Brain MRI image super-resolution reconstruction method based on second-order propagation and grid connection

Abstract

The invention belongs to the technical field of image processing, and relates to a brain MRI image super-resolution reconstruction method based on second-order propagation and grid connection, and the method comprises the steps: decomposing a brain MRI image into a plurality of low-resolution slices, and extracting the features of the low-resolution slices to obtain a shallow feature map; fusing the shallow-layer feature map with related features of two adjacent continuous low-resolution slices to obtain fused features, aggregating the fused features to obtain representative features, and carrying out channel segmentation on the representative features to obtain spatial features and related features; the related features are propagated among the slices, and the spatial features and the related features of two adjacent continuous representative features are iteratively fused for four times in total to obtain a feature map; according to the method, the feature map is subjected to up-sampling processing, low-resolution slices are subjected to bicubic up-sampling and then added to obtain a high-resolution image, the continuity of an anatomical structure of brain tissue is reflected by using related information between MRI image sequences, and edge textures and structures in slice images can be recovered.

Description

Technical Field

[0001] The invention belongs to the technical field of image processing and relates to a brain MRI image super-resolution reconstruction method based on second-order propagation and grid connection. Background Art

[0002] MRI images can provide doctors with rich pathological information and improve the reliability of diagnosis. It can highlight the details of different tissues through multi-directional and multi-parameter imaging, and has high resolution for human brain structures and soft tissues, which can show subtle lesions that cannot be distinguished by the human eye. However, due to the limitations of imaging equipment, imaging technology and external interference, the quality of MRI images obtained cannot meet the higher requirements of high-definition images, details are lost and texture features are not obvious. Super-resolution (SR) reconstruction (WANG Z, CHEN J, HOI SC H. Deep Learning for Image Super-resolution: A Survey[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2021, 43(10): 3365-3387.) is a post-processing method that can reconstruct low-quality images into high-resolution images, accurately locate lesion targets, and describe detailed information. Super-resolution reconstruction has many applications in medicine, and high-quality images are also an important basis for doctors to judge the state of the disease. Therefore, studying the super-resolution of MRI images has important scientific significance for precision medicine and promoting the development of human medicine.

[0003] Medical image super-resolution refers to restoring low-resolution medical images from various medical imaging devices into high-resolution medical images with rich details and clear textures, which is helpful for clinical diagnosis and medical research. MRI images have rich prior information, which provides an ideal application environment for super-resolution reconstruction. Researchers can propose different super-resolution reconstruction algorithms based on different prior knowledge and theories. Based on the superior performance of super-resolution algorithms, SR reconstruction has been applied to the field of medical imaging by researchers in the field of computer vision. PELED et al. (PELED S, YESHURUN Y. Superresolution in MRI-perhaps sometimes[J]. Magnetic Resonance in Medicine, 2002,48(2): 409-409.) first applied super-resolution algorithms to the reconstruction of MRI images to improve the detail information of MRI images. DOWSEY et al. (DOWSEY AW, KEEGAN J, LEROTIC M, et al. Motion-compensated MRvalve imaging with COMB tag tracking and super-resolution enhancement[J].Medical Image Analysis, 2007, 11(5): 478-491.) proposed a motion-compensated adaptive imaging method for MRI valve imaging, which can achieve clear 3DMRI reconstruction and visualization. SHI et al. (SHI F, CHENG J, WANGL, et al. LRTV: MR image super-resolution with low-rank and total variation regularizations[J]. IEEE transactions on medical imaging, 2015, 34(12): 2459-2466.) proposed an MRI image super-resolution method based on low-rank matrix complementarity, which effectively restored the edge texture of the image.SHI et al. (SHI J, LI Z, YING S, et al. MR image super-resolution via wideresidual networks with fixed skip connection[J]. IEEE journal of biomedicaland health informatics, 2019, 23(3): 1129-1140.) used a wide residual network combined with a skip connection strategy to alleviate the feature reuse degradation and reduction problems in deep CNN. ZHANG et al. (ZHANG Y, LI K, LI K, etal. MR Image Super-Resolution with Squeeze and Excitation Reasoning Attention Network[C] / / Proceedings of the IEEE Conference in Computer Vision and Pattern Recognition(CVPR). 2021: 13420-13429.) proposed a compressed stimulus reasoning attention network (SERAN) and used attention vectors to achieve accurate detail and texture reconstruction of MRI images. ZHAO et al. (ZHAO X, ZHANG Y, ZHANG T, et al. Channel Splitting Network for Single MR image Super-Resolution[J]. IEEE Transactions on Image Processing, 2019, 28(11): 5649-5662.) proposed a channel segmentation network (CSN) to improve the quality of MRI super-resolution images by adopting hierarchical features processed in different ways. LI et al. (LI Z, YU J, WANG Y, et al. DeepVolume: Brain Structureand Spatial Connection-Aware Network for Brain MRI Super-Resolution[J]. IEEE Transactions on Cybernetics, 2021, 51(7): 3441-3454.) introduced DeepVolume to improve the network reconstruction accuracy by embedding a recursive convolutional network in a convolutional long short-term memory block.Feng et al. (Feng C, Fu H, Yuan S, et al. Multi-contrast MRI Super-Resolution via a Multi-stage Integration Network[C] / / Proceedings of the Medical Image Computing and Computer Assisted Intervention (MICCAI). 2021: 410-420.) proposed a multi-stage integration network to guide image super-resolution by explicitly modeling the dependencies between multi-contrast images at different stages. Feng et al. (Feng C, Wang K, Lu S, et al. Brain MRI super-resolution using coupled-projection residual network[J]. Neurocomputing, 2021, 456: 190-199.) proposed a coupled-projection residual network, which effectively improved the super-resolution of MRI images by associating information from deep and shallow networks and strengthening feature propagation. DONG et al. (DONG S, HANGEL G, BOGNER W, et al. Multi-scale Super-Resolution Magnetic Resonance Spectroscopic Imaging with Adjustable Sharpness[C] / / Proceedings of the Medical Image Computing and Computer Assisted Intervention (MICCAI). 2022: 410-420.) used a filter scaling strategy to solve the multi-scale super-resolution problem, which modulates the convolution filter according to the magnification factor.GEORGESCU et al. (GEORGESCUM I, IONESCU RT, MIRON AI, et al. Multimodal Multi-Head ConvolutionalAttention with Various Kernel Sizes for Medical Image Super-Resolution[C] / / Proceedings of the IEEE / CVF Winter Conference on Application of Computer Vision (WACV) .2023: 2195-2205.) proposed a multi-head convolutional attention module to capture information between MRI images of different modes. CHEN et al. (CHEN Y, SHI F, CHRISTODOULOU AG, et al. Efficient and accurate MRI superresolution using a generative adversarial network and 3D multilevel densely connected network [C] / / Proceedings of the Medical Image Computing and Computer Assisted Intervention (MICCAI). 2018: 9199.) proposed a multi-level densely connected super-resolution network as the generator of GAN, and optimized the network through adversarial training to solve the high computational and memory requirements of 3D CNN models. LIU et al. (LIU C, WU X, YU X, et al. Fusing multi-scale information in convolution network for MR image super-resolution reconstruction [J]. Biomedical engineering online, 2018, 17(1): 114.) proposed a multi-scale fusion convolutional network, which contains multiple multi-scale fusion units (MFUs), each of which corresponds to an estimate obtained using a specific scale filter. MFU helps to reconstruct super-resolution images with different scale features.PHAM et al. (PHAM CH, DUCOURNAU A, FABLET R, et al. Brain MRI super-resolution using deep 3D convolutional networks[C] / / Proceedings of the International Symposium on Biomedical Imaging. 2017: 197-200.) tried to use the SRCNN framework to perform SR on 3D MRI brain images. The results showed that SRCNN 3D always outperformed SRCNN 2D. PARK et al. (PARK S, GAHM K. Super-Resolution of 3D Brain MRI With Filter Learning Using Tensor Feature Clustering [J]. IEEE Access, 2022, 10: 4957-4968.) proposed a cost-effective 3D super-resolution method. To address the boundary problem in MRI data, a tensor using 3D gradient information was introduced for processing. By utilizing the shape of the tensor and the directional features extracted from it, a clustering model is designed to create labels, and filters are trained by collecting similar blocks of each label, and a method of incorporating changes in the direction of the tensor to reduce the block range is proposed to learn fine block features. SANCHEZ et al. (SANCHEZ I, VILAPLANA V. Brain MRI super-resolution using 3D generative adversarial networks[C] / / Proceedings of theInternational conference on Medical Imaging with Deep Learning. 2018: 1-8.) performed super-resolution reconstruction of 3D brain MRI images in the SRGAN framework, using 3D convolution to better utilize the structural information in the three-dimensional image. Adversarial loss is used in the generator loss to create more realistic samples, and content loss is used to reduce the difference between real images and generated images.YOU et al. (YOU S, LEI B, WANG S, et al. Fineperceptive GANs for brain MR image super-resolution in wavelet domain [J]. IEEE transactions on neural networks and learning systems, 2022: 1-13.) proposed fine-perceptual generative adversarial networks (FP-GANs) to solve the problem of detail insensitivity in super-resolution models. FP-GANs divides MRI images into low-frequency global approximation and high-frequency anatomical texture in the wavelet domain. Then, each sub-band generative adversarial network handles the super-resolution process of each individual sub-band image. At the same time, sub-band attention is applied to adjust the attention between global and texture information, which can focus on sub-band images instead of feature maps to enhance the anatomical reconstruction ability of FP-GANs. FANG et al. (FANG C, ZHANG D, WANG L, et al. Cross-modality high-frequency transformer for MR image super-resolution[C] / / Proceedings of the ACMInternational Conference on Multimedia. 2022: 1584-1592.) proposed a cross-modality high-frequency Transformer model for MRI image super-resolution reconstruction. The model uses the Transformer module to explore structural prior knowledge from the gradient domain and obtain cross-modal context information from additional modalities. This method can extract dependencies within and between modalities. FENG et al. (FENG C, YAN Y, FU H, et al. Task Transformer Network for Joint MRI Reconstruction and Super-Resolution[C] / / Proceedings of the International conference on medical image computing and computer-assisted intervention. 2021: 307-317.) believe that there is a complementary and promoting relationship between image reconstruction and super-resolution tasks. In order to utilize the correlation between them, a Transformer-based task transformation network is proposed for the joint MRI image reconstruction and super-resolution tasks.The network explores the correlation between reconstruction and super-resolution tasks by sharing features and representations, achieving feature complementarity.

[0004] MRI images contain important information such as the spatial structure and texture of brain tissue. There is a correlation between the structure and tissue between adjacent slices. The current MRI image super-resolution algorithm ignores this correlation between slices and only performs super-resolution processing on each slice independently, using only the spatial information within a single slice. However, in brain MRI images, spatial information can only describe the distribution of brain tissue, while related information can reflect the continuity of the anatomical structure of brain tissue, thereby helping to restore the edge texture and structure in the slice image. Therefore, it is necessary to distinguish between spatial information and related information in MRI images and process them separately. Summary of the invention

[0005] The purpose of the present invention is to provide a brain MRI image super-resolution reconstruction method based on second-order propagation and grid connection, so as to solve the technical problem that the MRI image super-resolution algorithm in the prior art ignores the correlation between slices and only performs super-resolution processing on each slice independently, which is not conducive to restoring the edge texture and structure in the slice image.

[0006] In order to achieve the above object, the present invention adopts the following technical solutions: In the first aspect, the present application proposes a brain MRI image super-resolution reconstruction method based on second-order propagation and grid connection, comprising: The brain MRI image is decomposed into several low-resolution slices, which are connected through a grid-connected second-order Markov chain. The features of each low-resolution slice are extracted to obtain the corresponding shallow feature map. The shallow feature map is fused with the relevant features of two adjacent continuous low-resolution slices to obtain fused features. The fused features are aggregated to obtain representative features. The representative features are segmented through channels to obtain spatial features and related features. The related features are propagated between slices through a second-order Markov chain. The spatial features are iteratively fused with the relevant features of two adjacent continuous representative features. After fusion for a total of 4 times, the feature map is obtained. The feature map is upsampled to obtain element one, the low-resolution slice is bicubicly upsampled to obtain element two, and element one and element two are added pixel by pixel to obtain a high-resolution image.

[0007] Preferably, the brain MRI image is decomposed into a plurality of low-resolution slices, the plurality of low-resolution slices are connected through a grid-connected second-order Markov chain, and the features of each low-resolution slice are extracted to obtain a corresponding shallow feature map, specifically including: S101: normalizing the brain MRI image to obtain a uniform threshold pixel image, decomposing the uniform threshold pixel image into two-dimensional slices along the depth direction to obtain low-resolution slices; S102: Extract the features of low-resolution slices through convolution to obtain a shallow feature map. The formula is as follows:

[0008]

[0009] in, This is a brain MRI image; represents normalization; For low-resolution slices; represents slicing along the depth direction, Represents feature extraction, Convolution composition; It is a shallow feature map.

[0010] Preferably, the grid connection is specifically: connecting the forward second-order Markov chain and the reverse second-order Markov chain to each other and stacking them twice in a grid connection manner.

[0011] Preferably, the shallow feature map is fused with the relevant features of two adjacent continuous low-resolution slices to obtain fused features, the fused features are aggregated to obtain representative features, the representative features are segmented by channels to obtain spatial features and related features; the related features are propagated between slices through a second-order Markov chain, the spatial features are iteratively fused with the relevant features of two adjacent continuous representative features, and after fusion for a total of 4 times, a feature map is obtained, which specifically includes the following steps: S201: The shallow feature map is first fused with the relevant features of two adjacent continuous slices to obtain fused features; the fused features are aggregated to obtain representative features, and the representative features are divided into two parts using a channel separation method, one part is the relevant features, and the other part is the spatial features;

[0012] in, is a shallow feature map; is the spatial feature after the first fusion; represents the relevant features of the first fusion, Represents fusion, aggregation, and channel splitting operations; For the The relevant features of the low-resolution slices; For the The relevant features of the low-resolution slices; S202: The related features are propagated between slices based on the second-order Markov chain; the spatial features continue to be fused with the related features from different directions; the fused features are aggregated to obtain representative features, and the representative features are divided into related features and spatial features using the channel separation method. The spatial features are iteratively fused with the related features of two adjacent continuous representative features, and after fusion for a total of 4 times, the feature map is obtained. :

[0013] when hour, ; when hour, ;when hour, ; in, For the The spatial characteristics of sub-fusion; Indicates the channel splicing operation, represents the residual network; for The fusion features obtained by the second fusion; For the The relevant features of the representative features; For the The relevant features of the representative features; The fusion features are aggregated to obtain representative features, and the channel separation method is used to divide the representative features into two parts, one is the correlation feature and the other is the spatial feature:

[0014]

[0015] in, Represents aggregation; To represent the characteristics; Indicates channel separation; For the The spatial characteristics of sub-fusion.

[0016] Preferably, upsampling the feature map to obtain element one, bicubic upsampling the low-resolution slice to obtain element two, and adding element one and element two pixel by pixel to obtain a high-resolution image specifically includes: S301: upsampling the feature map through a convolution layer and a sub-pixel convolution to obtain element one; S302: Perform bicubic upsampling on the low-resolution slice to obtain element two; S303: Adding element 1 and element 2 pixel by pixel to obtain a high-resolution image;

[0017] in represents 3×3 convolution, represents the sub-pixel convolution operation, represents bicubic upsampling; Represents a feature map; Represents a low-resolution slice; High resolution images.

[0018] In the second aspect, the present application proposes a brain MRI image super-resolution reconstruction system based on second-order propagation and grid connection, comprising: It is used to decompose the brain MRI image into several low-resolution slices. The several low-resolution slices are connected through a grid-connected second-order Markov chain, and the features of each low-resolution slice are extracted to obtain the corresponding shallow feature map; The feature fusion module is used to fuse the shallow feature map with the relevant features of two adjacent continuous low-resolution slices to obtain fused features. The fused features are aggregated to obtain representative features, and the representative features are segmented through channels to obtain spatial features and related features. The related features are propagated between slices through a second-order Markov chain, and the spatial features are iteratively fused with the relevant features of two adjacent continuous representative features. After fusion for a total of 4 times, a feature map is obtained. The upsampling module is used to upsample the feature map to obtain element one, perform bicubic upsampling on the low-resolution slice to obtain element two, and add element one and element two pixel by pixel to obtain a high-resolution image.

[0019] Preferably, the feature fusion module corresponds to 4 fusion times for iterative fusion. and related features , To merge, hour , get the fusion features , expressed as:

[0020] Indicates the channel splicing operation, represents the residual network; when hour, ;when hour, ; The merged features Use the ESA attention enhancement module to aggregate in texture-rich areas to obtain representative features , expressed as:

[0021] The channel separation strategy is used to divide the representative features into two parts, one of which is related features. Based on the second-order Markov strategy, the propagation between slices continues, and another part of the spatial features It is sent to the grid connection, connecting to the next layer of feature fusion module in the network, and continues to fuse related features from different directions, as shown below:

[0022] in Stands for channel separation.

[0023] Preferably, in the upsampling module, the feature map is upsampled to obtain a high-resolution image, specifically: Feature Map , upsample the features through convolutional layers and Pixel-shuffle, and then convert the low-resolution image After bicubic upsampling, element-wise addition is performed to obtain a high-resolution image. , as shown in the formula:

[0024] in represents 3×3 convolution, represents the sub-pixel convolution operation, Denotes bicubic upsampling.

[0025] In a third aspect, the present application proposes an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of any of the above-mentioned methods for super-resolution reconstruction of brain MRI images based on second-order propagation and grid connection when executing the computer program.

[0026] In a fourth aspect, the present application proposes a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of any of the above-mentioned methods for super-resolution reconstruction of brain MRI images based on second-order propagation and grid connection.

[0027] Compared with the prior art, the present invention has the following beneficial effects: 1) It makes better use of the relevant information between MRI image sequences, reflects the continuity of the anatomical structure of brain tissue, and thus helps to restore the edge texture and structure in the slice image. It adopts the second-order Markov strategy and grid connection bidirectional feature propagation. A series of experiments are conducted on it, and the comparison of indicators shows that it has reached the optimal level in this field.

[0028] 2) By introducing the second-order Markov strategy, the correlation between slices can be captured, and the information in the previous slice can be used to assist the super-resolution reconstruction of the current slice, which can more accurately restore the spatial structure, texture and edge features of brain tissue, while effectively avoiding the problem of information loss when processing each slice individually.

[0029] 3) In order to solve the limitation that features can only be propagated in one direction in the second-order Markov strategy, this study adopted a grid connection method to combine the second-order Markov chains in different directions to achieve multiple bidirectional transmissions of relevant features between slices. At the same time, these transmitted features are refined with the spatial features of different slices in the entire sequence, thereby further enhancing the ability to describe the details of the spatial features. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0031] Figure 1 is a flow chart of the method of the present invention; Figure 2 It is the algorithm structure framework diagram of the system of the present invention; Figure 3 It is a structural diagram of the feature fusion module of the present invention; Figure 4 is a propagation data flow graph of a second-order Markov chain of the present invention; Figure 5 A data flow diagram for grid connections of the present invention; Figure 6 A model diagram for removing second-order Markov propagation in the ablation experiment of the present invention; Figure 7 The model diagram of the present invention after removing grid stacking and second-order propagation, wherein (b) is the model diagram after removing grid stacking; (c) is the model diagram after removing grid stacking and second-order propagation; Figure 8 The following are visualization diagrams of the reconstruction effects of different brain MRI image super-resolution methods; (A) represents the LR MRI image, (B) represents the bidirectional network reconstruction effect diagram, (C) represents the network reconstruction effect diagram of this application, (D) represents the ground truth, and (E)-(H) represent the corresponding local detail diagrams of (A)-(D). DETAILED DESCRIPTION

[0032] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Generally, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations.

[0033] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention claimed for protection, but merely represents selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0034] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0035] In the description of the embodiments of the present invention, it should be noted that if the terms "upper", "lower", "horizontal", "inner", etc. indicate an orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the product of the invention is usually placed when in use, it is only for the convenience of describing the present invention and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0036] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly tilted. For example, "horizontal" only means that its direction is more horizontal than "vertical", which does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0037] In the description of the embodiments of the present invention, it is also necessary to explain that, unless otherwise clearly specified and limited, the terms "set", "install", "connect", and "connect" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal connection of two components. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0038] The present invention is further described in detail below in conjunction with the accompanying drawings: This application proposes a brain MRI super-resolution algorithm based on second-order propagation and grid connection. Specifically, this application regards MRI image slices as video frames, and the MRI images are decomposed and reorganized into a two-dimensional slice sequence to fully utilize the spatial information within the slices and the related information between slices.

[0039] See also Figure 1 The present application discloses a brain MRI image super-resolution reconstruction method based on second-order propagation and grid connection, comprising: S1: The brain MRI image is decomposed into several low-resolution slices, which are connected through a grid-connected second-order Markov chain. The features of each low-resolution slice are extracted to obtain the corresponding shallow feature map. S2: The shallow feature map is fused with the relevant features of two adjacent continuous low-resolution slices to obtain fused features. The fused features are aggregated to obtain representative features. The representative features are segmented through channels to obtain spatial features and related features. The related features are propagated between slices through a second-order Markov chain. The spatial features are iteratively fused with the relevant features of two adjacent continuous representative features. After fusion for a total of 4 times, the feature map is obtained. S3: Upsample the feature map to obtain element one, perform bicubic upsampling on the low-resolution slice to obtain element two, and add element one and element two pixel by pixel to obtain a high-resolution image.

[0040] In some embodiments, the brain MRI image is decomposed into a plurality of low-resolution slices, the plurality of low-resolution slices are connected through a grid-connected second-order Markov chain, and the features of each low-resolution slice are extracted to obtain the corresponding shallow feature map, specifically including: S101: normalizing the brain MRI image to obtain a uniform threshold pixel image, decomposing the uniform threshold pixel image into two-dimensional slices along the depth direction to obtain low-resolution slices; S102: Extract the features of low-resolution slices through convolution to obtain a shallow feature map. The formula is as follows:

[0041]

[0042] in, This is a brain MRI image; represents normalization; For low-resolution slices; represents slicing along the depth direction, Represents feature extraction, Convolution composition; It is a shallow feature map.

[0043] In some embodiments, the grid connection is specifically: connecting the forward second-order Markov chain and the reverse second-order Markov chain to each other and stacking them twice in a grid connection manner.

[0044] Further preferably, the second-order Markov chain propagation method is specifically as follows: through the second-order Markov chain propagation strategy of the RNN framework, the relevance of the previous slice is transferred, such as Figure 4 The sequence is i Spatial characteristics , related features By related features and spatial characteristics Aggregation is obtained, so the Markov chain strategy can effectively extract the deep features of the previous slices and provide relevant information for the subsequent slices.

[0045] In some embodiments, the shallow feature map is fused with the relevant features of two adjacent continuous low-resolution slices to obtain fused features, the fused features are aggregated to obtain representative features, the representative features are segmented by channels to obtain spatial features and related features; the related features are propagated between slices through a second-order Markov chain, the spatial features are iteratively fused with the relevant features of two adjacent continuous representative features, and after fusion for a total of 4 times, a feature map is obtained, which specifically includes the following steps: S201: The shallow feature map is first fused with the relevant features of two adjacent continuous slices to obtain fused features; the fused features are aggregated to obtain representative features, and the representative features are divided into two parts using a channel separation method, one part is the relevant features, and the other part is the spatial features;

[0046] in, is a shallow feature map; is the spatial feature after the first fusion; represents the relevant features of the first fusion, Represents fusion, aggregation, and channel splitting operations; For the The relevant features of the low-resolution slices; For the The relevant features of the low-resolution slices; S202: The related features are propagated between slices based on the second-order Markov chain; the spatial features continue to be fused with the related features from different directions; the fused features are aggregated to obtain representative features, and the representative features are divided into related features and spatial features using the channel separation method. The spatial features are iteratively fused with the related features of two adjacent continuous representative features, and after fusion for a total of 4 times, the feature map is obtained. :

[0047] when hour, ; when hour, ;when hour, ; in, For the The spatial characteristics of sub-fusion; Indicates the channel splicing operation, represents the residual network; for The fusion features obtained by the second fusion; For the The relevant features of the representative features; For the The relevant features of the representative features; The fusion features are aggregated to obtain representative features, and the channel separation method is used to divide the representative features into two parts, one is the correlation feature and the other is the spatial feature:

[0048]

[0049] in, Represents aggregation; To represent the characteristics; Indicates channel separation; For the The spatial characteristics of sub-fusion.

[0050] In some embodiments, upsampling the feature map to obtain element one, bicubic upsampling the low-resolution slice to obtain element two, and adding element one and element two pixel by pixel to obtain a high-resolution image specifically includes: S301: upsampling the feature map through a convolution layer and a sub-pixel convolution to obtain element one; S302: Perform bicubic upsampling on the low-resolution slice to obtain element two; S303: Adding element 1 and element 2 pixel by pixel to obtain a high-resolution image;

[0051] in represents 3×3 convolution, represents the sub-pixel convolution operation, represents bicubic upsampling; Represents a feature map; Represents a low-resolution slice; High resolution images.

[0052] The present application also discloses a brain MRI image super-resolution reconstruction system based on second-order propagation and grid connection, comprising: A feature extraction module is used to decompose the brain MRI image into several low-resolution slices. The several low-resolution slices are connected through a grid-connected second-order Markov chain, and the features of each low-resolution slice are extracted to obtain the corresponding shallow feature map; The feature fusion module is used to fuse the shallow feature map with the relevant features of two adjacent continuous low-resolution slices to obtain fused features. The fused features are aggregated to obtain representative features, and the representative features are segmented through channels to obtain spatial features and related features. The related features are propagated between slices through a second-order Markov chain, and the spatial features are iteratively fused with the relevant features of two adjacent continuous representative features. After fusion for a total of 4 times, a feature map is obtained. The upsampling module is used to upsample the feature map to obtain element one, perform bicubic upsampling on the low-resolution slice to obtain element two, and add element one and element two pixel by pixel to obtain a high-resolution image.

[0053] In some embodiments, a brain MRI image super-resolution reconstruction system based on second-order propagation and grid connection has an overall network structure as follows: The algorithmic structure framework of the brain MRI image super-resolution reconstruction system using second-order propagation and grid connection, such as Figure 2 As shown in Figure 1, it mainly consists of three modules: feature extraction module, feature fusion module and upsampling module. Specifically, given an MRI image , H, W and are the height, width and depth of the MRI image respectively. First, the MRI image is normalized and decomposed into a two-dimensional slice sequence along the depth direction. .like Figure 2 As shown, the low-resolution slice sequence first extracts shallow feature maps through the feature extraction module , the formula is:

[0054]

[0055] in represents the feature extraction module, represents normalization, Indicates decomposition along the depth direction.

[0056] Shallow feature map , and the depth features of adjacent slices It is sent to the first fusion module for feature fusion. The fused features are divided into spatial features and related features through channel segmentation. The formula is expressed as:

[0057] in represents the fusion module, and the fused spatial features are continuously fed into the next fusion module, while the relevant features are propagated between slices through the second-order Markov strategy to provide relevant information for subsequent slices. In particular, when hour, ;when hour, After the four fusion modules, the feature map is obtained. The feature passes through the upsampling module to obtain a high-resolution image. The formula is as follows:

[0058] in Represents an upsampling module.

[0059] This application proposes a new framework based on second-order Markov propagation chains and grid connections for MRI super-resolution tasks. First, the spatial features of each slice are extracted through a convolutional network. With the help of a second-order Markov strategy, the relevant features of the previous slice are propagated unidirectionally to other slices, and then these relevant features are fused and refined with the spatial information of the slices through a fusion module. Grid connections are used to combine second-order Markov chains in different directions to achieve bidirectional propagation of relevant features. After being refined by four fusion modules, the spatial features are upsampled by Pixel-shuffle and added element-by-element to the low-resolution image to obtain a high-resolution image reconstruction result.

[0060] In some embodiments, the specific contents of the feature extraction module are as follows: Since the pixel values ​​in different MRI images vary greatly, given the input 3D MRI image First, each 3D MRI image is normalized to convert the intensity of the pixel value to a threshold value (0-1 in this embodiment). Then the 3D MRI image is decomposed into two-dimensional slices along the depth direction to obtain low-resolution slices. ( ), i Represents the depth index of the slice, extracting the feature map through convolution , the formula is as follows:

[0061]

[0062]

[0063] in Indicates taking the maximum value, represents slicing along the depth direction, represents the feature extraction module, Convolution composition.

[0064] In some embodiments, the specific contents of the feature fusion module are as follows: The related features from different slices need to be effectively fused with the spatial features of the current slice, and the fused features need to propagate the features of the current slice to subsequent slices to continue to provide additional recovery information for subsequent slices. n As an example, this application uses the spatial feature fusion module and related features , To merge, hour , get the fusion features , expressed as:

[0065] Indicates the channel splicing operation, represents the residual network. In particular, when hour, ;when hour, .

[0066] Merged features Use the ESA attention enhancement module to aggregate in texture-rich areas to obtain more representative features , expressed as:

[0067] The fused features are divided into two parts using the channel separation strategy. Based on the second-order Markov strategy, the other part continues to propagate between slices. It is sent to the grid and connected to the next fusion module in the network to continue fusing related features from different directions. Figure 3 As shown, it means as follows:

[0068] in Represents a channel separation operation.

[0069] Further preferably, the specific method of grid connection is as follows: The information in a single second-order Markov chain can only flow in one direction, and the related features cannot be associated with subsequent slices, that is, the features can only be fused to the related features in a single direction. Specifically, the features extracted from the previous slice can obtain more information than the features extracted from the next slice, and the reconstruction quality of the image at the starting position in the reconstructed image sequence is poor. In order to solve the above problems, the forward second-order Markov chain and the reverse second-order Markov chain are interconnected and stacked twice in a grid connection. By stacking the forward and reverse second-order Markov chain branches, all features in the sequence can capture the depth information of the entire sequence, thereby improving performance, such as Figure 5 As shown, it is expressed as:

[0070]

[0071] in Indicates k Fusion Module , k When is an odd number, the spatial characteristics By feature map and related features Fusion, the sequence is i The feature map can only receive depth index less than i Other slice-related information. k When is an even number, the spatial characteristics By feature map and related features Fusion, the sequence is i The feature map can only receive depth index greater than i Through the grid connection, the two second-order Markov chains in different directions are connected together, and the feature map It can integrate relevant features information, utilizing relevant information from different directions.

[0072] In some embodiments, the specific contents of the upsampling module are as follows: After four fusion modules, the feature map is obtained , the features are upsampled through convolutional layers and Pixel-shuffle, and then the LR image After bicubic upsampling, element-wise addition is performed to obtain a high-resolution image. , as shown in the formula:

[0073] in represents 3×3 convolution, represents the sub-pixel convolution operation, Denotes bicubic upsampling.

[0074] In some embodiments, the SR network is optimized using the Charbonnier loss function. N LR images and its corresponding HR image , the super-resolution reconstructed MRI image is , the network loss function for:

[0075] in is a constant, is the set of parameters of the network.

[0076] Finally, this application summarizes the workflow of the entire method as follows: first, the spatial features of each slice are extracted through a convolutional network. With the help of a second-order Markov strategy, the relevant features of the previous slice are propagated unidirectionally to other slices, and then these relevant features are fused and refined with the spatial information of the slices through a fusion module. A grid connection is used to combine the second-order Markov chains in different directions to achieve bidirectional propagation of relevant features. After being refined by four fusion modules, the spatial features are upsampled by pixel-shuffle and added element-by-element to the low-resolution image to obtain a high-resolution image reconstruction result.

[0077] At present, the MRI image super-resolution algorithm ignores the relevant information between slices, and only performs super-resolution processing on each slice independently, and only uses the spatial information within a single slice. Compared with the prior art, the invention makes better use of the relevant information between MRI image sequences, reflects the continuity of the anatomical structure of brain tissue, and thus helps to restore the edge texture and structure in the slice image. It has the following advantages: it adopts a second-order Markov strategy and grid connection bidirectional feature propagation. A series of experiments are conducted on it, and the comparison of indicators shows that it has reached the optimal level in this field.

[0078] By introducing the second-order Markov strategy, the correlation between slices can be captured, and the information in the previous slice can be used to assist the super-resolution reconstruction of the current slice, which can more accurately restore the spatial structure, texture and edge features of brain tissue, while effectively avoiding the problem of information loss when processing each slice individually.

[0079] In order to solve the limitation that features can only be propagated in one direction in the second-order Markov strategy, this application adopts a grid connection method to combine the second-order Markov chains in different directions to achieve multiple bidirectional transmissions of relevant features between slices. At the same time, these transmitted features are refined with the spatial features of different slices in the entire sequence, thereby further enhancing the ability to describe the details of the spatial features.

[0080] A large number of experiments on the IXI dataset show that the method of this application can effectively improve the quality of MRI images and achieve the best performance in the current field.

[0081] The IXI dataset is used to construct the SR dataset of this application. This dataset is widely used in research in the fields of brain structure analysis, lesion detection, and brain deformation analysis. It includes three different modalities of brain MRI images, namely PD, T1, and T2 sequences. Among these modalities, this application randomly selected 500 volumes for training, 70 volumes for testing, and 6 volumes for verification, and all data are in NIFTI format. The size of each MRI image is 240×240×96 (H×W×D), where 96 represents the number of slices of the MRI image. This application decomposes the MRI image into a two-dimensional image sequence along the D direction, and obtains 500 training samples with a sequence length of 96. Use bicubic degradation to downsample all MRI images by 2 times, 3 times, and 4 times to obtain the corresponding LR images.

[0082] In order to quantitatively evaluate the proposed method and compare it with the baseline, this application adopts the method of most research works and uses two common image quality evaluation criteria to evaluate pixel-level differences, namely peak signal-to-noise ratio (PSNR) and structural similarity (SSIM), to accurately evaluate super-resolution performance. Generally speaking, the higher the values ​​of PSNR and SSIM, the better the SR reconstruction performance of MRI images.

[0083] The MR volume size in the dataset is 240×240×96 (H×W×D), where 96 represents the number of slices in the MR volume. Before training, the present application decomposes the MRI images into two-dimensional image sequences along the D direction to obtain 500 training samples with a sequence length of 96. All MRI images are downsampled using bicubic degradation of 2×, 3×, and 4× as LR images. In the experiment, the input image size is 32×32 and the sequence length is 31. During the training process, the corresponding LR images of the original image training set are randomly cut into corresponding sizes. Various data augmentation strategies are used to process the data, including random rotation, random flipping, sequence flipping, etc.

[0084] The network model in the experiment was built and trained using the PyTorch framework, a GeForce RTX 3090 graphics card and 24GB of memory. The initial learning rate of the network was set to , and the total number of iterations was 600K. Charbonnier loss was used, which can handle outliers and improve performance better than traditional losses. The number of residual blocks in each fusion module was set to 3, and the number of feature channels was 64.

[0085]

Comparative experiment

[0086] Table 1 Quantitative comparison of different methods on the IXI dataset

[0087] These models have achieved good results in MRI super-resolution, including SERAN, CSN and EDSR+MMHCA. For fairness, this application evaluates the average PSNR and SSIM scores of these methods in different modalities on the IXI dataset under 2×, 3× and 4× magnification. In PD modality, the method of this application has a PSNR higher than SERAN by 2.1dB, 0.9dB and 0.3dB respectively under 2×, 3× and 4× magnification factor settings, and is 2.3dB, 1.3dB and 0.7dB higher than CSN respectively. In T1 modality, the method of this application has a PSNR higher than SERAN by 0.6dB, 0.7dB and 0.5dB respectively under 2×, 3× and 4× magnification factor settings, and is 1.0dB, 1.2dB and 1.2dB higher than CSN respectively. In T2 mode, the PSNR of the method of the present application is 0.4dB and 0.1dB higher than that of EDSR+MMHCA at 2× and 4× amplification factor settings.

[0088]

Ablation experiment

[0089] This application studies the important influence of the second-order Markov propagation strategy in the network. By removing the second-order Markov propagation chain from the network, the network is simplified to Figure 6, explore the impact of introducing a second-order Markov propagation chain on the reconstruction performance. Table 2 gives the experimental results of the Markov chain network and the bidirectional network with a 2× scaling factor on the PD mode of the IXI dataset. The results show that the introduction of the second-order Markov chain propagation strategy improves the PSNR of the network by 0.1dB. The current slice has limited information available for reconstruction. In order to improve the output quality of these slices, effective information aggregation of previous slices is required. Using the second-order Markov propagation strategy, relevant information can be propagated between slices more robustly and effectively, which helps to restore detailed features.

[0090] To further study the impact of grid propagation on model performance, we remove the stacked forward and backward propagation paths in the network in the complete model and model (a), retaining only one forward and one backward propagation path, and simplify the network as follows: Figure 7 The experimental results of these models under the PD mode of the IXI dataset with a 4× scaling factor are compared to observe the impact of the grid propagation strategy on the network performance.

[0091] The experimental results are shown in Table 2. Compared with model (b) and model (c), the PSNR of the proposed method is improved by 0.6dB and 0.7dB respectively. This shows that the depth features are continuously refined on the additional propagation path, and the grid propagation enables the information of different depth directions of the slices to be continuously propagated in the sequence, which improves the utilization rate and expression ability of the features.

[0092] Table 2 Comparison of PD modal performance of second-order propagation and bidirectional mesh connection networks on the IXI dataset

[0093] Figure 8 The visualization of the reconstruction effects of different methods for brain MRI images is shown. (A) represents the LR MRI image, (B) represents the bidirectional network reconstruction effect diagram, (C) represents the network reconstruction effect diagram of this application, (D) represents the ground truth, and (E)-(H) represent the corresponding local detail diagrams of (A)-(D). It can be seen that the second-order Markov chain propagation network is more accurate than the bidirectional network model in restoring the detail texture of MRI images.

[0094] In summary, this application has important innovation and application potential in the field of MRI image processing, and can provide strong support for related research and clinical practice.

[0095] The present application also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the brain MRI image super-resolution reconstruction method based on second-order propagation and grid connection are implemented as described in any one of the above items.

[0096] The present application also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of any of the above-mentioned methods for super-resolution reconstruction of brain MRI images based on second-order propagation and grid connection.

[0097] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0098] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0099] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0100] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0101] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A brain MRI image super-resolution reconstruction method based on second-order propagation and grid connection, characterized in that: include: The brain MRI image is decomposed into several low-resolution slices, which are connected through a grid-connected second-order Markov chain. The features of each low-resolution slice are extracted to obtain the corresponding shallow feature map. The shallow feature map is fused with the related features of two adjacent continuous low-resolution slices to obtain fused features. The fused features are aggregated to obtain representative features. The representative features are segmented through channels to obtain spatial features and related features. The relevant features are propagated between slices through the second-order Markov chain, and the spatial features are iteratively fused with the relevant features of two adjacent continuous representative features. After fusion for a total of 4 times, the feature map is obtained; The feature map is upsampled to obtain element one, the low-resolution slice is bicubicly upsampled to obtain element two, and element one and element two are added pixel by pixel to obtain a high-resolution image.

2. The method for super-resolution reconstruction of brain MRI images based on second-order propagation and grid connection according to claim 1, characterized in that: The brain MRI image is decomposed into a plurality of low-resolution slices, the plurality of low-resolution slices are connected through a grid-connected second-order Markov chain, and the features of each low-resolution slice are extracted to obtain the corresponding shallow feature map, specifically including: S101: normalizing the brain MRI image to obtain a uniform threshold pixel image, decomposing the uniform threshold pixel image into two-dimensional slices along the depth direction to obtain low-resolution slices; S102: Extract the features of low-resolution slices through convolution to obtain a shallow feature map. The formula is as follows: in, This is a brain MRI image; represents normalization; For low-resolution slices; represents slicing along the depth direction, Represents feature extraction, Convolution composition; It is a shallow feature map.

3. The method for super-resolution reconstruction of brain MRI images based on second-order propagation and grid connection according to claim 1, characterized in that: The grid connection specifically includes: connecting the forward second-order Markov chain and the reverse second-order Markov chain to each other, and stacking them twice in a grid connection manner.

4. The method for super-resolution reconstruction of brain MRI images based on second-order propagation and grid connection according to claim 1, characterized in that: The shallow feature map is fused with the relevant features of two adjacent continuous low-resolution slices to obtain fused features, the fused features are aggregated to obtain representative features, and the representative features are segmented through channels to obtain spatial features and relevant features; The relevant features are propagated between slices through the second-order Markov chain, and the spatial features are iteratively fused with the relevant features of two adjacent continuous representative features. After fusion for a total of 4 times, the feature map is obtained, which specifically includes the following steps: S201: The shallow feature map is first fused with the relevant features of two adjacent continuous slices to obtain fused features; the fused features are aggregated to obtain representative features, and the representative features are divided into two parts using a channel separation method, one part is the relevant features, and the other part is the spatial features; in, is a shallow feature map; is the spatial feature after the first fusion; represents the relevant features of the first fusion, Represents fusion, aggregation, and channel splitting operations; For the The relevant features of the low-resolution slices; For the The relevant features of the low-resolution slices; S202: The related features are propagated between slices based on the second-order Markov chain; the spatial features continue to be fused with the related features from different directions; the fused features are aggregated to obtain representative features, and the representative features are divided into related features and spatial features using the channel separation method. The spatial features are iteratively fused with the related features of two adjacent continuous representative features, and after fusion for a total of 4 times, the feature map is obtained. : when hour, ; when hour, ;when hour, ; in, For the The spatial characteristics of sub-fusion; Indicates the channel splicing operation, represents the residual network; for The fusion features obtained by the second fusion; For the The relevant features of the representative features; For the The relevant features of the representative features; The fusion features are aggregated to obtain representative features, and the channel separation method is used to divide the representative features into two parts, one is the correlation feature and the other is the spatial feature: in, Represents aggregation; To represent the characteristics; Indicates channel separation; For the The spatial characteristics of sub-fusion.

5. The method for super-resolution reconstruction of brain MRI images based on second-order propagation and grid connection according to claim 1, characterized in that: The method of upsampling the feature map to obtain element one, performing bicubic upsampling on the low-resolution slice to obtain element two, and adding element one and element two pixel by pixel to obtain a high-resolution image specifically includes: S301: upsampling the feature map through a convolution layer and a sub-pixel convolution to obtain element one; S302: Perform bicubic upsampling on the low-resolution slice to obtain element two; S303: Adding element 1 and element 2 pixel by pixel to obtain a high-resolution image; in represents 3×3 convolution, represents the sub-pixel convolution operation, represents bicubic upsampling; Represents a feature map; Represents a low-resolution slice; High resolution images.

6. A brain MRI image super-resolution reconstruction system based on second-order propagation and grid connection, characterized in that: include: A feature extraction module is used to decompose the brain MRI image into several low-resolution slices. The several low-resolution slices are connected through a grid-connected second-order Markov chain, and the features of each low-resolution slice are extracted to obtain the corresponding shallow feature map; The feature fusion module is used to fuse the shallow feature map with the relevant features of two adjacent continuous low-resolution slices to obtain fused features. The fused features are aggregated to obtain representative features, and the representative features are segmented through channels to obtain spatial features and related features. The relevant features are propagated between slices through the second-order Markov chain, and the spatial features are iteratively fused with the relevant features of two adjacent continuous representative features. After fusion for a total of 4 times, the feature map is obtained; The upsampling module is used to upsample the feature map to obtain element one, perform bicubic upsampling on the low-resolution slice to obtain element two, and add element one and element two pixel by pixel to obtain a high-resolution image.

7. According to the brain MRI image super-resolution reconstruction system based on second-order propagation and grid connection in claim 6, the feature fusion module corresponds to 4 fusion times for iterative fusion. and related features , To merge, hour , get the fusion features , expressed as: Indicates the channel splicing operation, represents the residual network; when hour, ;when hour, ; The merged features Use the ESA attention enhancement module to aggregate in texture-rich areas to obtain representative features , expressed as: The channel separation strategy is used to divide the representative features into two parts, one of which is related features. Based on the second-order Markov strategy, the propagation between slices continues, and another part of the spatial features It is sent to the grid connection, connecting to the next layer of feature fusion module in the network, and continues to fuse related features from different directions, as shown below: in Stands for channel separation.

8. According to the brain MRI image super-resolution reconstruction system based on second-order propagation and grid connection in claim 6, in the upsampling module, the feature map is upsampled to obtain a high-resolution image, specifically: Feature Map , upsample the features through convolutional layers and Pixel-shuffle, and then convert the low-resolution image After bicubic upsampling, element-wise addition is performed to obtain a high-resolution image. , as shown in the formula: in represents 3×3 convolution, represents the sub-pixel convolution operation, Denotes bicubic upsampling.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method for super-resolution reconstruction of brain MRI images based on second-order propagation and grid connection as described in any one of claims 1 to 5 when executing the computer program.

10. A computer-readable storage medium storing a computer program, wherein the computer program, when executed by a processor, implements the steps of the brain MRI image super-resolution reconstruction method based on second-order propagation and grid connection as described in any one of claims 1 to 5.

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