DW image super-resolution reconstruction method and system, computer equipment and medium

Abstract

The invention provides a DW image super-resolution reconstruction method and system, computer equipment and a medium, and belongs to the technical field of image processing. The method comprises the following steps: in a Q space, calculating the similarity between a target direction and other directions through cosine similarity, and selecting DW image slices with the maximum cosine similarity in N directions to form N adjacent images; extracting features of the images in the target direction and the N adjacent directions by using an RDN network architecture; performing orthogonal projection fusion on the target direction feature and the features of the N adjacent direction images to generate a fusion feature; and through an implicit neural network module, the fusion features and high-resolution image coordinates are combined and mapped into a continuous function, and data fidelity loss, space gradient change loss and structural similarity loss are added by adopting an image-to-image learning mode to reconstruct a super-resolution DW image of any scale. By adopting the method, the super-resolution quality of the DW image can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of image processing, and in particular, to a DW image super-resolution reconstruction method, system, computer device and medium. Background Art

[0002] Diffusion weighted (DW) imaging is a technique for tissue imaging using the Brownian motion of water molecules, and it is currently the only technique that can non-invasively detect the diffusion information of water molecules in living biological tissues. The water molecules in living tissues are subject to restricted diffusion under the influence of nerves, cells and surrounding tissue structures, and the diffusion displacement distribution can reflect the microscopic structure of the tissue. At present, DW images have been widely used in the detection of complex fiber structures such as the brain, myocardium, and liver. The resolution of DW images is usually restricted by various factors. On the one hand, to obtain high-resolution DW images, more precise imaging equipment is required, but this places a great financial burden on patients and hospitals. On the other hand, from the perspective of imaging technology, in order to ensure the accuracy of IVIM parameter mapping and reconstruct other forms of dMRI images such as DTI, it is usually necessary to acquire diffusion weighted images with multiple b-values and multiple motion directions, but this will inevitably increase the acquisition time. However, long-term acquisition will bring many problems, such as motion artifacts. Therefore, the resolution of the acquired images is usually reduced to shorten the acquisition time. Many research methods have been proposed to obtain high-resolution DW images, such as EDSR, RDN, etc. However, current methods for DW image super-resolution reconstruction often only target integers or fixed multiples. For each reconstruction multiple, the model needs to be retrained and saved, which will cause waste of computing resources and storage resources, greatly limiting clinical applications.

[0003] In summary, using the same model to achieve arbitrary spatial scale super-resolution reconstruction of DW images can meet the doctor's need to observe images at different resolutions, and at the same time, reconstruct high-resolution images with richer detail textures to improve the doctor's diagnostic accuracy, which is more in line with the actual clinical applications. Summary of the Invention

[0004] The object of the present invention is to provide a DW image super-resolution reconstruction method, system, computer device and medium. Considering that the spatial structures among multi-directional slices of DW images have a certain similarity due to being from the same position of the brain, and the gray-scale distributions have certain differences due to the influence of different directional gradient fields, the method uses multi-directional projection fusion to enhance feature independence to solve the problem of insufficient ability of INR to represent detailed texture features. At the same time, the point-to-point manner of INR is changed to an image-to-image learning method, and on the basis of data fidelity loss, spatial gradient loss and structural similarity loss are added to constrain the model to learn the spatial information and structural information of the image, so as to reconstruct a high-quality high-resolution picture containing rich texture information.

[0005] To achieve the above object, the present invention provides a DW image super-resolution reconstruction method, including the following steps: Step S1, in the Q space, calculate the similarity between the target direction and the remaining directions through cosine similarity, and select the DW image slices in the directions with the largest cosine similarity to form adjacent images; Step S2, use the RDN network architecture to extract the features of the target direction and the images in N adjacent directions respectively; Step S3, perform orthogonal projection fusion on the features of the target direction and the features of the images in N adjacent directions to generate fused features; Step S4, through an implicit neural network module, combine the fused features with the high-resolution image coordinates, and map the features and coordinates of the image to image pixel values through a multi-layer perceptron. In this way, the discrete image is obtained as a continuous function representation of the image through the multi-layer perceptron, and an image-to-image learning method is adopted, adding data fidelity loss, spatial gradient change loss, and structural similarity loss to reconstruct super-resolution DW images of any scale; In the implicit neural network module, the fused features respectively obtain the frequency and amplitude of the features through a convolutional layer, and after upsampling the frequency information, it is multiplied by the x and y of the two-dimensional coordinates of the input high-resolution image respectively and then added element by element. Then, the scale information of the grid size of the high-resolution image is mapped to the same dimension as the frequency information through a linear layer and added as the phase information of the features. Then, periodic feature information is obtained through the sin and cos activation functions, and finally, it is multiplied by the upsampled amplitude information and then passed through a multi-layer perceptron (continuous function representation) to obtain the reconstructed high-resolution image.

[0006] Preferably, in step S1, the cosine similarity calculation formula is as follows: ;

[0007] where, represents the cosine similarity, represents the three-dimensional coordinate vector of the target direction, represents the coordinate vectors of the remaining directions, represents and the included angle between represents the index of a direction in the Q space, represents the number of all directions in the Q space.

[0008] Preferably, in step S2, the RDN network architecture includes extracting shallow features through two convolutions, and the shallow features are used to extract deep features through 16 RDB blocks, and then through the convolution channel is dimension-reduced, and finally the deep features and shallow features are added together through residual connection to obtain the features of the image.

[0009] Preferably, in step S3, the target direction features are orthogonally projected and fused with the features of N neighboring direction images to generate fused features. The specific operation is as follows: The target direction features are respectively orthogonally projected onto each neighboring direction feature to obtain the projected residual features : ; All the projected residual features are concatenated with the target direction features to generate the fused features: ; wherein, represents the fused features, and N represents the number of neighboring images selected in the Q space.

[0010] Preferably, the resolution of the high-resolution image is 145x174.

[0011] Preferably, the data fidelity loss is as follows: ; wherein, represents the absolute value, represents the network super-resolution reconstructed image, represents the real label image; The structural similarity loss is as follows: ; ; wherein, and respectively represent the images and the image The average value of and respectively represent the variances of the two, represents the covariance of the two, and are constants less than 0.003; represents the structural similarity between the image Pred and the image GT, and the numerical range is from 0 to 1, represents the structural similarity loss between the image Pred and the image GT; Spatial gradient change loss is as follows: ; ; ; ; ; Among them, , respectively represent the Sobel operators in the horizontal and vertical directions, represents the splicing operation, is the splicing result of the prediction image Pred multiplied by the Sobel operator and by sliding, representing the spatial gradient change of the prediction image Pred, is the splicing result of the real image GT multiplied by the Sobel operator and by sliding, representing the spatial gradient change of the real image GT, The total loss is as follows: ; Among them, represents the total loss, , , represent hyperparameters.

[0012] The present invention also provides a DW image super-resolution reconstruction system, including: A multi-directional projection fusion module, which is used to calculate the similarity between the target direction and other directions in the Q space through cosine similarity, select the DW image slices in the N directions with the largest cosine similarity to form an adjacent image, and use the RDN network architecture to extract the features of the target direction and the images in the N adjacent directions respectively; perform orthogonal projection fusion on the target direction features and the features of the images in the N adjacent directions to generate fusion features; An implicit neural network module is used to combine the fused features with the high-resolution image coordinates, map them into a continuous function, and adopt an image-to-image learning method. By adding data fidelity loss, spatial gradient change loss, and structural similarity loss, it reconstructs super-resolution DW images of any scale. A loss calculation module is used to calculate the data fidelity loss, spatial gradient change loss, and structural similarity loss, and optimize the model based on these losses.

[0013] The present invention also provides a computer device, including a memory and a processor. The memory is used to store instructions, and the processor is used to execute the instructions to implement the above-mentioned DW image super-resolution reconstruction method.

[0014] The present invention also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the above-mentioned DW image super-resolution reconstruction method.

[0015] Therefore, the present invention adopts the above-mentioned DW image super-resolution reconstruction method, system, computer device, and medium, and the beneficial technical effects are as follows: (1) The method proposed by the present invention makes full use of the characteristics of DW multi-directionality, fully explores the fact that the spatial structures between slices in different diffusion gradient directions are similar and the gray-scale distributions are different, extracts adjacent direction features and fuses them with the target direction features through projection, thereby enhancing the independence of the target direction characteristic information, and effectively overcoming the problem of lack of characterization of detailed texture features due to poor independence of INR features.

[0016] (2) Through an implicit neural network, a single model is used to perform super-resolution reconstruction of DW images at any spatial scale. At the same time, a new loss constraint model and a new image-to-image learning method are proposed, enabling the model to have the ability to perceive spatial changes and reconstruct detailed structural texture information, thereby improving the quality of the reconstructed images. Description of the Drawings

[0017] Figure 1 Images and gray-scale distributions for the target direction and three different directions; Figure 2 Flowchart of the DW image super-resolution reconstruction method; Figure 3 Implicit neural network module; Figure 4 Implicit neural network learning method diagram; Figure 5 Results of 2.5-fold super-resolution reconstruction; Figure 6 Results of 3.5-fold super-resolution reconstruction; Figure 7 Feasibility of the projection method Figure 8 For the visualization of feature independence; Figure 9 To verify the effectiveness of the loss function and the learning method. Detailed implementation manners

[0018] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0019] Unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs.

[0020] Embodiment 1 The DW image is a 4D image, which has direction information in addition to spatial information. In order to use multi-directional information in the INR framework to assist the spatial structure super-resolution reconstruction of the target direction. Visualize the target direction in the Q space and the slices in three different directions, and statistically analyze the histograms of the gray-level distributions of the target direction in the Q space and the slices in three different directions as Figure 1 . From Figure 1 , it can be obtained that the spatial structures between the multi-directional slices of the DW image have a certain similarity due to being at the same position in the brain, while the gray-level distributions have a certain difference due to the influence of different direction gradients. Therefore, the method proposed by the present invention utilizes the characteristics that the multi-directional slices have similar spatial structures and different gray-level distributions to solve the problem of insufficient representation ability of detailed texture features caused by poor feature independence in implicit neural representation through projection to fuse multi-directional information. In addition, a new image-to-image learning method and a new loss function are used to constrain the INR model to learn the spatial change information and texture information of the DW image, so as to reconstruct high-quality high-resolution pictures.

[0021] As Figure 2 shown, it is a flowchart of the DW image super-resolution reconstruction method. In the Q space, the similarity between the target direction and the other directions is calculated through cosine similarity, and the DW image slices in the directions with the largest cosine similarity are selected to form N adjacent images. The cosine similarity calculation formula is as follows: ;

[0022] Wherein, represents the cosine similarity, represents the three-dimensional coordinate vector of the target direction, represents the coordinate vectors of the other directions, represents and the included angle between them, represents the index of a direction in the Q space, represents the number of all directions in the Q space.

[0023] Step S2: Use the RDN network architecture to extract the features of the target direction and the N-direction images respectively; For each input image, first extract shallow features through two convolutions , and then extract deep features from the shallow features through 16 RDB blocks (residual dense blocks). Through convolution channel dimensionality reduction, and then add the deep features and the shallow features through residual connection to obtain the features of the image . Each RDB consists of 8 convolutions and activation functions, which are combined through dense connection and residual connection. In RDN, to obtain the features of the th convolution layer of the th RDB , it is necessary to combine the features of each previous convolution layer in the th RDB, that is, to features, where is the output feature of the th RDB. To obtain the output of the th RDB, it is necessary to splice the outputs of each convolution layer in the th RDB in the channel dimension. After passing through convolution output, and then adding it to through residual connection to obtain the output feature . Among them, [ ] represents the splicing operation, represents the activation function, represents that a total of convolutions are in one RDB. Similarly, the final image features of RDN can be obtained, represents a total of D RDB blocks.

[0024] ; ; ; Step S3: Perform orthogonal projection fusion on the target direction feature and the N adjacent direction image features to generate a fusion feature.

[0025] Project the target direction feature orthogonally onto each adjacent direction feature respectively to obtain the projection residual feature : ; Splice all the projection residual features with the target direction feature to generate a fusion feature: ; Among them, represents the fused feature, and N is the number of selected neighboring directions.

[0026] Step S4: Through the implicit neural network module, combine the fused feature with the high-resolution image coordinates, map the features and coordinates of the image to image pixel values through a multi-layer perceptron, obtain a continuous function representation of the image, and adopt an image-to-image learning method to add spatial gradient change loss and structural similarity loss to reconstruct super-resolution DW images of any scale.

[0027] The implicit neural network module will use the feature representation enriched by the feature projection fusion module to combine with the HR coordinates to realize the mapping from features and coordinates to pixel values. This process can represent the discrete 2D image as a continuous function as follows: ; Among them, is the pixel value, is the feature, is the coordinate, is the network parameter.

[0028] The specific network architecture is as Figure 3 , and the frequency and amplitude of the features are extracted through a convolutional layer respectively. After upsampling the frequency information, it is multiplied by the and components of the two-dimensional coordinates of the input original high-resolution image respectively, and element-wise addition is performed. This way of adding coordinates can obtain a better coordinate feature representation. Then, the scale information of the grid size of the original high-resolution image is mapped to the same dimension as the frequency information through a linear layer (Linear) and added as the phase information (Phase) of the feature. Next, use the sin and cos activation functions to obtain periodic change features that can represent high-frequency information. Finally, multiply these features by the upsampled amplitude information and output the reconstructed high-resolution image through a four-layer multi-layer perceptron (MLP) ( Pred ).

[0029] The sampling strategy adopted by traditional INR has limitations when learning image representations. As Figure 4 shown on the left, by sampling pixel values in the high-resolution (HR) space as the supervision signal to constrain the model to learn the mapping relationship between features and coordinates. However, this point-to-point learning method makes it difficult for the model to capture the texture information and spatial gradient changes of the image, resulting in insufficient details and excessive smoothness in the reconstructed image. To solve this problem, the present invention proposes an image-to-image learning method, asFigure 4 As shown on the right. High-resolution images are generated through network learning, and a spatial gradient change loss and a structural similarity loss are introduced to constrain the model learning process, enabling the model to learn the spatial change information and detailed texture information of the images. Through this new loss function and learning method, the model can reconstruct more realistic and detailed high-resolution images. The new loss function is as follows: ; Data fidelity loss is as follows: ; where denotes the absolute value, denotes the super-resolution reconstructed image by the network, denotes the real label image; Structural similarity loss is as follows: ; ; where and respectively denote the averages of images and image , and respectively denote the variances of the two, denotes the covariance of the two, and are constants less than 0.003; denotes the structural similarity between image Pred and image GT, with a numerical range from 0 to 1, denotes the structural similarity loss between image Pred and image GT; Spatial gradient change loss is as follows: ; ; ; ; ; where , respectively denote the Sobel operators in the horizontal and vertical directions, denotes the concatenation operation, is the concatenation result of the predicted image Pred multiplied by the Sobel operators and by sliding, representing the spatial gradient change of the predicted image Pred, For the real image GT and the Sobel operator respectively and The splicing result of sliding multiplication represents the spatial gradient change of the real image GT.

[0030] The following is a further illustration of the present invention through specific examples.

[0031] Experiments were carried out on the HCP dataset. The original image was downsampled at multiple scales to reduce the resolution and then super-resolution reconstructed back to the original resolution, and the PSNR (Peak Signal to Noise Ratio) and SSIM (Structural Similarity Index) metrics were calculated. Compared with 7 comparison methods, the optimal reconstruction results were obtained. At the same time, the Var of PSNR on the test data was calculated to verify the stability of the validation data. The calculation method of SSIM is the same as the above-mentioned SSIM calculation method, the difference is that a square Gaussian kernel with hard-coded parameters and an explicit data range input are used when calculating the loss, and the output is a tensor format compatible with automatic differentiation. The circular Gaussian kernel and dynamic range estimation are used to evaluate the image quality, and a scalar result is directly returned. In addition, the resolutions (58x69) and (41x49) after downsampling by 2.5 times and 3.5 times were also visualized, and the super-resolution reconstruction back to the original resolution (145x174) using the method of the present invention was compared with 7 comparison methods, and the method of the present invention obtained the optimal reconstruction result.

[0032] The calculation formulas of PSNR and Var are as follows: ; ; Where represent the network-reconstructed image and the real image respectively, and H and W represent the height and width of the image. , represent the pixel values of the reconstructed image and the real image in the m-th row and the -th column. represents the maximum pixel value in the image Pred, is the mean square error between the image Pred and the image GT. Var represents the variance of PSNR, represents the PSNR of the l-th image in the test set, represents the mean value of PSNR of all test images, The smaller it is, the better the data stability.

[0033] As shown in Table 1, the quantitative index results of the reconstructions of different methods are shown. All results are for b value The super-resolution reconstruction results under [conditions]. In-Scale in the table represents the super-resolution scale contained in the training model, and Out-of-Scale represents the super-resolution scale beyond the training range. In addition, the dataset of the present invention is the HCP dataset denoised by patch2self. It can be seen from the table that the method of the present invention has better PSNR and SSIM at any scale than the comparative method, and at the same time the variance does not increase, and the data stability is good. In addition, as the super-resolution scale increases, the PSNR and SSIM of the present invention are improved more compared to the best comparative method LTE, and the method of the present invention has a better reconstruction effect for larger scales.

[0034] Table 1 PSNR and SSIM of the reconstruction results of each method ;

[0035] Figure 5 , Figure 6 are the super-resolution reconstruction results of 2.5 times and 3.5 times respectively. The first row of the pictures respectively contains the real HR picture (GT) and the pictures reconstructed by the method of the present invention and other 7 comparative methods. The comparative methods are ARSSR, OPESR, CLIT, LIIF, ITSRN, GAUSR, LTE. The second and fourth rows of the pictures are the enlarged areas in red and blue in the first row respectively. The first column of the third and fifth rows is the downsampled low-resolution image, and the remaining columns are the residual maps of the enlarged areas in red and blue and the enlarged areas of the true labels. The lighter the color of the residual map, the better the reconstruction effect. From Figure 5 the results of the 2.5 super-resolution reconstruction, it can be seen that the method of the present invention is better than other comparative methods in the detailed texture area, and the residual map does not show the structural texture, proving that the reconstruction result is closer to the real GT image. Figure 6 From the 3.5 times super-resolution reconstruction results, it can be seen that the results reconstructed by the method of the present invention are significantly better than other methods in the detailed texture reconstruction, and the edge structure of the texture is closer to the real (GT) image. At the same time, the residual map also shows that the reconstruction of the texture area is significantly better than other comparative methods. Comparing the results of the 2.5 times and 3.5 times super-resolution reconstructions, it can be seen that the method of the present invention has a better reconstruction effect at large scales, that is, it can reconstruct pictures closer to the real image when lacking more image information, and reconstruct more real and more detailed textures.

[0036] To verify the feasibility of the projection fusion of the method of the present invention, project Figure 7 the second feature A in [reference] onto the first feature B, and the projected feature obtained is the projected feature map of the third picture. Subtract the second picture from the third picture to obtain the fourth projected residual feature map after projection subtraction. It can be concluded that projection subtraction can indeed enhance feature independence and remove the influence of irrelevant features. The visualization of feature independence is as shown in Figure 8, in the present invention, any point in the images downsampled by 2.0 times and 3.5 times is selected, and the feature similarity of the selected point and the eight surrounding points is calculated. Among them, the first image is the position of the selected point, the second image is the cosine similarity between the selected point and the eight surrounding points in the original features without projection fusion, and the third image is the cosine similarity between the selected point and the eight surrounding points in the features after projection fusion. From the comparison of the second and third images, it can be obtained that the feature similarity between the selected point and the surrounding points is reduced, thereby enhancing the feature independence of the point. The enhancement of feature independence can solve the problem of insufficient ability to represent texture information caused by poor feature independence of INR features.

[0037] To verify the effectiveness of adding losses and image-to-image learning in the method of the present invention, new learning methods and new loss reconstruction results are added to the baseline model respectively as Figure 9 , the first row of the picture is the ground truth image GT and the reconstructed high-score image using the new learning method and new loss. The second and third rows are the enlarged red areas and the residual maps of the enlarged red areas in the first row respectively, and the fourth row is the residual map of the whole image. The blue numbers above represent the mean residual error, and the smaller the better. The results show that the proposed losses and learning methods achieve the best performance in the detailed texture area, the PSNR and SSIM metrics reach the highest, and the overall mean error reaches the minimum, proving that the losses proposed in the present invention and the image-to-image learning method using the de-sampling strategy can solve the problem that the original method cannot learn image texture and spatial information, so that the model has the ability to perceive image texture and spatial information.

[0038] Embodiment 2 A DW image super-resolution reconstruction system, comprising: A multi-directional projection fusion module, which is used to calculate the similarity between the target direction and other directions in the Q space through cosine similarity, select the DW image slices in the N directions with the largest cosine similarity to form an adjacent image, and use the RDN network architecture to extract the features of the target direction and the N adjacent direction images respectively; perform orthogonal projection fusion on the target direction features and the features of the N adjacent direction images to generate fusion features; An implicit neural network module, which is used to combine the fusion features with the high-resolution image coordinates, map them into a continuous function, and adopt an image-to-image learning method, adding data fidelity loss, spatial gradient change loss, and structural similarity loss to reconstruct super-resolution DW images of any scale; A loss calculation module, which is used to calculate the data fidelity loss, spatial gradient change loss, and structural similarity loss, and optimize the model based on these losses.

[0039] When the above functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs.

[0040] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a predefined sequence list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by an instruction execution system, apparatus, or device (such as a computer-based system, a system including a processor, or other systems that can fetch and execute instructions from the instruction execution system, apparatus, or device), or in conjunction with these instruction execution systems, apparatus, or devices. For the purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by or in conjunction with an instruction execution system, apparatus, or device.

[0041] More specific examples (non-exhaustive list) of computer-readable media include the following: an electrical connection part with one or more wirings (electronic device), a portable computer disk cartridge (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disc read-only memory (CDROM). Additionally, the computer-readable medium can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, interpretation, or other appropriate processing as necessary, and then stored in a computer memory.

[0042] It should be noted that the content not elaborated in detail in the present invention is all prior art and well-known to those skilled in the art.

[0043] Therefore, the present invention adopts the above-mentioned DW image super-resolution reconstruction method, system, computer device and medium. Since the spatial structure among multi-directional slices of the DW image considered by this method is similar due to the same position in the brain, and the gray-scale distribution has certain differences due to the influence of different directional gradient fields, the method uses multi-directional projection fusion to enhance feature independence to solve the problem of insufficient ability of INR to represent detailed texture features. At the same time, the point-to-point modification of INR is changed to an image-to-image learning method, and the spatial gradient loss and structural similarity loss are used to constrain the model to learn the spatial information and structural information of the image, so as to reconstruct a high-quality high-resolution picture containing rich texture information.

[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A DW image super-resolution reconstruction method, characterized in that, It includes the following steps: Step S1. In the Q space, calculate the similarity between the target direction and the remaining directions by cosine similarity, and select the DW image slices in the directions with the largest cosine similarity to form adjacent images; Step S2: Use the RDN network architecture to extract the features of the target direction and the images in N neighboring directions respectively; Step S3: Perform orthogonal projection fusion on the target direction feature and the features of the N neighboring direction images to generate a fused feature; Step S4: Through the implicit neural network module, combine the fused feature with the high-resolution image coordinates, map the features and coordinates of the image to image pixel values through a multi-layer perceptron to obtain a continuous function representation of the image, and adopt an image-to-image learning method, adding data fidelity loss, spatial gradient change loss, and structural similarity loss to reconstruct the super-resolution DW image at any scale; In the implicit neural network module, the fused features obtain the frequency and amplitude of the features through a convolutional layer respectively. After upsampling the frequency information, it is multiplied by the x and y of the two-dimensional coordinates of the input high-resolution image and then added element by element. Then, the scale information of the grid size of the high-resolution image is mapped to the same dimension as the frequency information through a linear layer and added as the phase information of the features. Then, the periodically varying feature information is obtained through the sin and cos activation functions. Finally, it is multiplied by the upsampled amplitude information and then passed through a multi-layer perceptron to obtain the reconstructed high-resolution image.

2. The method for super-resolution reconstruction of DW images according to claim 1, wherein In Step S1, the cosine similarity calculation formula is as follows: ； Among them, represents the cosine similarity, represents the three-dimensional coordinate vector of the target direction, represents the coordinate vectors of the remaining directions, represents and the included angle between represents the index of a direction in the Q space, represents the number of all directions in the Q space.

3. A DW image super-resolution reconstruction method according to claim 1, characterized in that In step S2, the RDN network architecture includes extracting shallow features through two convolutions. The shallow features are used to extract deep features through 16 RDB blocks, and then the dimensionality of the convolution channels is reduced. Finally, the deep features and shallow features are added together through residual connection to obtain the features of the image.

4. A DW image super-resolution reconstruction method according to claim 1, characterized in that In Step S3, perform orthogonal projection fusion on the target direction feature and the features of the N neighboring direction images to generate a fused feature. The specific operation is as follows: Project the target direction feature onto each adjacent direction feature orthogonally to obtain the projected residual feature : ； Combine all the projection residual features with the target direction features to generate a fused feature: ； Among them, represents the fused feature, and N represents the number of neighboring images selected in the Q space.

5. A method for super-resolution reconstruction of DW images according to claim 1, characterized in that The resolution of the high-resolution image is 145x174.

6. A DW image super-resolution reconstruction method according to claim 1, wherein, Data fidelity loss As follows: ； Among them, represents the absolute value, represents the network super-resolution reconstructed image, represents the real label image; Structural similarity loss As follows: ； ； Among them, and respectively represent the average values of the images and the images ; and respectively represent the variances of the two; represents the covariance of the two; and are constants less than 0.003; represents the structural similarity between the images and the images ; represents the structural similarity loss between the images and the images ; Spatial gradient change loss As follows: ； ； ； ； ； Among them, , respectively represent the Sobel operators in the horizontal and vertical directions, represents the splicing operation, is the predicted image and the Sobel operator and The splicing result of sliding multiplication represents the predicted image spatial gradient change, is the real image and the Sobel operator and The splicing result of sliding multiplication represents the real image spatial gradient change, The total loss is as follows: ； Among them, represents the total loss, , , represent hyperparameters.

7. A DW image super-resolution reconstruction system, characterized in that, It includes: A multi-directional projection fusion module, which is used to calculate the similarity between the target direction and other directions through cosine similarity in the Q space, select the DW image slices in N directions with the largest cosine similarity to form neighboring images, and use the RDN network architecture to extract the features of the target direction and the images in N neighboring directions respectively; perform orthogonal projection fusion on the target direction feature and the features of the N neighboring direction images to generate a fused feature; An implicit neural network module, which is used to combine the fused feature with the high-resolution image coordinates, map them to a continuous function, and adopt an image-to-image learning method, adding data fidelity loss, spatial gradient change loss, and structural similarity loss to reconstruct the super-resolution DW image at any scale; A loss calculation module, which is used to calculate the data fidelity loss, spatial gradient change loss, and structural similarity loss, and optimize the model based on these losses.

8. A computer device, characterized in that, It includes a memory and a processor. The memory is used to store instructions, and the processor is used to execute the instructions to implement the DW image super-resolution reconstruction method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the DW image super-resolution reconstruction method according to any one of claims 1 to 6.

Images