A cross-type multi-dimensional network based on feature enhancement and triple interactive attention for LDCT denoising

Abstract

Background

Numerous deep leaning methods for low-dose computed technology (CT) image denoising have been proposed, achieving impressive results. However, issues such as loss of structure and edge information and low denoising efficiency still exist.

Objective

To improve image denoising quality, an enhanced multi-dimensional hybrid attention LDCT image denoising network based on edge detection is proposed in this paper.

Methods

In our network, we employ a trainable Sobel convolution to design an edge enhancement module and fuse an enhanced triplet attention network (ETAN) after each $3 \times 3$ convolutional layer to extract richer features more comprehensively and suppress useless information. During the training process, we adopt a strategy that combines total variation loss (TVLoss) with mean squared error (MSE) loss to reduce high-frequency artifacts in image reconstruction and balance image denoising and detail preservation.

Results

Compared with other advanced algorithms (CT-former, REDCNN and EDCNN), our proposed model achieves the best PSNR and SSIM values in CT image of the abdomen, which are 34.8211and 0.9131, respectively.

Conclusion

Through comparative experiments with other related algorithms, it can be seen that the algorithm proposed in this article has achieved significant improvements in both subjective vision and objective indicators.

Keywords

low-dose CT denoising convolutional network feature enhancement attention mechanism

Introduction

In recent years, computed tomography (CT) technology has been widely used in clinical practice. CT technology can quickly extract the tissue structure with high resolution. The study shows that, excessively high doses of CT radiation¹ will seriously harm the health of subjects during clinical testing. Low dose CT(LDCT) can reduce the radiation harm effectively. However, LDCT will cause artifacts and noise in the reconstruction image, which will reduce the image quality and be not conducive to clinical diagnosis.² Therefore, LDCT image denoising technology³ has become a hot topic research.

The current methods used to improve the quality of LDCT images⁴ mainly include projection domain filtering algorithms,⁵ iterative reconstruction algorithm,⁶ image domain post-processing algorithms⁷ and deep learning-based LDCT image denoising algorithms. The projection domain filtering algorithm, also known as the domain processing algorithm, directly uses the projection image as an optimization variable to filter out the random noise of the projection image,⁸ and finally applies the filtered back-projection algorithm to obtain the reconstructed image.⁹ Typical methods mainly include: structural adaptive filtering, bilateral filtering and penalized weighted least-square algorithm (Penalized weighted least-square, PWLS). Iterative reconstruction algorithms use mathematical optimization techniques to iteratively reconstruct images from projection data¹⁰ to reduce noise and improve image quality, such as maximum likelihood algorithms and algebraic reconstruction techniques.¹¹ Image domain post-processing algorithms apply various signal processing techniques, such as wavelet transform, to enhance structural information in the image and suppress noise.¹² These methods typically rely on physical models and mathematical theories. In recent years, denoising methods based on deep learning have emerged and have achieved great improvements in LDCT image denoising performance. These algorithms produce higher quality images than traditional algorithms.¹³ Liang et al.¹⁴ proposed an Edge enhancement-based densely connected network with compound loss for LDCT denoising which emphasizes the balance between noise suppression and edge detail retention, resulting in significantly improved visual and quantitative quality of de-noised LDCT images. By connecting the deconvolution network¹⁵ and the residual¹⁶ Combined into the CNN model simultaneously, Chen et al.¹⁷ proposed a residual encoder-decoder convolutional neural network (RED-CNN) for LDCT image denoising, improving the quality of LDCT denoised images greatly. However, due to the use of mean squared error (MSE) loss function, the denoised image is over-smooth, making diagnosis difficult for clinicians. In view of this, Yang et al.¹⁸ added Wasserstein distance and perceptual similarity to the Generative Adversarial Network (GAN), and introduced perceptual loss to better retain feature information in CT images. Chen et al.¹⁹ proposed a deep network based on edge enhancement that can restore the details lost during the denoising process. However, traditional edge extractors have the property of converting all edge values into 0 and 1, which will lead to severe information loss and the appearance of false edges. Zhang et al.²⁰ proposed a comprehensive learning enabled adversarial reconstruction (CLEAR) network, which combines projection domain networks and image domain networks, demonstrating its excellent performance, but its network is complex and the training time is long. Wang, et al.²¹ have proposed a non-convolution visual transformer (CT-former) for LDCT images denoising which preserves the local context information well. In addition, the attention mechanism is also widely used in LDCT image denoising tasks. The purpose of introducing the attention mechanism into the neural network is to recalibrate the feature response so that it tends to the most informative and important component of the input. Anwar et al.²² introduced the SE(Squeeze-Excitation) attention mechanism into the field of image denoising and proposed a denoising network RIDNet based on the SE attention mechanism. Li et al.²³ proposed a Residual Attention Module (RAM) by adding the CBAM (Convolutional Block Attention Module) attention mechanism to the residual connection. Futhermore, by incorporating the RAM module into two neural networks for LDCT image denoising, they developed two networks called RED-CNN-RAM and WGAN-RAM respectively, obtaining good denoising performance. However, the model is complex and runs slowly. It is worth noting that all of the mentioned mechanisms use first-order statistics to count channels or spaces, ignoring high-order statistics of channels or spaces, thus hindering the network's ability to distinguish important parts of input features.

Some literature shows that the loss function is very important in image reconstruction and it directly affects the quality of the image.²⁴ One of the most popular loss functions is the MSE loss function, which calculates the squared mean of the pixel-wise error between the denoised image and the normal dose image. Although it achieves good results on the peak signal to noise ratio (PSNR) indicator, MSE often results in over-smoothing of the image and has poor correlation with the image quality perceived by human observers. In response to this phenomenon, researchers have studied many loss functions suitable for LDCT image denoising, such as perceptual loss,²⁵ adversarial loss,²⁶ structural similarity (SSIM) loss,²⁷ etc. Zhou et al. introduced contrast learning²⁸ in the field of image dehazing into LDCT image denoising, proposed a contrast regularization loss function, and achieved excellent denoising performance compared with other deep learning algorithms. But the pre-trained VGG-19 network²⁹ was used as the intermediate feature extraction network, which used more parameters and consumed more computing resources.

Although many algorithms and models have been proposed, existing technologies still have problems such as loss of detail and edge information, and lack of generalization. Therefore, extracting more useful features, increasing the model's attention to important features,³⁰ effectively improving the model's understanding and utilization of feature maps, and thereby enhancing the model's performance are key issues we need to address. In the paper, we drew on the advantages of the attention mechanism and edge extraction network³¹ and proposed a cross-latitude hybrid attention model³² for LDCT image denoising.

Materials and methods

Dataset and LDCT image noise description

In the experimental study, a dataset from the 2016 NIH AAPM-Mayo Clinic LDCT Challenge is used. It contains paired normal-dose CT (NDCT) images from 10 patients and synthesized one-quarter dose abdominal CT images, one-quarter dose head CT images, and one-tenth dose of chest images

LDCT images can be seen as a complex degraded results of the NDCT images. Due to the end-to-end characteristics of deep learning, we do not need to model the distribution of data, but can directly learn to obtain high-dose images after de-noising low-dose CT images. Assuming that $z \in R_{H \times W}$ represents the LDCT image, $X \in R_{H \times W}$ represents the corresponding NDCT image, and the denoising problem is transformed to find an optimal approximation finction. It is expressed as f, which is expressed as:

\underset{f}{\arg min} {‖ f (z) - x ‖}_{2}^{2}

(1)

f : z \to x

(2)

where

f

represents the network model and refers to the end-to-end mapping function.¹⁹

The main contributions of this article are summarized as follows:

We utilized a discrete differential operator, named the gradient edge enhancement module specifically for edge detection. It effectively extracts edge features in the image and makes the edge areas more prominent.

We introduced an innovative ETAN module that combines a multi-dimensional hybrid attention with a detail enhancement module. Through the integration of these two modules, our model can parse and utilize feature maps more effectively, thus significantly improve denoising performance.

A hybrid loss function that combined regularization techniques with MSE loss is proposed to guide the model's training process, retaining more image details during denoising and improving the output image quality.

The proposed network architecture

The article proposed a multi-dimensional hybrid attention model based on edge extraction and detail enhancement. The overall structural framework is shown in Figure 1. It includes three parts: edge feature extraction network, ETAN module, and densely connected network. Specifically, we pipe the output of the Sobel operator to each convolutional block via skip connections and link them via dense links.³³ The convolutional layers are composed of convolution kernels with sizes of $1 \times 1$ and $3 \times 3$ , and the number of convolution filters is set to 32. In the last layer, the number of $3 \times 3$ convolution filter is 1 to obtain a single-channel output. The activation function is LeakReLU. In each block, the outputs of the previous layer and the Sobel operator are fused using convolutional operator with $1 \times 1$ kernel, and features in the image are typically learned using convolution with a $3 \times 3$ kernel. The ETAN module integrates the feature enhancement module (FEM)³⁴ and the cross-hybrid attention module³⁵ to parse and utilize feature maps more effectively. We import the output results of the Sobel convolution and the first seven $3 \times 3$ convolutions into the ETAN module, and get the final output through dense connections.

Figure 1.

Overall architecture of our proposed model. FEM and TIR are our proposed Feature enhancement module model and Multi-dimensional hybrid attention module which is shown in Figure 3 and Figure 4.

We will introduce each part in detail in the following parts.

Edge feature extraction module

The Sobel operator is a classic discrete differential operator widely used in edge detection.³⁶ This operator cleverly combines the principles of Gaussian smoothing and differential derivation, it smoothes the image to some extent before detecting edges during differential derivation. Gaussian smoothing is a technique for reducing image noise and detail, while differential derivatives are used to calculate the rate of change of image brightness, which is the edge. Therefore, it has been effectively used in various image processing practices.

In this process, we used the trainable Sobel operator, as shown in Figure 2. The Sobel operator we set has four directions including 0°, 45°, 90° and 135°. The Sobel trainable factor is denoted as α, which can be adjusted adaptively during the training process. The general form of the Sobel operator can be expressed as:

S_{θ} = α \cdot S_{f i x r d} + (1 - α) \cdot S_{l e a r n a b l e}

Figure 2.

Four different Sobel convolution operations.

Where $S_{f i x r d}$ is the traditional Sobel core, $S_{l e a r n a b l e}$ is the kernel learned by the network during training.

By introducing the trainable Sobel operator, our network can adaptively adjust the edge detection process to make it more suitable for specific image features. For example, for some data sets, edges may be blurrier or contain more noise, in these cases, trainable operators can better extract useful edge information by optimizing α values. This not only improves the accuracy of edge detection, but also preserves the detected edge information during the subsequent image reconstruction process.

ETAN module

The ETAN module consists of two parts, one is the FEM and the other is the multi-dimensional hybrid attention module (TIR). The FEM module is responsible for improving the local details of the image, while the TIR focuses on establishing effective connections between different feature dimensions to promote information exchange between features. Through this combined application, the ETAN module can significantly improve the model's understanding and utilization of image features, thereby optimizing the overall performance of the model.

Feature enhancement module

In modern deep learning architectures, feature extraction and enhancement are key steps in achieving high-performance visual recognition tasks. The FEM aims to enhance the representational capability of features by capturing multi-scale contextual information, thereby improving the model's understanding of features. The proposed FEM module, as shown in Figure 3, is a lightweight network component that can integrate feature information under different receptive fields through parallel multi-scale convolution kernels. Specifically, three different convolutional kernels including $1 \times 1$ , $3 \times 3$ , and $5 \times 5$ are operated on the input respectively to cover different ranges of receptive fields. The $1 \times 1$ kernel is responsible for refining fine local features, while the $3 \times 3$ and $5 \times 5$ kernels capture medium and large spatial features, respectively. The combination of sizes allows the FEM to comprehensively consider the diversity and richness of features. After each convolution operation, the ReLU activation function follows immediately, aiming to introduce non-linear characteristics to enhance the model's ability to recognize and distinguish features. Finally, by integrating the outputs of each scale convolution layer through an element-wise addition, the FEM module produces an enhanced feature map that integrates multi-scale information, laying a solid feature foundation for downstream visual tasks. Furthermore, the design of the FEM module fully considers compatibility with existing network architectures, allowing it to be easily embedded into various CNNs, whether as an independent feature enhancement layer or as part of an end-to-end training.

Figure 3.

Feature enhancement module network structure.

Multi-dimensional hybrid attention module

CNN architectures with increasing depth have achieved significant success in many computer vision tasks. Many recent works have proposed the use of channel attention, spatial attention, or CBAM. CBAM is implemented by integrating two sub-modules, channel attention and spatial attention, which can effectively capture global information, thereby guiding the network to pay more attention to useful features. However, this serial processing may limit the model's ability to capture complex interactions between channels and spatial dimensions. In this paper, we use the TIR, as shown in Figure 4. It can be seen that TIR operates in three dimensions including simultaneously, allows the model to more fully understand the interdependencies between different features and may be more suitable for capturing more complex patterns.

Figure 4.

Three-dimensional interactive attention module.

Specifically, the TIR module consists of three parallel branches. From top to bottom, the first and the second branches are responsible for capturing cross-dimensional interactions between the channel dimension and other two dimensions H and W. The Third branch is similar to CBAM，which is used to construct spatial attention. Finally, the outputs of the three branches are aggregated by performing an averaging operation. The output of the TIR module not only combines cross-dimensional information but also integrates triplet information, improving the ability to acquire complex features effectively. At the same time, three-dimensional attention provides a more flexible way to capture the interaction between features by rotating and operating different dimensions of the input tensor, which may provide better adaptability when processing different types of data.

The Z-Pool operation performs max pooling and average pooling on each $(H \times W)$ two-dimensional plane of the original tensor, and then stacks the two results. Since max pooling and average pooling each produce a $(H \times W)$ feature map, the final output tensor shape is $(2 \times H \times W)$ . This design enables this layer to reduce the depth of the tensor while maintaining its original rich representation, thereby reducing the complexity of subsequent calculations. Mathematically, it can be expressed by the following equation:

z - p o o l (χ) = [{M a x p o o l}_{0 d} (χ), {A v g p o o l}_{0 d} (χ)]

(3)

where 0d is the 0th dimension where max pooling and average pooling operations occur, here is the channel dimension C. For example, the Z-pool of a tensor of shape

(C \times H \times W)

produces a tensor of shape

(2 \times H \times W)

Under our framework, triplet attention is defined as a module with three branches, which receives input tensors and outputs refined tensors of the same shape. For a given input tensor $χ \in R^{C \times H \times W}$ , it is first passed to the three branches of the triple attention module respectively.

In the first branch, in order to establish an interaction between the height dimension ( $H$ ) and the channel dimension ( $C$ ), the input tensor $χ$ is rotated 90° counterclockwise along the H axis to obtain the rotation tensor ${\hat{χ}}_{1}$ , whose shape becomes $(W \times H \times C)$ . This rotation tensor ${\hat{χ}}_{1}$ is then fed into the Z-pooling layer and is reduced to ${\hat{χ}}_{1} *$ of shape $(2 \times H \times C)$ . Then ${\hat{χ}}_{1} *$ goes through a standard convolutional layer with kernel size $k \times k$ and a batch normalization layer, producing an intermediate output of dimension $(1 \times H \times C)$ . The final attention weights are then generated through the sigmoid activation function ( $σ$ ). The resulting attention weights are applied to ${\hat{χ}}_{1}$ , and subsequently rotated 90° clockwise along the H-axis to restore the original input shape of $χ$ .

The operations in the second branch is similar to the first branch. The difference between them is that the counterclockwise and clockwise rotation operations are performed along the W-axis instead of the H-axis.

For the last branch, the channel dimension of the input tensor is reduced to two by Z-pool. Next, the reduced tensor ${\hat{x}}_{3}$ of shape $(2 \times H \times W)$ passes through a standard convolutional layer defined by the kernel size $k \times k$ and the batch normalization layer. Afterwards, attention weights of shape $(1 \times H \times W)$ are generated through the sigmoid activation layer ( $σ$ ) and then applied to the original input $χ$ .

Finally, the three branches are aggregated by simple averaging to complete the output of the triplet attention module.

To sum up, for the input tensor $χ \in R^{C \times H \times W}$ , the process of obtaining the refined attention application tensor from triple attention can be expressed by the following equation:

y = \frac{1}{3} (\bar{{\hat{χ}}_{1} ω_{1}} + \bar{{\hat{χ}}_{2} ω_{2}} + χ ω_{3}) = \frac{1}{3} (\bar{y_{1}} + \bar{y_{2}} + y_{3})

(4)

where

ω_{1}

ω_{2}

and

ω_{3}

are the three cross-dimensional attention weights calculated in triple attention.

\bar{y_{1}}

and

\bar{y_{2}}

in the formula represent a 90° clockwise rotation to retain the original input shape

(C \times H \times W)

Densely connected networks

Compared to traditional CNN,³⁷ which usually have a single connection between a layer and its neighbors, DenseNet adopts an innovative dense connectivity strategy. In this strategy, each layer of the network receives concatenated information from the outputs of all preceding layers as input, significantly enhancing the flow of information within the network and ensuring the efficiency and continuity of feature transmission.³⁸ In order to keep the spatial dimensions of the feature map unchanged during the transfer, we padded the feature map appropriately. Furthermore, to facilitate rapid convergence of the model, we have adopted a strategy that allows the model to directly learn the distribution characteristics of noise.³⁹ In the last denoising step, the output of the last convolutional block is subtracted from the original input image to obtain the denoised image. This residual learning framework not only simplifies the learning process but also improves denoising performance because it allows the network to focus on noise patterns rather than the overall image structure.⁴⁰ Through this dense connection operator, feature reuse is greatly enhanced and the network training efficiency is improved obviously.

Loss function

MSE is a commonly used performance measure in regression analysis. Mathematically, MSE can be expressed as the average of the sum of squared prediction errors over all data points. Specifically, given a data set, MSE can be calculated by the following formula:

L_{m s e} = \frac{1}{N} \sum_{i = 1}^{N} ∥ F (χ_{i}, θ) - y_{i} ∥^{2}

(5)

where

χ_{i}

are the pixels of the input image,

y_{i}

are the pixels of the target image, and N is the total number of pixels in

χ_{i}

. However, MSE tends to evaluate the independent errors between pixels without considering the correlation between pixels, which may cause the model to lose the details and texture information of the image while denoising. In other words, MSE optimization may lead to overly smooth denoising results, causing the image to lose its natural visual texture.

TVloss originates from total variation denoising in image processing, whose basic idea is to remove noise by reducing the total variation of the image. However, TVloss contains both horizontal and vertical gradient information, which means that the edge information of the denoised images is taken into account during the denoising process. From this perspective, TVloss can preserve important details including edge information while denoising, supplementing the shortcomings of MSE loss. TVLoss is a regularization term. It reduces noise by penalizing high-frequency changes in the image, but relative to MSE, it is better at preserving the edges and texture structure of the image. By combining TVLoss with MSE, not only is the error between pixels minimized, but the visual quality of the image is also promoted. Its expression is as follows:

L_{T V} = \sum_{i = 1}^{M} \sum_{j = 1}^{N} {(x_{i, j} - x_{i + 1, j})}^{2} + {(x_{i, j} - x_{i, j + 1})}^{2}

(6)

where

x_{i, j}

represents the pixel value at the

i^{t h}

row and

j^{t h}

column of the image, and the summation ranges over all pixels in the image domain such that

1 \leq x \leq M

and

1 \leq j \leq N

To sum up, our total loss function is

L_{l o s s} = L_{m s e} + λ L_{T V}

(7)

In this study, we set to 0.0005, which is selected through cross-validation experiments to achieve the best denoising effect.

Experiments and results

Experimental data

The dataset of the 2016 NIH AAPM-Mayo Clinic Low-Dose CT Grand Challenge is the most used one for various experiments in the field of LDCT image denoising. In the paper, the abdomen, head and chest datasets are used for our experiments. They contain paired NDCT images, quarter-dose CT images and a one-tenth dose of CT images collected from 10 patients, with dimensions of $512 \times 512$ pixels. The CT image window width/window position: 300/40. The LDCT images are the inputs of the network and the NDCT images are the targets used for supervising the training process. The dataset is divided to two parts, images from 9 patients are used for training the network and the remaining ones are for testing.

Experimental setup

The running environment of our experiments is Pytorch 1.11, Windows 10, CUDA11.3, and NVIDA GeForce RTX 3080GPU.

The flexibility of this framework allows us to initialize the convolutional layers of the model with default random weights and initialize the weights of the Sobel operators in all edge extraction modules to 1. The parameter $λ$ in formula (6) is set to 0.0005 to promote image smoothness and reduce noise. In the training process, the Adam optimizer is used. The learning rate is set to 1e-5, batch-size is set to $16 \times 16$ , and the training epochs is set to 200. When testing the model, use the $64 \times 64$ LDCT images as the input and directly output the denoising results. This process can improve the model's learning ability and denoising performance.

Experimental results

This section shows the experimental results. Three related algorithms including REDCNN, EDCNN and CTformer are used for comparison. To evaluate the performance of these networks objectively, three commonly used criteria are used, including peak signal-to-noise ratio (PSNR), structural similarity (SSIM) and root mean square error (RMSE). PSNR is the PSNR in dB. The higher the PSNR value, the better the image denoising effect. The higher SSIM value means a higher similarity between the denoised image and the NDCT image. The RMSE value represents the error between the denoised image and the NDCT image. The smaller the RMSE value, the better the quality of the denoised image.

Subjective evaluation

Figure 5 illustrates the processing results of the abdominal LDCT images by using the different methods mentioned above. Figure 5(a1) is the original LDCT image. Figure 5(b1)-(e1) are the results of CTformer, REDCNN, EDCNN and our proposed method, respectively. Figure 5(f1) is the corresponding NDCT image. In order to view the results clearly, a region of interest (ROI) marked with rectangular frame in Figure 5(a1) is selected and enlarged for better observation. The enlarged results are shown in Figure 5(a2)-(f2), respectively. We can see that there is less noise in Figure 5(b2) than in Figure 5(a2), however the denoising effect is not obvious. In Figure 5(c2), we can see that REDCNN has a better denoising effect, but the details and edges are over-smoothed. In Figure 5(d2), edge information is preserved better, but there are residual noise in the denoised result. By contrast, the proposed method performs the best. It can be seen form Figure 5(e) that it not only achieves good denoising effect but also protects rich edge information.

Figure 5.

Denoising results of different models in abdominal images and enlargement of the region of interest (ROI) in the yellow box.

Figure 6 shows the denoising results of head datasets. Figure 6(a1) is the original LDCT image. Figure 6(b1)-(e1) are the results of CTformer, REDCNN, EDCNN and our proposed method, respectively. Figure 6(f1) is the corresponding NDCT image. The enlarged results are shown in Figure 6(a2)-(f2), respectively. From (b2) and (c2), we can see that although Ctformer and REDCNN can remove noise to a certain extent, part of the information is lost. In Figure 6(d2), the denoising effect is improved, but the denoised image are over-smoothed. By contrast, our method in Figure 6(e) achieves the best result, which is the closest to the NDCT image shown in Figure 6(f).

Figure 6.

Denoising results of different models in the head image and enlargement of the region of interest (ROI) in the red rectangle.

Figure 7 shows the denoising results of chest datasets. Figure 7(a1) is the original LDCT image. Figure 7(b1)-(e1) are the results of CTformer, REDCNN, EDCNN and our proposed method, respectively. Figure 7(f1) is the corresponding NDCT image. The enlarged results are shown in Figure 7(a2)-(f2), respectively. From (b2), we can see that CTformer has obvious residual noise. In Figure 7(c2) and (d2), we can see that REDCNN has better denoising effect than EDCNN and although REDCNN can remove noise to a certain extent, part of the information is lost. By contrast, our method in Figure 7(e1) and 7(e2) achieves the best result, which is the closest to the NDCT image shown in Figure 7(f).

Figure 7.

Denoising results of different models in the chest image and enlargement of the region of interest (ROI) in the red rectangle.

In the experiment part, a real dataset, the piglet dataset, is add to verify the generalization and robustness of the proposed method. The objective indicators and subjective results are shown in Table 6 and Figure 8, respectively.

Figure 8.

Denoising results of different models in the piglet image and enlargement of the region of interest (ROI) in the red rectangle.

Figure 8 illustrates the processing results of the piglet LDCT images by using the different methods mentioned above. Figure 8(a1) is the original LDCT image. Figure 8(b)-(e1) are the results of CTformer, REDCNN, EDCNN and our proposed method, respectively. Figure 8(f1) is the corresponding NDCT image. In order to view the results clearly, a region of interest (ROI) marked with rectangular frame in Figure 8(a1) is selected and enlarged for better observation. The enlarged results are shown in Figure 8(a2)-(f2), respectively. We can see that there is less noise in Figure 8(b2) than in Figure 8(a2), however the denoising effect is not obvious. In Figure 8(c2), we can see that REDCNN has a better denoising effect, but the details and edges are over-smoothed. In Figure 8(d2), edge information is preserved better, but there are residual noise in the denoised result. By contrast, the proposed method performs the best. It can be seen form Figure 8(e) that it not only achieves good denoising effect but also protects rich edge information.

Objective evaluation

Table 1, Table 2 and Table 3 show the objective metric values of each model after denoising the abdominal image，the head image and the chest, respectively. The label LDCT in the three Table represents the unprocessed LDCT image. The symbol $↑$ indicates the higher the value is, the better the performance. On the contrary, the symbol $↓$ means the lower the better. It can be seen from the three Table, compared with the other three models, our method obtains the highest value on both PSNR and SSIM indicators, and the minimum value on the MSE indicator.

Table 1.

Comparative results of different algorithms under objective indicators (abdomen).

Methods	PSNR $↑$	SSIM $↑$	MSE $↓$
LDCT	31.4735	0.8650	10.8164
CTformer	33.8608	0.9027	8.1952
REDCNN	34.1800	0.9127	7.7137
EDCNN	34.3856	0.9103	7.5040
Ours	34.8211	0.9131	7.3207

Note. Bold shows the best results for each metric.

Table 2.

Comparative results of different algorithms under objective indicators (head).

Methods	PSNR $↑$	SSIM $↑$	MSE $↓$
LDCT	45.4293	0.9790	2.5898
CTformer	45.9333	0.9839	2.3493
REDCNN	46.3132	0.9876	2.2047
EDCNN	46.9873	0.9889	2.0675
Ours	47.5988	0.9896	1.9524

Note. Bold shows the best results for each metric.

Table 3.

Comparative results of different algorithms under objective indicators (chest).

Methods	PSNR $↑$	SSIM $↑$	MSE $↓$
LDCT	12.2754	0.5835	98.3768
CTformer	16.9417	0.6314	51.7165
REDCNN	18.1487	0.6349	49.3100
EDCNN	18.0632	0.6411	49.7316
Ours	18.3086	0.6551	49.3835

Note. Bold shows the best results for each metric.

Through subjective and objective comparisons, we can clearly find that compared with other methods, the image obtained by our proposed denoising technology is closest to NDCT, showing excellent denoising ability and image recovery quality.

Table 4 show the objective metric values of each model after denoising the piglet image. The label LDCT in the Table represents the unprocessed LDCT image. The symbol $↑$ indicates the higher the value is, the better the performance. On the contrary, the symbol $↓$ means the lower the better. It can be seen from the Table, compared with the other three models, our method obtains the highest value on both PSNR and SSIM indicators, and the minimum value on the MSE indicator.

Table 4.

Comparative results of different algorithms under objective indicators (piglet).

Methods	PSNR $↑$	SSIM $↑$	MSE $↓$
LDCT	25.2487	0.8047	0.0127
CTformer	26.0336	0.8166	0.0116
REDCNN	26.5265	0.8238	0.0108
EDCNN	26.5132	0.8240	0.0109
Ours	26.5349	0.8248	0.0104

Note. Bold shows the best results for each metric.

Ablation studies

In order to explore the influence of each module on the network structure we conducted a step-by-step deconstructive analysis of the model's architecture bellow. For ease of description, we define six abbreviations as follows.

TCNN: A traditional neural network. It is a simplified model which removes the ETAN module and the edge extraction modules from the structure shown in Figure 1 and uses MSE loss to guide network training.

CI: The traditional extraction module which uses the mature Sobel operator with static parameters.

SI: The learnable Sobel edge operators which makes the Sobel operator learnable, allowing image edge extraction in a more dynamic and context-aware manner.

ETAN: The proposed module, which is a combination of FEM and TIR modules.

TCNN + CI: The network constructed by adding the CI module to TCNN.

TCNN + SI: The network constructed by adding the SI module to TCNN.

TCNN + SI + ETAN: The network constructed by adding the SI module and ETAN module to TCNN.

TCNN + SI + ETAN + TVLOSS: The proposed network, which is constructed by adding SI module, ETAN module to TCNN, using MSE loss and TVLOSS functions to guide the network training.

We conducted a comprehensive ablation study to quantitatively analyze the contribution of each proposed module to the denoising performance of our network. Table 5 shows the PSNR, SSIM and RMSE values of the six networks mentioned above. It is evident from the data that the basic TCNN network serves as a baseline, with subsequent additions of individual modules resulting in incremental improvements. It can be seen that the basic network TCNN don’t show significant performance improvement without preprocessing steps. The introduction of the CI module leads to a statistically significant improvement in PSNR and SSIM (p < 0.05, paired t-test), indicating its effectiveness in noise reduction. Furthermore, when integrating our designed trainable Sobel operator, the performance is further improved compared to the traditional Sobel operator. The PSNR increases to 34.4405 dB. In addition, by incorporating the FEM and TIR module, all evaluation metrics are significantly improved. The FEM module alone contributes to an increase in PSNR to 34.6882 dB, which is statistically significant (p < 0.01). The TIR module, when added to the TCNN + SI + FEM configuration, further improves the PSNR to 34.7933 dB and reduces the MSE. These results not only confirm the importance of the ETAN module we proposed but also highlight its central role in enhancing model performance. Finally, by using the mixed loss function combined by MSE loss and TVLoss to guide the network training, the proposed network achieves optimal performance in all of the three metrics. This optimal configuration, TCNN + SI + FEM + TIR + TVLOSS, achieves a PSNR of 34.8519, an SSIM of 0.9130, and the lowest MSE of 7.2949, which are all statistically significant improvements over the baseline TCNN model (p < 0.001). Through step-by-step verification, it can be seen that the modules and mixed loss functions proposed in this article are effective in improving the denoising performance of the network.

Table 5.

Comparison of model structure performance.

Methods	PSNR $↑$	SSIM $↑$	MSE $↓$
LDCT	31.4735	0.8650	10.8164
TCNN	32.8699	0.8897	9.1797
TCNN + CI	34.4405	0.9092	7.6499
TCNN + SI	34.5146	0.9097	7.5840
TCNN + SI + FEM	34.6882	0.9112	7.4327
TCNN + SI + FEM + TIR	34.7933	0.9130	7.3437
TCNN + SI + FEM + TIR + TVLOSS	34.8519	0.9130	7.2949

Note. Bold shows the best results for each metric.

In order to prove the effectiveness of the TIR module we proposed more objectively. we conducted comparative experiments with different attention modules, comparing our module with the channel attention module(CAM), spatial attention module(SAM) and CBAM on three objective indicators: PSNR, SSIM and MSE. The results are shown in the Table 6.

Table 6.

Comparison of different attention modules.

Methods	PSNR $↑$	SSIM $↑$	MSE $↓$
TCNN + SI + FEM + CAM + TVLOSS	34.6418	0.9087	7.4803
TCNN + SI + FEM + SAM + TVLOSS	34.6671	0.9100	7.4507
TCNN + SI + FEM + CBAM + TVLOSS	34.7492	0.9112	7.3809
TCNN + SI + FEM + TIR + TVLOSS	34.8519	0.9130	7.3437

Note. Bold shows the best results for each metric.

As can be seen from the above table, the attention module we proposed achieved optimal values in all three indicators, with PSNR of 34.8519, SSIM of 0.9130, and MSE of 7.3437. It can be seen that the TIR module is valid.

Conclusion

This paper proposes a LDCT image denoising model based on multi-dimensional hybrid attention and composite loss. The proposed model improves the network's LDCT image denoising performance from three aspects. First, the learnable Sobel edge extraction operator is used to obtain richer image edge information, and the utilization of edge feature information is improved through dense connections, which is beneficial to the protection of image edges. Second, we make full use of rotation and anti-rotation operations and use information interaction in different dimensions to propose a multi-dimensional hybrid attention module, which fully integrates channel attention and spatial attention in different dimensions, further improving the attention of the network. Third, taking advantage of the respective advantages of MSE Loss function and TVloss function, the hybrid attention is proposed to guide the network training process, further improving the denoising performance of the network. Through step-by-step ablation experimental research, it is shown that each improvement in the network proposed in this article has a certain contribution to the improvement of network denoising performance. Finally, through comparative experiments with other related algorithms, it can be seen that the algorithm proposed in this article has improved the performance on the three indicators of PSNR, SSIM and MSE.

The range of improvement in the PSNR indicator is (1.267%—10.636%), the range of improvement in the SSIM indicator is (0.341%—5.561%), and the range of decrease in the MSE indicator is (−32.323%—−2.443%). It can be seen that our algorithm is effective.

Footnotes

Ethical approval

Not applicable.

Code availability

The code can be made available on request.

Author contributions

All authors develop the idea and accomplished the manuscript writing and performed the experiments. All authors read and approved the final manuscript.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported in part by the Natural Science Foundation of Shanxi Province under Grant 202203021222015, in part by Practice and Grant 2023SJ011 and the 21st and 22st Innovation and Entrepreneurship Training Programme for Undergraduates at Shanxi University.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data availability statement

The data that support the findings of this study are available from TCIA (The Cancer Imaging Archive) but restrictions apply to the availability of these data, which were used under licence for the current study, and so are not publicly available. Data are however available from the authors upon reasonable request and with permission of TCIA.

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