A medical image volume super-resolution method based on hybrid attention and fourier convolution network

Abstract

The application discloses a medical image volume super-resolution method based on a mixed attention and Fourier convolution network, and relates to the technical field of computer vision, and the technical solution points are as follows: by designing an HFPB module and a multi-stage decoder-encoder structure, the network can fully utilize the information between adjacent layers, integrate the global information from the frequency domain, realize multi-scale information aggregation, and fully utilize the information from non-adjacent areas to restore medical details; the HFPB enhances feature extraction by activating more non-local context information, uses overlapping windows for cross attention, better aggregates cross-window information, captures complementary information in different perception fields on different branches, and thus enhances the spatial domain features; the model can well fuse the correlation between local areas and global areas in medical images, enable the network to perceive important information for layer reconstruction, improve the volume resolution of three-dimensional medical images, and thus assist medical diagnosis.

Description

Technical Field

[0001] This invention relates to the field of computer vision technology, and more specifically, to a method for volumetric super-resolution of medical images based on hybrid attention and Fourier convolutional networks. Background Technology

[0002] In modern medicine, magnetic resonance imaging (MRI) and computed tomography (CT) are widely used to acquire a series of two-dimensional image slices from potential lesion areas of a patient, thereby aiding in medical diagnosis. However, obtaining high-resolution medical images with sufficient depth information is challenging in clinical practice due to factors such as patient safety and scanning efficiency. During high-resolution MRI image acquisition, longer scan times are typically required to mitigate motion artifacts caused by patient movement; therefore, sparse sampling is often employed to acquire fewer slices and expedite the image acquisition process. While CT image acquisition is much faster than MRI, the ionizing X-ray radiation used may increase the risk of cancerous cell mutation in patients. Therefore, larger slice thicknesses are generally used to ensure accurate diagnosis, and sparse sampling with large slice thicknesses is employed to reduce the number of scans, thereby minimizing radiation exposure to the patient.

[0003] Volumetric super-resolution of medical images is a key technology for computer-aided surgery and intelligent surgical robots. Its purpose is to improve the resolution in the depth dimension of medical imaging, providing more slice information, enhancing the clarity of 3D models, offering doctors additional pathological details, improving diagnostic accuracy, and reducing the risk of misdiagnosis.

[0004] Uncovering hidden details in medical images through volumetric super-resolution is a highly challenging task. Unlike traditional natural image super-resolution methods, volumetric super-resolution algorithms need to process multiple sequential images simultaneously and learn the most relevant features for image reconstruction. Unlike traditional video interpolation algorithms, the changes between consecutive video frames are generally relatively small, while the changes between consecutive layers in medical images are significant, making the small convolutional methods used in typical video interpolation infeasible. Most volumetric super-resolution works use traditional convolution for reconstruction, resulting in a small receptive field that fails to recover detailed information through the correlation between local semantic features and global features. SAINT proposed a spatially aware interpolation network to synthesize medical slices. This method reconstructs volumetric images with multiple upsampling factors using a single network, but struggles to recover fine details. DAVSR proposed a domain-adaptive volumetric super-resolution network that addresses the volumetric SR problem by performing segmented SR and combining supervised training for feature generation with unsupervised learning for adjusting test sample features, but its network parameters are too large. TVSRN proposed a Transformer-based volumetric super-resolution network that utilizes positional encoding and self-attention mechanisms to predict inter-layer images. However, this method does not establish relevant concerns between different interlayer channels. Summary of the Invention

[0005] The purpose of this invention is to overcome the problem that low-resolution anisotropic medical images cannot provide detailed information to doctors or computer-aided diagnostic algorithms, thus leading to difficulties in medical diagnosis. This invention provides a medical image volumetric super-resolution method based on hybrid attention and Fourier convolutional networks.

[0006] The above-mentioned technical objective of the present invention is achieved through the following technical solution: a medical image volumetric super-resolution method based on hybrid attention and Fourier convolutional networks, the method comprising the following steps:

[0007] S1: Construct a multi-scale image volumetric super-resolution model that includes an encoder, a positional coding block, and a decoder;

[0008] S2: Keep the original input image size unchanged, perform shallow feature extraction on the image through linear mapping, and expand the number of channels;

[0009] S3: The encoder uses hybrid attention and Fourier convolutional perceptual blocks (HFPB) to extract features from the original input image and outputs results at different stages. The scale of the encoder outputs results at each stage is different.

[0010] S4: Reshape the output of the last stage of the encoder, and then insert blank layers based on the number of image layers that need to be expanded. The number of blank layers is the number of complete image sets minus the number of initial input image layers. Then add positional encoding with inter-layer sequence order.

[0011] S5: The feature maps of each stage are concatenated with the output of the encoder at the corresponding scale. The decoder then uses HFPB to enhance the features of the position-encoded result, and then upsamples it through deconvolution. The number of stages in the sub-module of the decoder is the same as the number of stages in the sub-module of the encoder.

[0012] S6: Reconstruct the decoder output using linear projection to form a reconstructed image;

[0013] S7: Optimize network parameters by minimizing L1 pixel loss, and calculate the loss by comparing it with the real image.

[0014] The present invention is further configured such that: in S3, feature enhancement is performed using HFPB in each stage of the encoder, and the specific process of the encoder includes:

[0015] Except for the final stage of the encoder, the HFPB, which fuses local and global features, and the downsampling block are combined as modules for different stages of each encoder; the mathematical expression is:

[0016] (1)

[0017] (2)

[0018] (3)

[0019] (4)

[0020] in, This represents the original features input into HFPB. This represents the characteristics of the encoder generated by HFPB. This indicates the downsampling module.

[0021] The present invention is further configured such that: the HFPB consists of three parts: a window transformation block (WCB), an overlapping cross attention block (OCAB), and a Fourier domain fusion convolutional block (FCB). Feature enhancement is achieved by activating more non-local contextual information on the input feature map through multiple consecutive WCB blocks. The mathematical expression is:

[0022] (5)

[0023] Cross-window information is aggregated by using an OCAB block with overlapping windows for cross-focusing, and complementary information from different receptive fields on different branches is captured using an FCB module, thereby enhancing spatial domain features. The mathematical expression is as follows:

[0024] (6)

[0025] in, This represents the feature map input through the j-th WCB module of the HFPB module in the i-th encoder. Let represent the final output feature map of the HFPB module in the i-th encoder, where , , These represent the j-th WCB module, OCAB module, and FCB module, respectively.

[0026] The present invention is further configured such that: the WCB block consists of two parts, a Swin Transformer Layer (STL) and a ChannelAttention (CA), and the mathematical expression is:

[0027] (7)

[0028] (8)

[0029] (9)

[0030] in, Represents the j-th STL layer of the i-th WCB; This represents the CA module, which represents the i-th branch of the network; To calculate the results of the two layers of self-focus; Channel weight; This represents matrix multiplication.

[0031] The present invention is further configured such that: the OCAB block performs self-focus computation by using overlapping windows and generates key / value pairs larger than the window used for the query, as expressed mathematically as:

[0032] (10)

[0033] Among them, the query matrix Key matrix Sum matrix All calculations are performed using linear mappings in this network. / Calculated using a magnification factor of 1.5.

[0034] The present invention is further configured such that the FCB block consists of two branches: a frequency domain branch and a spatial branch;

[0035] The frequency domain branch consists of three parts: convolution of aggregated information, Fourier transform, and inverse Fourier transform; firstly, the... After shallow feature extraction using a 3x3 convolutional layer, the input is transformed to the frequency domain using Fourier transform. Then, the spectral data is efficiently updated globally. Finally, the data is transformed back to the spatial format using the inverse FFT operation, as shown in the following formula:

[0036] (11)

[0037] in Indicates a convolutional layer. Indicates Fourier transform, Indicates the inverse Fourier transform;

[0038] The spatial branch consists of three parts: a depthwise convolution that aggregates local information, a dilated convolution that captures long-range dependencies, and a channel attention (SE) module. First, local information is extracted using a 3x3 convolution. Then, long-range dependencies are established using a 5x5 depthwise convolution and a 5x5 dilated convolution. Next, the SE module is added for adaptive processing. Finally, the number of channels is adjusted using a 1x1 convolution. The formula is as follows:

[0039] (12)

[0040] in Indicates a convolutional layer. Represents depthwise convolution. This represents depthwise dilated convolution. Indicates a channel attention block;

[0041] Finally, the outputs of the frequency domain branch and the spatial branch are fused, as shown in the following formula:

[0042] (13).

[0043] The present invention is further configured such that, in order for the model to utilize the known sequence order of the three-dimensional medical image layers, the position encoding module in S4 needs to incorporate information about relative or absolute positions. Specifically, the method is as follows:

[0044] By inserting between every two layers Layers are used to create a set of digitally complete images; each blank layer is represented by a learnable tensor indicating the presence of missing patches that need to be reconstructed; then positional encodings are added to all layers to form a complete set of images with a priority positional order; the positional encodings are added to the input images, as shown in the following formula:

[0045] (14)

[0046] In the formula This indicates a position encoding operation. Indicates a connection operation;

[0047] Position codes are calculated using sine and cosine functions of different frequencies:

[0048] (15)

[0049] (16)

[0050] In the formula This represents the location information of each layer, and i represents the dimension.

[0051] The present invention is further configured such that: in S5, each stage decoder merges the output of the previous stage decoder with the output of the corresponding encoder, then uses HFPB for feature enhancement, and uses a deconvolution module for size recovery, as shown in the following formula:

[0052] (17)

[0053] (18)

[0054] (19)

[0055] in, This represents the features after positional encoding. This indicates the characteristics of the decoder enhanced by HFPB. This indicates the deconvolution module.

[0056] The present invention is further configured such that: in step S7, the parameters of the network are optimized by minimizing the L1 pixel loss, and the output is... R D×H×W The L1 pixel loss formula is expressed as:

[0057] (20)

[0058] In summary, the present invention has the following beneficial effects:

[0059] 1. By designing an HFPB module and a multi-stage decoder-encoder structure, this invention enables the network to fully utilize information between adjacent layers, integrate global information from the frequency domain, achieve multi-scale information aggregation, and fully utilize information from non-neighboring domains to recover medical details.

[0060] 2. The HFPB of the present invention enhances feature extraction by activating more non-local contextual information and uses overlapping windows for cross-focusing, which better aggregates cross-window information and enhances spatial domain features by capturing complementary information from different perceptual fields on different branches.

[0061] 3. The model of this invention can effectively integrate the correlation between local and global regions in medical images, enabling the network to perceive important information and reconstruct layers, thereby improving the volumetric resolution of three-dimensional medical images and assisting in medical diagnosis. Attached Figure Description

[0062] Figure 1 This is a flowchart of the medical image volumetric super-resolution method in an embodiment of the present invention;

[0063] Figure 2 This is an overall network structure diagram of the medical image volumetric super-resolution method in this embodiment of the invention;

[0064] Figure 3 This is a schematic diagram of the HFPB module in an embodiment of the present invention;

[0065] Figure 4 This is a schematic diagram of each module in HFPB in an embodiment of the present invention;

[0066] Figure 5 This is a schematic diagram illustrating the effect of the device of the present invention on volumetric super-resolution of medical images. Detailed Implementation

[0067] To enable those skilled in the art to better understand the present invention, the technical solution of the present invention will be described in further detail below with reference to the embodiments and accompanying drawings. Obviously, the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort should fall within the scope of protection of the present invention.

[0068] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the embodiments.

[0069] Example:

[0070] like Figures 1 to 5As shown, a medical image volumetric super-resolution method based on hybrid attention and Fourier convolutional networks includes the following steps:

[0071] S1: Construct a multi-scale image volumetric super-resolution model that includes an encoder, a positional coding block, and a decoder;

[0072] S2: Keep the original input image size unchanged, perform shallow feature extraction on the image through linear mapping, and expand the number of channels;

[0073] S3: The encoder uses hybrid attention and Fourier convolutional perceptual blocks (HFPB) to extract features from the original input image and outputs results at different stages. The scale of the encoder outputs results at each stage is different.

[0074] Feature enhancement is performed using HFPB in each stage of the encoder. The specific encoder process includes:

[0075] The HFPB, which fuses local and global features, and downsampling blocks are combined as modules for different stages of each encoder. Note: The final stage of the encoder does not require downsampling blocks. The mathematical expression is:

[0076] (1)

[0077] (2)

[0078] (3)

[0079] (4)

[0080] in, This represents the original features input into HFPB. This represents the characteristics of the encoder generated by HFPB. This indicates the downsampling module.

[0081] Furthermore, the HFPB consists of three parts: a window transformation block (WCB), an overlapping cross attention block (OCAB), and a Fourier domain fusion convolutional block (FCB). Mathematically, it can be represented as:

[0082] (5)

[0083] (6)

[0084] in, This represents the feature map input through the j-th WCB module of the HFPB module in the i-th encoder. Let represent the final output feature map of the HFPB module in the i-th encoder, where , , Let represent the j-th WCB module, OCAB module, and FCB module, respectively. Equation (23) indicates that feature enhancement is achieved by activating more non-local contextual information on the input feature map through multiple consecutive WCB blocks. Equation (24) indicates that cross-window information is gathered by using an OCAB block with overlapping windows, and complementary information from different receptive fields on different branches is captured by an FCB module, thereby enhancing spatial domain features.

[0085] Furthermore, the WCB block consists of two parts: a Swin Transformer Layer (STL) and a Channel Attention (CA), and its mathematical representation is as follows:

[0086] (7)

[0087] (8)

[0088] (9)

[0089] in, Representing the j-th STL layer of the i-th WCB, due to the sliding window, two consecutive layers are usually designed as a group; This represents the CA module, which represents the i-th branch of the network. In WCB, the result of the self-attention calculation of two layers is... and channel weight Multiply element-wise. Because... and The dimensions don't match, so we need to perform the operation before multiplication. The window is flipped, in which This represents matrix multiplication.

[0090] Furthermore, the OCAB block is similar to STL. It performs self-focused computation using overlapping windows and generates key / value pairs larger than the window used for the query. Its mathematical representation is as follows:

[0091] (10)

[0092] Among them, the query matrix Key matrix Sum matrix It is computed using a linear mapping. In our network, / Calculated using a magnification factor of 1.5.

[0093] Furthermore, the FCB block consists of two branches: a global frequency domain branch operating in the frequency domain, which extracts global information through Fast Fourier Convolution (FFC); and a local spatial branch performing large-kernel convolution on the input feature channels to enhance local feature representation. Different paths can capture complementary information through different receptive fields, and the two paths are ultimately combined for information fusion.

[0094] Specifically, the frequency domain branch consists of three parts: convolution of aggregated information, Fourier transform, and inverse Fourier transform. First, we will... After shallow feature extraction using a 3x3 convolutional layer, the input is transformed to the frequency domain via Fourier transform, converting the original shallow spatial features into the spectral domain. Then, the spectral data is efficiently updated globally. Finally, the data is converted back to its spatial format using an inverse FFT operation. The formula is as follows:

[0095] (11)

[0096] in Indicates a convolutional layer. Indicates Fourier transform, This represents the inverse Fourier transform.

[0097] Specifically, the spatial branch consists of three parts: a depthwise convolution that aggregates local information, a dilated convolution that captures long-range dependencies, and a channel attention (SE) module. First, local information is extracted using 3x3 convolutions. Then, 5x5 depthwise convolutions and 5x5 dilated convolutions are used to establish long-range dependencies. Next, the SE module is added for adaptive processing. Finally, 1x1 convolutions are used to adjust the number of channels. The formula is as follows:

[0098] (12)

[0099] in Indicates a convolutional layer. Represents depthwise convolution. This represents depthwise dilated convolution. This indicates a channel attention block.

[0100] Finally, the outputs of the frequency domain branch and the spatial branch are fused, as shown in the following formula:

[0101] (13)

[0102] S4: Reshape the output of the last stage of the encoder, and then insert blank layers based on the number of image layers that need to be expanded. The number of blank layers is the number of complete image sets minus the number of initial input image layers. Then add positional encoding with inter-layer sequence order.

[0103] In order for the model to utilize the known sequence order of three-dimensional medical image layers, it is necessary to incorporate information about relative or absolute positions.

[0104] By inserting k layers between each pair of layers, a digitally complete set of images is created. It's worth noting that other upsampling rates can be easily adapted by adjusting the value of k. Each blank layer is represented by a learnable tensor indicating the presence of missing patches that need to be reconstructed. Positional encodings are then added to all layers to form a complete set of images with a priority positional order. The positional encodings have the same dimension as the input images, so they can be added together. The mathematical formula is as follows:

[0105] (14)

[0106] In the formula This indicates a position encoding operation. This indicates a join operation.

[0107] In this work, sine and cosine functions of different frequencies are used to calculate position codes:

[0108] (15)

[0109] (16)

[0110] In the formula The position information of each layer is represented by 'i', where 'i' represents the dimension. Each dimension of the position encoding corresponds to a sine wave, with wavelengths forming a geometric series from 2π to 10000·2π. The choice of function makes it easy for the attention mechanism in the deep learning model to notice relative positions.

[0111] S5: The decoder uses the position-encoded result for feature enhancement via HFPB. Note that the feature maps at each stage are concatenated with the encoder's output at the corresponding scale before feature enhancement via the hybrid attention module. Then, upsampling is performed using deconvolution. The number of stages in the decoder's sub-modules is the same as the number of stages in the encoder's sub-modules.

[0112] In each stage of the decoder, the output of the previous stage decoder is combined with the output of the corresponding encoder, then HFPB is used for feature enhancement, and a deconvolution module is used for size recovery. The mathematical formula is as follows:

[0113] (17)

[0114] (18)

[0115] (19)

[0116] in, This represents the features after positional encoding. This indicates the characteristics of the decoder enhanced by HFPB. This indicates the deconvolution module.

[0117] S6: Reconstruct the decoder output using linear projection to form a reconstructed image;

[0118] S7: Optimize network parameters by minimizing L1 pixel loss, and calculate the loss by comparing it with the real image;

[0119] The network parameters are optimized by minimizing the L1 pixel loss, and the output is R D×H×W The L1 pixel loss formula is:

[0120] (20).

[0121] like Figure 2 As shown, this embodiment provides an apparatus for implementing the medical image volumetric super-resolution method of the present invention, specifically including:

[0122] The building unit is configured to construct a multi-scale volumetric super-resolution model that includes an encoder, a positional encoding module, and a decoder.

[0123] The encoder extracts features through the HFPB block and constructs multi-scale images using the downsampling module. The encoding results output by the encoder at each stage have different scales.

[0124] The location encoding module first expands the number of layers in the medical image to the size of the complete set, and then determines the order of different layers by using sine and cosine functions of different frequencies and incorporates them into the model, so that the model can use the location prior information contained in the medical image itself.

[0125] The decoder first merges the output results of the corresponding stages in the stitching encoder, then performs feature enhancement through the HFPB block in the decoder, and gradually restores the size of the image using the deconvolution module;

[0126] The loss is optimized by minimizing the L1 pixel loss.

[0127] This specific embodiment is merely an explanation of the present invention and is not intended to limit the invention. After reading this specification, those skilled in the art can make modifications to this embodiment without contributing any inventive step, but such modifications are protected by patent law as long as they are within the scope of the claims of the present invention.

Claims

1. A medical image volumetric super-resolution method based on hybrid attention and Fourier convolutional networks, characterized by: The method includes the following steps: S1: Construct a multi-scale image volumetric super-resolution model that includes an encoder, a positional coding block, and a decoder; S2: Keep the original input image size unchanged, perform shallow feature extraction on the image through linear mapping, and expand the number of channels; S3: The encoder uses hybrid attention and Fourier convolutional perceptual block (HFPB) to extract features from the original input image and outputs results at different stages. The scale of the encoder outputs results at each stage is different. S4: Reshape the output of the last stage of the encoder, and then insert blank layers based on the number of image layers that need to be expanded. The number of blank layers is the number of complete image sets minus the number of initial input image layers. Then add positional encoding with inter-layer sequence order. S5: The feature maps of each stage are concatenated with the output of the encoder at the corresponding scale. The decoder then uses HFPB to enhance the features of the position-encoded result, and then upsamples it through deconvolution. The number of stages in the sub-module of the decoder is the same as the number of stages in the sub-module of the encoder. The HFPB consists of three parts: a window transformation block (WCB), an overlapping cross attention block (OCAB), and a Fourier domain fusion convolutional block (FCB). It enhances features by activating more non-local contextual information on the input feature map through multiple consecutive WCB blocks. The mathematical expression is: （5） Cross-window information is aggregated by using an OCAB block with overlapping windows for cross-focusing, and complementary information from different receptive fields on different branches is captured using an FCB module, thereby enhancing spatial domain features. The mathematical expression is as follows: （6） in, This represents the feature map input through the j-th WCB module of the HFPB module in the i-th encoder. Let represent the final output feature map of the HFPB module in the i-th encoder, where , , These represent the j-th WCB module, OCAB module, and FCB module, respectively. The WCB block consists of two parts: STL and CA, and its mathematical expression is: （7） （8） （9） in, Represents the j-th STL layer of the i-th WCB; This represents the CA module, which represents the i-th branch of the network; To calculate the results of the two layers of self-focus; Channel weight; Represents matrix multiplication; S6: Reconstruct the decoder output using linear projection to form a reconstructed image; S7: Optimize network parameters by minimizing L1 pixel loss, and calculate the loss by comparing it with the real image.

2. The medical image volumetric super-resolution method based on hybrid attention and Fourier convolutional networks according to claim 1, characterized in that: In S3, feature enhancement is performed using HFPB in each stage of the encoder. The specific process of the encoder includes: Except for the final stage of the encoder, the HFPB, which fuses local and global features, and the downsampling block are combined as modules for different stages of each encoder; the mathematical expression is: （1） （2） （3） （4） in, This represents the original features input into HFPB. This represents the characteristics of the encoder generated by HFPB. This indicates the downsampling module.

3. The medical image volumetric super-resolution method based on hybrid attention and Fourier convolutional networks according to claim 1, characterized in that: The OCAB block performs self-focused computation by using overlapping windows and generates key / value pairs that are larger than the window used for the query, as expressed mathematically: （10） Among them, the query matrix Key matrix Sum matrix All calculations are performed using linear mappings in this network. / Calculated using a magnification factor of 1.

5.

4. The medical image volumetric super-resolution method based on hybrid attention and Fourier convolutional networks according to claim 1, characterized in that: The FCB block consists of two branches: a frequency domain branch and a spatial branch. The frequency domain branch consists of three parts: convolution of aggregated information, Fourier transform, and inverse Fourier transform; firstly, ... After shallow feature extraction using a 3x3 convolutional layer, the input is transformed to the frequency domain using Fourier transform. Then, the spectral data is efficiently updated globally. Finally, the data is transformed back to the spatial format using the inverse FFT operation, as shown in the following formula: （11） in Indicates a convolutional layer. Indicates Fourier transform, Indicates the inverse Fourier transform; The spatial branch consists of three parts: a depthwise convolution that aggregates local information, a dilated convolution that captures long-range dependencies, and a channel attention SE module. First, local information is extracted using a 3x3 convolution. Then, a 5x5 depthwise convolution and a 5x5 dilated convolution are used to establish long-range dependencies. Next, the SE module is added for adaptive processing. Finally, a 1x1 convolution is used to adjust the number of channels. The formula is as follows: （12） in Indicates a convolutional layer. Represents depthwise convolution. This represents depthwise dilated convolution. Indicates a channel attention block; Finally, the outputs of the frequency domain branch and the spatial branch are fused, as shown in the following formula: （13）。 5. The medical image volumetric super-resolution method based on hybrid attention and Fourier convolutional networks according to claim 1, characterized in that: In order for the model to utilize the known sequence order of the three-dimensional medical image layers, the position encoding module in S4 needs to incorporate information about relative or absolute positions. The specific method is as follows: By inserting between every two layers Layers are used to create a set of digitally complete images; each blank layer is represented by a learnable tensor indicating the presence of missing patches that need to be reconstructed; then positional encodings are added to all layers to form a complete set of images with a priority positional order; the positional encodings are added to the input images, as shown in the following formula: （14） In the formula This indicates a position encoding operation. Indicates a connection operation; Position codes are calculated using sine and cosine functions of different frequencies: （15） （16） In the formula This represents the location information of each layer, and i represents the dimension.

6. The medical image volumetric super-resolution method based on hybrid attention and Fourier convolutional networks according to claim 1, characterized in that: In step S5, each stage decoder merges the output of the previous stage decoder with the output of the corresponding encoder, then uses HFPB for feature enhancement, and uses a deconvolution module for size recovery. The formula is as follows: （17） （18） （19） in, This represents the features after positional encoding. This indicates the characteristics of the decoder enhanced by HFPB. This indicates the deconvolution module.

7. The medical image volumetric super-resolution method based on hybrid attention and Fourier convolutional networks according to claim 1, characterized in that: In step S7, the network parameters are optimized by minimizing the L1 pixel loss, and the output is... R D ×H×W The L1 pixel loss formula is expressed as: （20）。

Images