Open AccessArticle

Edge Detection Attention Module in Pure Vision Transformer for Low-Dose X-Ray Computed Tomography Image Denoising

Luella Marcos

Paul Babyn

and

Javad Alirezaie

^1,*

Department of Electrical, Computer and Biomedical Engineering, Toronto Metropolitan University, Toronto, ON M5B 2K3, Canada

Department of Medical Imaging, University of Saskatchewan, Saskatoon, SK S7N 0W8, Canada

Author to whom correspondence should be addressed.

Algorithms 2025, 18(3), 134; https://doi.org/10.3390/a18030134

Submission received: 20 January 2025 / Revised: 19 February 2025 / Accepted: 27 February 2025 / Published: 3 March 2025

(This article belongs to the Special Issue Algorithms and Applications of Machine Learning Techniques for Healthcare)

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Figure 1
Not-well-preserved anatomical details in the highlighted blue ROI, produced using a pure vision transformer for LDCT denoising. Image generated from running the PViT model in [<a href="#B19-algorithms-18-00134" class="html-bibr">19</a>] using the piglet dataset for this study. (a) Piglet LDCT (15 mAs) slice. (b) Piglet NDCT (300 mAs) slice. (c) Generated output from PViT. "> Figure 2
Pure transformer block for LDCT denoising with the integration of gradient–Laplacian attention module. "> Figure 3
Attention modules in the pure vision transformer for LDCT denoising. (a) Multi-head self attention module for PViT. (b) Proposed gradient–Laplacian attention module for PViT. "> Figure 4
Edge enhancement at each upsampling and downsampling checkpoint labeled in <a href="#algorithms-18-00134-f002" class="html-fig">Figure 2</a> using different filters in the attention module. (a–c) The feature maps generated from checkpoint at the encoder; (d–f) the feature maps generated from the checkpoint at the decoder. "> Figure 5
Benchmark test visual results for piglet data: (a) input LDCT image reference with blue ROI, (b) ROI of LDCT image, (c) ROI of NDCT image, and ROI of output image using (d) RED-CNN, (e) PViT, (f) DSC-GAN, (g) DRLEMP, (h)TED-Net, (i) GLAM-PViT. "> Figure 6
Loss, PSNR, and SSIM trend over 150 epochs using piglet dataset. (a) Loss. (b) PSNR. (c) SSIM. "> Figure 7
PSNR and SSIM trend over 150 epochs using thoracic dataset. (a) Loss. (b) PSNR. (c) SSIM. "> Figure 8
Benchmark test visual results for thoracic data: (a) input LDCT image reference with blue ROI, (b) ROI of LDCT image, (c) ROI of NDCT image, and ROI of output image using (d) RED-CNN, (e) PViT, (f) DSC-GAN, (g) DRLEMP, (h) TED-Net, (i) GLAM-PViT. "> Figure 9
PSNR and SSIM trend over 150 epochs using head dataset. (a) Loss. (b) PSNR. (c) SSIM. "> Figure 10
Benchmark test visual results for dead data: (a) input LDCT image reference with blue ROI, (b) ROI of LDCT image, (c) ROI of NDCT image, and ROI of output image using (d) RED-CNN, (e) PViT, (f) DSC-GAN, (g) DRLEMP, (h) TED-Net, (i) GLAM-PViT. "> Figure 11
PSNR and SSIM trend over 150 epochs using abdomen dataset. (a) Loss. (b) PSNR. (c) SSIM. "> Figure 12
Benchmark test visual results for abdomen data: (a) input LDCT image reference with blue ROI, (b) ROI of LDCT image, (c) ROI of NDCT image, and ROI of output image using (d) RED-CNN, (e) PViT, (f) DSC-GAN, (g) DRLEMP, (h) TED-Net, (i) GLAM-PViT. "> Figure 13
PSNR and SSIM trend over 150 epochs using chest dataset. (a) Loss. (b) PSNR. (c) SSIM. "> Figure 14
Benchmark test visual results for chest data: (a) input LDCT image reference with blue ROI, (b) ROI of LDCT image, (c) ROI of NDCT image, and ROI of output image using (d) RED-CNN, (e) PViT, (f) DSC-GAN, (g) DRLEMP, (h) TED-Net, (i) GLAM-PViT. ">

Versions Notes

Abstract

X-ray computed tomography (CT) is vital for medical diagnostics, but frequent radiation exposure raises concerns, driving the adoption of low-dose CT (LDCT) to mitigate risks. However, LDCT often introduces noise, compromising diagnostic accuracy. This paper proposes a pure vision transformer (PViT) for LDCT denoising, enhanced with a gradient–Laplacian attention module (GLAM) to improve edge preservation and fine structural detail reconstruction. The model’s robustness was validated across five diverse datasets (piglet, head, abdomen, chest, thoracic), demonstrating consistent performance in preserving anatomical structures. Extensive ablation studies on attention configurations and loss functions further substantiated the contributions of each module. Quantitative evaluation using PSNR and SSIM, alongside radiologist assessment, confirmed significant noise suppression and sharper anatomical boundaries, particularly in regions with fine details such as organ interfaces and bone structures. Additionally, in benchmark comparisons against state-of-the-art LDCT models (RED-CNN, TED-Net, DSC-GAN, DRL-EMP) and traditional methods (BM3D), the model exhibited lower parameter and stable training performance. These findings highlight the model’s robustness, efficiency, and clinical applicability, making it a promising solution for improving LDCT image quality while maintaining computational efficiency.

Keywords:

gradient–Laplacian attention modules; low-dose CT denoising; deep learning; medical image processing; machine learning; vision transformers

1. Introduction

In the field of medical imaging, X-ray computed tomography (CT) plays a crucial role in diagnosing a wide range of conditions. However, the cumulative frequent exposure to radiation is a significant concern, prompting the need for low-dose computed tomography (LDCT) [1,2]. While LDCT reduces radiation exposure, it often results in noisy, low-quality images, which can compromise diagnostic accuracy. To address this, image denoising techniques are essential to enhance the quality of LDCT images while preserving critical anatomical structures [2]. Traditional low-dose computed tomography (LDCT) denoising methods are divided into several key categories: filter-based, model-based, transform-domain, and statistical methods. These methods each have unique strengths but also face specific limitations in maintaining an optimal balance between noise reduction and image detail retention, particularly in modern clinical settings.

Filter-based methods such as Gaussian, median, and bilateral filtering reduce noise by smoothing or averaging pixel intensities but differ in how they handle edges [3]. Gaussian filtering, for instance, reduces noise by averaging pixel values, though it often blurs fine details, which limits its suitability for highly detailed LDCT images [4]. Recent advancements like adaptive filtering [4,5] adjust filter strength based on image regions, improving edge preservation and reducing oversmoothing. However, adaptive filters may still struggle in regions with high noise levels, where detail is lost due to excessive smoothing in non-homogeneous areas. Approaches like non-local means (NLMs) [6,7], anisotropic diffusion [8], and total variation (TV) minimization [4] are designed to maintain image structure while reducing noise. NLM denoising, for example, compares and averages similar pixel patches across the image, as demonstrated by Zhang et al. [9], who modified NLMs to improve denoising in LDCT images. While effective, this approach is computationally intensive, limiting its efficiency in real-time applications, especially for large datasets. Anisotropic diffusion, another model-based technique, diffuses noise differently across regions to retain edges while smoothing uniform areas [10], but it can amplify artifacts in areas with low contrast, impacting diagnostic accuracy [8]. TV minimization, a popular choice for iterative reconstruction, reduces noise by minimizing image gradients [11]. He et al. [12] presented a TV-based method optimized for LDCT imaging, which retains edges well; however, this method can lead to staircase artifacts, particularly in areas with smooth gradients. Transform-domain methods decompose the image into wavelet or frequency components, making it easier to filter out noise selectively [13]. Wavelet transform denoising, for instance, decomposes an image into wavelet coefficients and selectively thresholds these coefficients to remove noise. Li et al. [14] improved on traditional wavelet methods with a multi-scale adaptive thresholding approach, which enhances detail preservation by handling noise at various frequencies. Despite their benefits, wavelet-based methods often require tuning across multiple scales, making them computationally complex and difficult to adapt for heterogeneous noise patterns, a limitation highlighted in Li et al.’s work. Fourier transform denoising, which uses frequency-based filtering, is also widely applied but can inadvertently blur details by removing high-frequency noise components indiscriminately, reducing diagnostic value in areas with high texture or detail [15]. Statistical denoising relies on probabilistic models to distinguish between noise and useful signals. Techniques such as K-SVD (sparse representation) utilize dictionary learning to construct a sparse, noise-free representation of the image [16]. The K-SVD method is adaptable and effective for LDCT, particularly in low-contrast areas; however, it can fail in high-noise or high-contrast regions where the learned basis functions may inadequately represent essential details. Bayesian estimation models, including maximum a posteriori (MAP) estimations, apply statistical priors to separate noise from signal [17]. While MAP estimation can yield high-quality denoising results, it relies heavily on accurate prior models, and incorrect priors can lead to oversmoothing, reducing the visibility of small or subtle structures. These studies reveal that while traditional denoising methods offer significant noise reduction capabilities for LDCT, each has inherent limitations. Recent model improvements attempt to address these issues, but achieving a perfect balance among noise reduction, computational efficiency, and detail retention remains an ongoing challenge.

Recently, deep learning models have emerged as powerful tools in medical image processing. Vision transformers (ViTs) offer a promising alternative to convolution-based networks by leveraging self-attention mechanisms to capture the long-range dependencies in images [18]. This study serves as the continuation of the paper by the authors, with the use of a pure vision transformer (PViT)-based architecture [19]. However, directly applying ViTs to LDCT denoising introduces challenges in accurately retaining fine structural details and edges, as shown in Figure 1. Comparing Figure 1b with the denoised image in Figure 1c using PViT alone, it is evident that the anatomical details within the highlighted blue region of interest are not well preserved. This discrepancy arises primarily from PViT’s limited ability to enhance fine structural details and detect subtle edge variations in low-dose CT images. Therefore, this paper primarily addresses the mentioned limitation by implementing an edge detection attention module. The used gradient and Laplacian filters, integrated into an attention module, are designed to enhance edge information by capturing both first- and second-order derivatives, detecting changes in the boundaries and textural details of the image, thus improving the representation of critical anatomical boundaries in the CT images. By combining attention mechanisms with these edge detectors, the PViT model aims to deliver high-quality, denoised LDCT images with greater edge consistency. The contributions of this paper are as follows:

There have been few transformer-based studies for LDCT denoising, so we aimed to address this gap by introducing a novel pure vision transformer with an edge detection attention module.
We leveraged the concept of edge detection attention modules in vision transformers that target the preservation of CT image edges and textural details.
We investigated the effectiveness of each edge detection attention module in LDCT denoising by performing ablation experiments using various kernels, datasets, and objective functions.
Benchmark testing with state-of-the-art LDCT denoising models was also performed to compare the proposed model with the recent developments in the LDCT denoising task in the research community.

2. Materials and Methods

2.1. System Model

The innovation of this work lies in the multi-head self-attention module of the pure vision transformer (PViT) for LDCT denoising, as developed in [19], incorporating a Noise2Neighbours reshaping module. Figure 2 shows the enhanced PViT structure, which originally used a multi-scale dot product operation for its multi-head self attention (MHSA) modules, as illustrated in Figure 3a, being replaced with the proposed gradient–Laplacian attention module (GLAM) displayed in Figure 3b, which is discussed further in the next section. The overall framework of the system used in the experiment follows a UNet framework, which is composed of the PViT blocks in Figure 2.

2.2. Gradient–Laplacian Attention Module

Yan, Fang and Qiao [20] introduced a U-shaped transformer containing Sobel pixel attention and channel attention modules for LDCT denoising. Their experiment mainly focused on the architecture of the internal structure of their dual-attention block: (i) series vs. (ii) parallel. Unlike the common multi-head self attention (MHSA) for the PViT in Figure 3a, we propose the use of a parallel dual attention block that focuses on the use of a gradient and Laplacian operation, as shown in Figure 3b.

We compute the edge map for the input feature map X using gradient kernels,

G_{i}

, which includes horizontal, vertical, and diagonal edge detection variation to allow detecting image edges in multiple directions. For the Laplacian operator, we use an 8-neighbor Laplacian kernel for a stronger edge detection,

L_{8}

, instead of the typical

3 \times 3

kernel,

L_{3}

, to compute the second-order derivative in capturing regions with abrupt intensity changes. Equation (1) defines the computation of the edge magnitude map M using both gradient and Laplacian operators:

M = \sqrt{\sum {(X \times G_{i})}^{2} + {(X \times L_{8})}^{2}}

(1)

where X represents the input feature map that undergoes edge detection. The gradient kernels

G_{i}

(where i denotes the directions: horizontal, vertical, and diagonal variations) allow for detecting edges in multiple directions. The Laplacian operator is applied using an 8-neighbor Laplacian kernel (

L_{8}

) instead of the standard

3 \times 3

kernel (

L_{3}

), providing stronger edge detection by capturing higher-order intensity variations.

The resulting edge map M is used within the gradient–Laplacian attention module (GLAM) to refine attention weights, emphasizing the structural details in the transformer’s self-attention mechanism. It is important to note that X in this equation is not the attention score matrix

Q K^{T}

; rather, it is the feature representation upon which edge detection is performed before computing attention weights.

Hence, the overall attention module using only the proposed edge detection gradient–Laplacian kernels is as follows:

A t t e n t i o n (Q, K, V, M) = s o f t m a x (\frac{Q K^{T} + β M}{\sqrt{d_{k}}}) V

(2)

where

β

balances the contribution of all edge directions in the attention modules as the model is being trained.

Figure 4 shows how each filter highlights or detects the edges of the image edges and image texture at the marked checkpoints on the system design in Figure 2. Please note that, at these checkpoints, an N2N reshaping module is applied in order to see the actual feature map of the whole CT image and not just the patched images. The gradient operator emphasizes gradient-based edge detection by capturing directional changes in intensity—such as vertical, horizontal, and diagonal edges. This makes it particularly effective in detecting sharp transitions between regions of different densities or intensities, such as the boundaries between bones and soft tissues in CT images. The Laplacian operator, on the other hand, highlights areas of rapid intensity change by focusing on second-order derivatives, effectively enhancing fine details in the image and preserving subtle features like small structures and textures that might otherwise be lost during denoising. Further discussion about the results is provided in Section 3, including quantitative results.

2.3. Evaluation Metrics and Loss Functions

Evaluating the effectiveness of LDCT denoising methods is crucial, and using metrics like Peak Signal-to-Noise Ratio (PSNR), Mean Squared Error (MSE), and Structural Similarity Index Measure (SSIM) are important for assessing both the quantitative and qualitative aspects of denoised images. Each metric provides distinct insights, which together give a more comprehensive evaluation. As for the objective functions used, using thr Mean Squared Error (MSE) and the Structural Dissimilarity Index Measure (DSSIM) as loss functions can be effective in LDCT denoising because they offer complementary advantages in training deep learning models.

The Peak Signal-to-Noise Ratio (PSNR) is widely used to measure the similarity between an original high-quality image (usually the normal-dose CT) and the denoised image. The PSNR is calculated based on the ratio of the maximum pixel intensity to the noise power, measured in decibels (dB) [21], shown mathematically in Equation (3). A higher PSNR value typically indicates less noise and closer resemblance to the reference image. However, the PSNR alone does not account for perceptual quality, such as structural details and textures, which are crucial in medical imaging. Therefore, the PSNR is often used alongside other metrics.

P S N R (x, y) = 10 {log}_{10} \frac{{(max (x_{j}))}^{2}}{M S E}

(3)

The SSIM is one of the most significant metrics for LDCT denoising as it considers human visual perception, focusing on structural similarity, luminance, and contrast. SSIM values range from 0 to 1, with values closer to 1 indicating high structural similarity to the reference image [22]. This is calculated as in Equation (4). The SSIM of denoised image (x) and the reference NDCT image (y) can be calculated using Equation (4), where

μ

is the mean,

σ

is the sample deviation,

σ_{x y}

stands for the sample covariance, while

α, β, γ \geq 0

and

α, β, γ > 0

are used for controlling the luminance, contrast, and structure similarities between the two images. The SSIM is particularly relevant in medical imaging because preserving anatomical structures is crucial for accurate diagnosis. Unlike the PSNR and MSE, the SSIM gives more weight to perceptual quality, making it a better metric for assessing how well a denoised image retains essential details.

\begin{matrix} S S I M (x, y) & = \frac{(2 μ_{x} μ_{y} + c_{1}) (2 σ_{x y} + c_{2})}{(μ_{x}^{2} + μ_{y}^{2} + c 1) (σ_{x}^{2} + σ_{y}^{2} + c_{2})} \\ = {(\frac{2 μ_{x} μ_{y}}{μ_{x}^{2} + μ_{y}^{2}})}^{α} {(\frac{2 σ_{x y}}{σ_{x}^{2} + σ_{y}^{2}})}^{β} {(\frac{σ_{x y}}{σ_{x} σ_{y}})}^{γ} \end{matrix}

(4)

The standard error of the mean (SEM) can also be used to calculate the uncertainty of a result. This can be calculated using the expression in (5), where

σ

is the standard deviation, and

\hat{N}

is the mean [23].

S E M = \frac{σ}{\sqrt{\hat{N}}}

(5)

The MSE calculates the average squared differences between predicted pixel values and target values, penalizing larger errors more heavily. This makes it highly effective for ensuring pixel-wise accuracy in reconstructed images. In the context of LDCT denoising, the MSE is straightforward to implement, calculated by applying Equation (6), and works well for minimizing noise while encouraging the model to match the intensities of the normal-dose reference image

y_{i}

. However, the MSE focuses only on pixel differences and does not account for human perceptual quality, so it may lead to overly smooth results that miss important structural details.

L_{M S E} (θ) = \frac{1}{N} \sum_{i = 1}^{N} {∥f (x_{i}; θ) - y_{i}∥}_{F}^{2} .

(6)

The Structural Dissimilarity Index Measure (DSSIM) as a loss function is derived from the Structural Similarity Index Measure (SSIM). It focuses on structural dissimilarity rather than pixel-wise error, as calculated in Equation (7). Unlike the MSE, the DSSIM penalizes loss in structural features, like edges and textures, by assessing differences in luminance, contrast, and structural composition. Using the DSSIM as a loss function helps the model preserve anatomical structures, which is crucial for diagnostic accuracy in medical images. It also aligns better with human perception, as small pixel differences matter less than overall structural integrity. However, the DSSIM alone can overlook intensity accuracy and may not perform as well in areas without strong structural patterns, making it useful in combination with other loss terms.

L_{D S S I M} (θ) = \frac{1}{N} \sum_{i = 1}^{N} (1 - S S I M (f (x_{i}; θ) - y_{i})) / 2

(7)

Perceptual loss (PL) is calculated using the last four blocks of the VGG16-pretrained network [24]. Unlike the MSE, perceptual loss takes high-level features into consideration, which accurately models the human visual system due to its ability to learn the features. The feature maps,

ϕ_{i}

, are extracted from the last convolutional layer in blocks

i = 1, 2, 3, 4

of the VGG16 with size

h_{i} \times w_{i} \times d_{i}

, which can be expressed as

L_{P L} (x, y) = \sum_{i = 1}^{N} \frac{1}{h_{i} w_{i} d_{i}} {∥ϕ_{i} (x) - ϕ_{i} (y)∥}^{2}

(8)

The overall proposed loss function can be calculated as follows, where

γ

represents the contribution of each loss function depending on how the model is being trained. To determine the optimal balance, we conducted ablation studies with different loss weightings, which is discussed in Section 4.

L (θ) = γ_{1} L_{M S E} (θ) + γ_{2} L_{D S S I M} (θ) + γ_{3} L_{P L} (θ)

(9)

2.4. Dataset & Training Details

Five different datasets of

512 \times 512

NDCT–LDCT image pairs were used for this experiment. The piglet dataset and the thoracic dataset were from Yi and Babyn [25], and the abdomen, chest dataset, and the head dataset were obtained from the Cancer Imaging Archive (TCIA) Mayo Clinic [26]. Table 1 below shows the X-ray current dose used for obtaining the images. These images were in the form of Digital Imaging and Communications in Medicine (DICOM) files, which included metadata such as the image pixel size and medical information about the patient. For data preparation, the CT images were calibrated to the standard Hounsfield unit (HU), which refers to the specific substance being observed in the image. In this experiment, the calibration method was the same as in [27]. For this experiment, Hounsfield unit (HU) windowing was applied. Table 1 also shows a summary of the window level (WL) and window width (WW) for each dataset normalization. The dataset partition used for this experiment was 60% training, 30% validation, and 10% testing for each type of dataset. It is also important to note that all data in this work were analyzed in 2D slices, and all the models were trained for 150 epochs using the Adam optimizer with a learning rate of 0.0001, decay steps of 0.5, rate of 0.9, and batch sizes of 4–8. The experiments were carried using Pytorch and Tensorflow-Keras API on a Windows operating system with an Intel(R) Core(TM)i7-10700k CPU @2.90 GHz processor (Santa Clara, CA, USA), and NVIDIA GeForce RTX 3070 and 1080 (Santa Clara, CA, USA).

3. Results

The results in Table 2, Table 3, Table 4, Table 5 and Table 6 provide a detailed quantitative comparison of different low-dose CT (LDCT) denoising models, including the pure vision transformer (PViT) and its variations utilizing attention modules and loss functions. The uncertainty values, provided as standard errors of the mean (SEMs), give us deeper insight into the consistency of these models in producing denoised images. To strengthen the validity of the proposed model and its variations, we also compared their results with the following benchmark models: (i) traditional BM3D [28]; (ii) convolution-based denoising networks, RED-CNN and DRL-E-MP [27]; (iii) hybrid convolution-transformer based model TED-Net [29]; and, finally, (iv) a recent generative denoising network, DSC-GAN [30]. Figure 5 and Figure 6 illustrate visual comparisons and training trends for the piglet dataset. Similarly, Figure 7 and Figure 8 present results for the thoracic dataset, while Figure 9 and Figure 10 correspond to the head dataset. For the abdomen dataset, Figure 11 and Figure 12 provide the respective visual comparisons and training trends. Finally, Figure 13 and Figure 14 showcase the results for the chest dataset.

4. Discussion

4.1. Optimal Balance for Loss Function

To determine the optimal weighting strategy, we conducted ablation studies using each loss function individually and analyzed their influence on noise suppression and structural detail preservation.

Our results revealed that MSE loss alone, despite its effectiveness in reducing pixel-wise errors, often led to oversmoothed reconstructions, potentially obscuring fine anatomical details. In contrast, the DSSIM loss significantly improved edge preservation and contrast by penalizing structural inconsistencies, ensuring that organ boundaries and fine textures were more accurately reconstructed. Additionally, PL loss contributed to perceptually realistic restorations by utilizing high-level feature similarities rather than solely relying on pixel-wise accuracy. These observations align with prior studies demonstrating that structural and perceptual losses play a key role in preserving the diagnostic information in LDCT imaging. Based on these insights, we adopted a detail-preserving loss weighting strategy with

γ_{1} = 0.2, γ_{2} = 0.4, γ_{3} = 0.4

. This configuration prioritizes the DSSIM and PL over the MSE, effectively balancing noise suppression and anatomical structure retention. Benchmark comparisons further validated the effectiveness of this approach, as GLAM-PViT outperformed state-of-the-art models (RED-CNN, TED-Net, DSC-GAN, DRL-EMP, BM3D) in preserving fine details while maintaining high PSNR and SSIM scores.

4.2. Piglet Dataset

The baseline piglet LDCT images exhibit poor quality (SSIM: 0.6152, PSNR: 25.12) with significant noise. The PViT model achieves a marked improvement (SSIM: 0.9631, PSNR: 43.34) with low uncertainty, demonstrating robust denoising capability. Gradient attention modules (GAMs) further enhance performance, with the diagonal-vertical-horizontal (DVH) configuration achieving the highest SSIM (0.9730) and PSNR (43.62) with low uncertainty. The gradient–Laplacian attention module (GLAM) paired with a combined loss function (MSE + SSIM + PL) delivers the best results (SSIM: 0.9756, PSNR: 43.84) with consistency, outperforming benchmark models like RED-CNN, TED-Net, and DSC-GAN.

4.3. Thoracic Dataset

The thoracic dataset starts with poorer baseline image quality (SSIM: 0.2617, PSNR: 19.75) than the piglet dataset. The PViT model achieves improvements (SSIM: 0.6651, PSNR: 31.26), though the denoising results are less pronounced compared to the piglet dataset. GAM-PViT (DVH) achieves an SSIM of 0.6712 and a PSNR of 32.11, reflecting moderate enhancement. The GLAM-PViT model with the proposed loss function yields the best performance (SSIM: 0.6788, PSNR: 32.92), showcasing its ability to handle more complex noise patterns. Despite these challenges, GLAM-PViT remains competitive and consistent across varied noise levels.

4.4. Head Dataset

The baseline head dataset images (SSIM: 0.2264, PSNR: 30.43) suffer from significant structural artifacts. The PViT model achieves notable improvements (SSIM: 0.6888, PSNR: 42.66), performing better than on thoracic data but falling short of the piglet results. GAM-PViT (DVH) and LAM-PViT show further enhancement, with GLAM-PViT providing the best results (SSIM: 0.6893, PSNR: 44.16). These results highlight the effectiveness of combining attention mechanisms and a tailored loss function for addressing the structural artifacts and noise in head CT images.

4.5. Abdomen Dataset

The baseline abdomen dataset images (SSIM: 0.6234, PSNR: 30.14) show moderate noise levels. The PViT model achieves significant improvement (SSIM: 0.8609, PSNR: 41.21), outperforming the head and thoracic datasets. GAM-PViT (DVH) shows modest gains, while LAM-PViT (SSIM: 0.8613, PSNR: 40.66) provides superior edge and contour preservation. The GLAM-PViT model with the combined loss function achieves the highest performance (SSIM: 0.8742, PSNR: 43.25), underscoring the model’s robustness in handling moderate noise and preserving structural integrity.

4.6. Comparison Across Datasets

The PViT variants consistently outperform the traditional models, such as RED-CNN, TED-Net, and DSC-GAN, on all datasets. The GLAM-PViT model with the proposed loss function delivers the best denoising results, achieving high SSIM and PSNR values with low uncertainty. The performance variations across datasets reflect the differences in noise complexity and structural features, with the piglet and abdomen datasets showing better results compared to the thoracic and head datasets. This demonstrates the adaptability of GLAM-PViT to diverse noise patterns and anatomical structures.

4.7. Training Performance

Figure 6, Figure 7, Figure 9, Figure 11 and Figure 13 provide insights into the performance, convergence behavior, and the generalization ability of the models. For the loss trends (Figure 6a, Figure 7a, Figure 9a, Figure 11a, and Figure 13a), the steady decrease indicates stable training and convergence, which can be observed in the GLAM-PViT (proposed), TED-NET, PViT and DRLEMP models. In contrast, GLAM-PViT (PL), BM3D, DSC-GAN, and RED-CNN show a downward trend with sudden oscillations, which indicate instability. Similar patterns were observed on each dataset.

Next, regarding the PSNR trends (Figure 6b, Figure 7b, Figure 9b, Figure 11b and Figure 13b), slight fluctuations can be noticed for all the models, which indicate sensitivity to noise. Despite this discrepancy, the GLAM-PViT (proposed), TED-NET, DRLEMP, attention module, and loss function variants of the proposed model show an early steeper PSNR improvement as well as a consistently higher PSNR and stabilize without a decline. These behaviors indicate a strong denoiser model and higher training efficiency. The traditional modesl, BM3D, CNN-based model, and RED-CNN, lag behind the other models.

Lastly, for the SSIM trends (Figure 6c, Figure 7c, Figure 9c, Figure 11c and Figure 13c) of all the models, slight fluctuations can also be observed, which could indicate instability in texture preservation. Similar to the PSNR trends, the transformer-based models including the proposed model still show a steady increase and a significantly higher SSIM while maintaining the PSNR, meaning that these models have better perceptual quality.

4.8. Visual and Clinical Implications

The visual results confirm that the proposed GLAM-PViT model produces cleaner, sharper images with reduced noise and artifacts. These improvements make the images diagnostically useful, closely resembling high-dose CT scans. The low uncertainties across datasets ensure consistent performance, highlighting the model’s robustness for clinical applications.

While numerous unsupervised denoising models, such as Noise2Self [31] and Patch2Self [32], have demonstrated strong performance in self-supervised noise learning, our study followed a supervised approach, leveraging paired LDCT–NDCT data to train a model with explicit noise-to-clean mappings. This allows for more precise noise suppression and structural preservation compared to unsupervised methods, which rely on statistical assumptions about noise. However, exploring hybrid or self-supervised approaches for LDCT denoising remains an interesting avenue for future research, particularly for scenarios where paired training data are scarce.

5. Conclusions

The proposed gradient–Laplacian attention module (GLAM), integrated into the vision transformer (PViT) network, significantly enhanced edge detection and detail preservation across all datasets (piglet, head, abdomen, chest, and thoracic) by sharpening image edges during the denoising process. This improvement stems from the combined use of Sobel and Laplacian filters, each focusing on distinct edge characteristics. A series of ablation studies validated the effectiveness of the proposed network. First, we compared the performance of the baseline PViT using traditional MHSA with various attention mechanisms, including GAM-PViT (diagonal, vertical, horizontal, VH, DVH), LAM-PViT, and the proposed GLAM-PViT. Next, we evaluated the proposed loss function with different combinations—MSE, SSIM, PL, and MSE+SSIM+PL—to determine optimal performance. Benchmark comparisons were then conducted with state-of-the-art denoising models (RED-CNN, TED-Net, DSC-GAN, BM3D, and DRLEMP) to assess the proposed model’s competitiveness.

The results indicate that leveraging transformer-based models for denoising in low-dose CT imaging can enhance diagnostic accuracy, potentially benefiting patient care across various medical fields. This approach shows particular promise in cancer diagnostics, where early tumor detection, accurate lesion segmentation, staging, and treatment planning are critical. Integrating these models into clinical workflows could reduce false positives and negatives, streamline interpretation, support large-scale screening, and stimulate further advancements in medical imaging research.

Author Contributions

The authors confirm contribution to this paper as follows: study conception: J.A. and P.B.; methodology and investigation: L.M.; data curation: P.B.; analysis and interpretation of results: L.M., J.A., and P.B.; draft manuscript preparation: L.M.; review and editing: J.A. and P.B.; funding acquisition: J.A. All authors have read and agreed to the published version of this manuscript.

Funding

This research was supported by an NSERC Discovery grant RGPIN-202004441 that was awarded to Javad Alirezaie.

Data Availability Statement

The data (thoracic, chest, abdomen, and head) used for this study are openly available from the The Cancer Imaging Archive (TCIA): https://doi.org/10.7937/9NPB-2637 (accessed on 26 February 2025). The Piglet dataset was provided by Dr. Paul Babyn; further inquiries can be directed to the corresponding author.

Acknowledgments

The authors would like to thank Cynthia McCollough, the Mayo Clinic, and the American Association of Physicists in Medicine for making the CT data available for this study.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Not-well-preserved anatomical details in the highlighted blue ROI, produced using a pure vision transformer for LDCT denoising. Image generated from running the PViT model in [19] using the piglet dataset for this study. (a) Piglet LDCT (15 mAs) slice. (b) Piglet NDCT (300 mAs) slice. (c) Generated output from PViT.

Figure 2. Pure transformer block for LDCT denoising with the integration of gradient–Laplacian attention module.

Figure 3. Attention modules in the pure vision transformer for LDCT denoising. (a) Multi-head self attention module for PViT. (b) Proposed gradient–Laplacian attention module for PViT.

Figure 4. Edge enhancement at each upsampling and downsampling checkpoint labeled in Figure 2 using different filters in the attention module. (a–c) The feature maps generated from checkpoint at the encoder; (d–f) the feature maps generated from the checkpoint at the decoder.

Figure 5. Benchmark test visual results for piglet data: (a) input LDCT image reference with blue ROI, (b) ROI of LDCT image, (c) ROI of NDCT image, and ROI of output image using (d) RED-CNN, (e) PViT, (f) DSC-GAN, (g) DRLEMP, (h)TED-Net, (i) GLAM-PViT.

Figure 6. Loss, PSNR, and SSIM trend over 150 epochs using piglet dataset. (a) Loss. (b) PSNR. (c) SSIM.

Figure 7. PSNR and SSIM trend over 150 epochs using thoracic dataset. (a) Loss. (b) PSNR. (c) SSIM.

Figure 8. Benchmark test visual results for thoracic data: (a) input LDCT image reference with blue ROI, (b) ROI of LDCT image, (c) ROI of NDCT image, and ROI of output image using (d) RED-CNN, (e) PViT, (f) DSC-GAN, (g) DRLEMP, (h) TED-Net, (i) GLAM-PViT.

Figure 9. PSNR and SSIM trend over 150 epochs using head dataset. (a) Loss. (b) PSNR. (c) SSIM.

Figure 10. Benchmark test visual results for dead data: (a) input LDCT image reference with blue ROI, (b) ROI of LDCT image, (c) ROI of NDCT image, and ROI of output image using (d) RED-CNN, (e) PViT, (f) DSC-GAN, (g) DRLEMP, (h) TED-Net, (i) GLAM-PViT.

Figure 11. PSNR and SSIM trend over 150 epochs using abdomen dataset. (a) Loss. (b) PSNR. (c) SSIM.

Figure 12. Benchmark test visual results for abdomen data: (a) input LDCT image reference with blue ROI, (b) ROI of LDCT image, (c) ROI of NDCT image, and ROI of output image using (d) RED-CNN, (e) PViT, (f) DSC-GAN, (g) DRLEMP, (h) TED-Net, (i) GLAM-PViT.

Figure 13. PSNR and SSIM trend over 150 epochs using chest dataset. (a) Loss. (b) PSNR. (c) SSIM.

Figure 14. Benchmark test visual results for chest data: (a) input LDCT image reference with blue ROI, (b) ROI of LDCT image, (c) ROI of NDCT image, and ROI of output image using (d) RED-CNN, (e) PViT, (f) DSC-GAN, (g) DRLEMP, (h) TED-Net, (i) GLAM-PViT.

Table 1. Dataset X-ray current information and Hounsfield unit [HU] windowing for normalization.

Dataset	NDCT	LDCT	WL [HU]	WW [HU]
Piglet	300 mAs	15 mAs	40	400
Thoracic	480 mAs	60 mAs	−650 to −700	1500 to 2000
Abdomen	502 mAs	498 mAs	40	40
Chest	712 mAs	690 mAs	40	400
Head	202 mAs	180 mAs	30 to 50	80 to 100

Table 2. Piglet Dataset. Average SSIM and PSNR with No. of parameters using two transformer blocks for the PViT model variants (GAM: gradient attention module, LAM: Laplacian attention module, GLAM: gradient–Laplacian attention module) and variants of the loss functions (MSE, SSIM, PL, proposed: MSE + SSIM + PL) used for the training (150 epochs). Uncertainties were calculated using SEM.

Model	SSIM ↑	PSNR ↑	#Param	Training Time
LDCT	0.6152 ± 0.0023	25.12 ± 0.03	—	—
PViT	0.9631 ± 0.0015	43.34 ± 0.02	1.68 M	15 min
GAM-PViT (DVH)	0.9730 ± 0.0011	43.62 ± 0.01	1.66 M	15 min
LAM-PViT	0.9622 ± 0.0017	42.12 ± 0.03	1.66 M	15 min
GLAM-PViT (MSE)	0.9728 ± 0.0013	43.51 ± 0.02	1.70 M	18 min
GLAM-PViT (SSIM)	0.9727 ± 0.0015	43.49 ± 0.02	1.71 M	18 min
GLAM-PViT (PL)	0.9732 ± 0.0010	43.62 ± 0.01	1.75 M	20 min
GLAM-PViT (proposed)	0.9756 ± 0.0010	43.84 ± 0.01	1.82 M	30 min
Benchmark 1: RED-CNN	0.9321 ± 0.0021	39.68 ± 0.04	3.33 M	50 min
Benchmark 2: TED-Net	0.9536 ± 0.0019	43.15 ± 0.03	3.28 M	80 min
Benchmark 3: DSC-GAN	0.9602 ± 0.0018	42.23 ± 0.03	4.16 M	120 min
Benchmark 4: BM3D *	0.8263 ± 0.0027	36.55 ± 0.04	n/a	60 min
Benchmark 5: DRLEMP	0.9529 ± 0.0018	41.66 ± 0.03	2.80 M	60 min

↑ Higher SSIM/PSNR values indicates more accurate denoised image. * BM3D involves algorithmic parameters and settings (e.g., block size, search window size, thresholding parameters) that can be tuned, but these are not learned from data in the same manner as neural network weights.

Table 3. Thoracic dataset. Average SSIM and PSNR with No. of parameters using two transformer blocks for the PViT model variants (GAM: gradient attention module, LAM: Laplacian attention module, GLAM: gradient–Laplacian attention module) and variants of the loss functions (MSE, SSIM, PL, proposed: MSE + SSIM + PL) used for the training (100 epochs). Uncertainties were calculated using standard error of the mean (SEM).

Model	SSIM ↑	PSNR ↑	#Param	Training Time
LDCT	0.2617 ± 0.0028	19.75 ± 0.03	—	—
PViT	0.6651 ± 0.0019	31.26 ± 0.02	1.68 M	15 min
GAM-PViT (DVH)	0.6712 ± 0.0015	32.11 ± 0.01	1.66 M	15 min
LAM-PViT	0.6601 ± 0.0019	29.81 ± 0.03	1.66 M	15 min
GLAM-PViT (MSE)	0.6756 ± 0.0014	32.36 ± 0.02	1.70 M	18 min
GLAM-PViT (SSIM)	0.6742 ± 0.0015	32.25 ± 0.02	1.71 M	18 min
GLAM-PViT (PL)	0.6769 ± 0.0013	32.43 ± 0.01	1.75 M	20 min
GLAM-PViT (proposed)	0.6788 ± 0.0012	32.92 ± 0.01	1.82 M	30 min
Benchmark 1: RED-CNN	0.4926 ± 0.0030	26.85 ± 0.04	3.33 M	50 min
Benchmark 2: TED-Net	0.6231 ± 0.0024	30.28 ± 0.03	3.28 M	80 min
Benchmark 3: DSC-GAN	0.6433 ± 0.0021	29.25 ± 0.03	4.16 M	120 min
Benchmark 4: BM3D *	0.4621 ± 0.0035	26.85 ± 0.04	n/a	60 min
Benchmark 5: DRLEMP	0.5283 ± 0.0028	27.31 ± 0.04	2.80 M	60 min

Table 4. Head dataset. Average SSIM and PSNR with No. of Parameters using two transformer blocks for the PViT model variants (GAM: gradient attention module, LAM: Laplacian attention module, GLAM: gradient–Laplacian attention module) and variants of the loss functions (MSE, SSIM, PL, proposed: MSE + SSIM + PL) used for the training (100 epochs). Uncertainties were calculated using standard error of the mean (SEM).

Model	SSIM ↑	PSNR ↑	#Param	Training Time
LDCT	0.2264 ± 0.015	30.43 ± 0.08	—	—
PViT	0.6888 ± 0.010	42.66 ± 0.07	1.68 M	15 min
GAM-PViT (DVH)	0.6811 ± 0.005	43.04 ± 0.07	1.66 M	15 min
LAM-PViT	0.6504 ± 0.015	41.68 ± 0.09	1.66 M	15 min
GLAM-PViT (MSE)	0.6820 ± 0.007	43.23 ± 0.06	1.70 M	18 min
GLAM-PViT (SSIM)	0.6822 ± 0.007	43.21 ± 0.08	1.71 M	18 min
GLAM-PViT (PL)	0.6813 ± 0.005	44.02 ± 0.05	1.75 M	20 min
GLAM-PViT (proposed)	0.6893 ± 0.005	44.16 ± 0.04	1.82 M	30 min
Benchmark 1: RED-CNN	0.4721 ± 0.012	36.88 ± 0.10	3.33 M	50 min
Benchmark 2: TED-Net	0.5713 ± 0.010	41.75 ± 0.07	3.28 M	80 min
Benchmark 3: DSC-GAN	0.5632 ± 0.015	39.62 ± 0.08	4.16 M	120 min
Benchmark 4: BM3D *	0.3156 ± 0.015	34.21 ± 0.09	n/a	60 min
Benchmark 5: DRLEMP	0.4893 ± 0.015	38.64 ± 0.08	2.80 M	60 min

Table 5. Abdomen dataset. Average SSIM and PSNR with No. of parameters using two transformer blocks for the PViT model variants (GAM: gradient attention module, LAM: Laplacian attention module, GLAM: gradient–Laplacian attention module) and variants of the loss functions (MSE, SSIM, PL, proposed: MSE + SSIM + PL) used for the training (100 epochs). Uncertainties were calculated using standard error of the mean (SEM).

Model	SSIM ↑	PSNR ↑	#Param	Training Time
LDCT	0.6234 ± 0.0035	30.14 ± 0.05	—	—
PViT	0.8609 ± 0.0012	41.21 ± 0.08	1.68 M	15 min
GAM-PViT (DVH)	0.8421 ± 0.0025	38.23 ± 0.08	1.66 M	15 min
LAM-PViT	0.8613 ± 0.0018	40.66 ± 0.06	1.66 M	15 min
GLAM-PViT (MSE)	0.8428 ± 0.0022	39.05 ± 0.07	1.70 M	18 min
GLAM-PViT (SSIM)	0.8452 ± 0.0019	39.16 ± 0.10	1.71 M	18 min
GLAM-PViT (PL)	0.8645 ± 0.0010	40.28 ± 0.05	1.75 M	20 min
GLAM-PViT (proposed)	0.8742 ± 0.0009	43.25 ± 0.03	1.82 M	30 min
Benchmark 1: RED-CNN	0.8413 ± 0.0030	36.92 ± 0.09	3.33 M	50 min
Benchmark 2: TED-Net	0.8603 ± 0.0016	41.03 ± 0.07	3.28 M	80 min
Benchmark 3: DSC-GAN	0.8524 ± 0.0025	40.35 ± 0.08	4.16 M	120 min
Benchmark 4: BM3D *	0.8152 ± 0.0040	34.27 ± 0.10	n/a	60 min
Benchmark 5: DRLEMP	0.8579 ± 0.0020	37.64 ± 0.06	2.80 M	60 min

Table 6. Chest dataset. Average SSIM and PSNR with No. of parameters using two transformer blocks for the PViT model variants (GAM: gradient attention module, LAM: Laplacian attention module, GLAM: gradient–Laplacian attention module), and variants of the loss functions (MSE, SSIM, PL, proposed: MSE + SSIM + PL) used for the training (100 epochs). Uncertainties were calculated using standard error of the mean (SEM).

Model	SSIM ↑	PSNR ↑	#Param	Training Time
LDCT	0.3489 ± 0.0040	26.32 ± 0.08	—	—
PViT	0.7932 ± 0.0015	36.19 ± 0.05	1.68 M	15 min
GAM-PViT (DVH)	0.8064 ± 0.0025	34.72 ± 0.06	1.66 M	15 min
LAM-PViT	0.8107 ± 0.0010	35.28 ± 0.05	1.66 M	15 min
GLAM-PViT (MSE)	0.8012 ± 0.0035	34.17 ± 0.09	1.70 M	18 min
GLAM-PViT (SSIM)	0.8056 ± 0.0028	35.19 ± 0.03	1.71 M	18 min
GLAM-PViT (PL)	0.8124 ± 0.0018	35.82 ± 0.04	1.75 M	20 min
GLAM-PViT (proposed)	0.8224 ± 0.0010	36.71 ± 0.02	1.82 M	30 min
Benchmark 1: RED-CNN	0.6423 ± 0.0035	29.63 ± 0.10	3.33 M	50 min
Benchmark 2: TED-Net	0.7725 ± 0.0020	34.92 ± 0.07	3.28 M	80 min
Benchmark 3: DSC-GAN	0.6234 ± 0.0045	33.25 ± 0.06	4.16 M	120 min
Benchmark 4: BM3D *	0.5673 ± 0.0050	27.31 ± 0.09	n/a	60 min
Benchmark 5: DRLEMP	0.6636 ± 0.0030	31.33 ± 0.05	2.80 M	60 min

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Marcos, L.; Babyn, P.; Alirezaie, J. Edge Detection Attention Module in Pure Vision Transformer for Low-Dose X-Ray Computed Tomography Image Denoising. Algorithms 2025, 18, 134. https://doi.org/10.3390/a18030134

AMA Style

Marcos L, Babyn P, Alirezaie J. Edge Detection Attention Module in Pure Vision Transformer for Low-Dose X-Ray Computed Tomography Image Denoising. Algorithms. 2025; 18(3):134. https://doi.org/10.3390/a18030134

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Marcos, Luella, Paul Babyn, and Javad Alirezaie. 2025. "Edge Detection Attention Module in Pure Vision Transformer for Low-Dose X-Ray Computed Tomography Image Denoising" Algorithms 18, no. 3: 134. https://doi.org/10.3390/a18030134

APA Style

Marcos, L., Babyn, P., & Alirezaie, J. (2025). Edge Detection Attention Module in Pure Vision Transformer for Low-Dose X-Ray Computed Tomography Image Denoising. Algorithms, 18(3), 134. https://doi.org/10.3390/a18030134

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