaging. However, it is essential to acknowledge the limitations of our study.
One of the significant limitations stems from the reliance on the AAPM-Mayo’s
LDCT dataset, which, to the best of our knowledge, is the only public resource
providing thin-thick slice pairs. The performance of our proposed method has
been evaluated primarily with respect to recreating the specific image
characteristics of the AAPM-Mayo’s LDCT dataset. It remains unclear how well
our algorithm would perform with images obtained from patients with different
health conditions. Furthermore, its exclusive provision of 3mm-1mm thick-thin
slice pairs, presents an inherent constraint in our study. In clinical
settings, various slice thicknesses, including 5mm, 10mm, or even 15mm, are
commonly used depending on the particularities of the clinical question and
the body region being scanned. The unique features and details that are
present in thicker slices may be vital for diagnosing certain conditions or
predicting disease progression. If our algorithm has only been validated for a
3mm-1mm pairing, it remains uncertain how well it can generate and maintain
these crucial features in thicker slices. In addition, the evaluation metrics
used (PSNR and RMSE) may not fully capture perceptual image quality and
radiomics features as perceived by human experts, thereby potentially limiting
the perceived accuracy of the simulation. Looking forward, further research
could explore more advanced SR models, such as diffusion-based generative
models [56]. Additionally, researchers could validate the utility of super-
resolved CT images by applying segmentation models that delineate anatomical
structures such as airway tree [57] and lung nodules [58]. Finally, these
results should prompt a reconsideration of the role of simulated data in
training SR models, urging further exploration and innovation in this area. By
providing a robust simulation method, we can help ensure the best possible
data for training these models, which in turn has the potential to improve the
overall quality and accuracy of medical imaging, particularly in the realm of
CT scanning.

In conclusion, this study successfully presented an innovative simulation
algorithm capable of generating thick-slice CT images closely resembling the
actual images in the AAPM-Mayo’s 2016 Low Dose CT Grand Challenge dataset.
Furthermore, Our method demonstrated its potential utility for training super-
resolution models aimed at the task of thick-to-thin CT image transformation.

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