23Na multi-core MRI reconstruction method based on mixed domain coding enhancement

Abstract

The invention discloses a 23Na multi-core MRI (Magnetic Resonance Imaging) reconstruction method based on mixed domain coding enhancement, which comprises the following steps of: inputting 2D (Two-Dimensional) full-sampling auxiliary mode k space data and 2D under-sampling target mode k space data into a mixed domain feature extraction network in a constructed mixed domain Transform reconstruction network to extract corresponding features; inputting into a decoding reconstruction network to obtain a target modal reconstruction image; according to the method, auxiliary modal data are introduced through a mixed domain Transform reconstruction network, information complementarity between multi-modal MRI data is utilized, detail information of a reconstructed image is enhanced, global and semantic cross-modal feature fusion and compensation are realized in a frequency domain, and the reconstruction quality of a target modal is remarkably improved; a cross frequency domain attention mechanism is used, frequency domain information and space information are fully utilized, and compared with a traditional space attention mechanism, the speed is higher, and feature extraction is more sufficient.

Description

Technical Field

[0001] This invention belongs to the field of imaging technology, specifically relating to hybrid domain coding enhancement. 23 Na multinucleus MRI reconstruction method. Background Technology

[0002] Sodium magnetic resonance imaging (SMI) 23 Na MRI is an emerging imaging technique that provides unique physiological and biochemical information by detecting the concentration and distribution of sodium ions in tissues. 23 NaMRI has broad application prospects in the medical field. However, 23 The development and application of Na MRI also face some technical challenges. First, 23 The signal strength of Na is much lower than that of commonly used signals. 1 H signal, which leads to 23 Na MRI has low image quality and signal-to-noise ratio. Secondly, 23 The signal attenuation of Na exhibits a double-exponential characteristic, which further increases the complexity of imaging. Furthermore, in order to obtain high-quality... 23 Na MRI images typically require a long imaging time, which may not be feasible in some scenarios where rapid diagnosis and treatment are needed.

[0003] In magnetic resonance imaging (MRI), k-space undersampling is a commonly used method to accelerate data acquisition. By reducing the number of data points sampled in k-space, MRI scan time can be significantly shortened. However, this undersampling can lead to artifacts in the image, affecting image quality.

[0004] Deep learning methods have demonstrated great potential in accelerating MRI imaging in recent years. Deep learning techniques have made significant progress in magnetic resonance imaging (MRI) reconstruction, improving image quality and accelerating the scanning process by utilizing multiple deep learning network models. These network models include gradient descent algorithms, proximal gradient descent algorithms, alternating direction multiplier method (ADMM), proximal dynamic programming (PDHG), and diffusion models combined with gradient descent. However, many deep learning-based MRI reconstruction methods primarily target single-nuclear MRI data, failing to fully exploit the correlations between MRI data from different nuclei. Research has found that… 1 H MRI and 23 Na MRI can reflect similar anatomical structures, and the information they provide can complement each other. Therefore, in multinucleated MRI... 23 During Na MRI reconstruction, combined with 1 The features of H MRI can significantly improve the quality of reconstructed images compared to existing single-core MRI (such as H MRI).23 Na MRI reconstruction method, this fusion strategy has obvious advantages.

[0005] Furthermore, existing deep learning reconstruction methods employ complex-valued convolutions with limited kernel sizes (e.g., 3×3 or 5×5), restricting their receptive fields to local areas. This makes it difficult to effectively capture long-range dependencies between missing points in k-space and distant reference points (e.g., autocalibration (ACS) lines located far apart in the phase encoding direction). Establishing such dependencies often requires stacking extremely deep network layers, leading to low computational efficiency, optimization difficulties, and difficulty in directly learning the frequency and phase encoding characteristics of k-space. Summary of the Invention

[0006] The purpose of this invention is to effectively utilize the complementary information between multi-core MRI data to further improve reconstruction quality, and to propose a hybrid domain coding enhancement method. 23 Na multinucleus MRI reconstruction method.

[0007] The above-mentioned objective of the present invention is achieved through the following technical solution: Enhanced based on hybrid domain coding 23 The Na multinucleus MRI reconstruction method includes the following steps: Step 1: Obtain the training set. The training set includes multiple sample groups. Each sample group includes 2D fully sampled auxiliary modality k-space data, 2D fully sampled target modality k-space data, 2D fully sampled target modality image, and 2D undersampled target modality k-space data of the same subject. Step 2: Construct a hybrid domain Transformer reconstruction network, which includes a hybrid domain feature extraction network and a decoding and reconstruction network. The 2D fully sampled auxiliary modal k-space data and the corresponding 2D undersampled target modal k-space data are input into the hybrid domain feature extraction network to extract the corresponding features and then perform channel stitching. The results are then input into the decoding and reconstruction network to obtain the corresponding target modal reconstruction image. Step 3: Define the total loss function; Step 4: Train the hybrid domain Transformer reconstruction network according to the total loss function set in Step 3; Step 5: Input the 2D fully sampled auxiliary modal k-space data to be processed and the corresponding 2D undersampled target modal k-space data into the hybrid domain Transformer reconstruction network trained in Step 4 to obtain the corresponding final reconstructed target modal image.

[0008] As described above, the hybrid domain feature extraction network includes two branch networks, each of which includes a PatchEmbedding block and multiple encoders. Multiple frequency domain cross-attention encoders are set between the two branch networks. 2D fully sampled auxiliary mode k-space data and 2D undersampled target mode k-space data are used as input mode k-space data, respectively, and are input to the Patch Embedding block of the corresponding branch network. Each Patch Embedding block extracts the frequency coding features and phase coding features of the corresponding input mode k-space data, fuses them, and then inputs them into the first layer encoder of the same branch network for further feature extraction. The features output from the first layer encoders of the two branch networks are simultaneously input into the first layer frequency domain cross-attention encoder. After interactive learning, the features corresponding to the 2D fully sampled auxiliary mode k-space data and the features corresponding to the 2D undersampled target mode k-space data are sequentially input into the second layer encoder and the second layer frequency domain cross-attention encoder of the corresponding branch networks, respectively, to continue the mixed domain feature extraction. This process is repeated layer by layer through the encoder and the frequency domain cross-attention encoder for feature extraction until the last layer frequency domain cross-attention encoder outputs the features corresponding to the 2D fully sampled auxiliary mode k-space data and the features corresponding to the 2D undersampled target mode k-space data, which are then concatenated and input into the decoding and reconstruction network.

[0009] As described above, the Patch Embedding block includes a vertically gated mixed-domain adaptive Fourier convolution module, a horizontally gated mixed-domain adaptive Fourier convolution module, and a two-dimensional inverse Fourier transform layer: The input modal k-space data is fed into the vertically gated hybrid domain adaptive Fourier convolution module of the corresponding Patch Embedding block to obtain the corresponding phase-encoded features. Simultaneously, the input modal k-space data is fed into the horizontally gated hybrid domain adaptive Fourier convolution module of the corresponding Patch Embedding block to obtain the corresponding frequency-encoded features. The phase-encoded features and frequency-encoded features are concatenated and then passed through a two-dimensional inverse Fourier transform layer and an absolute value function to obtain the feature output of the corresponding input modal k-space data.

[0010] For each gated hybrid domain adaptive Fourier convolution module as described above The input modal k-space data are fed into the full receptive field frequency domain adaptive filtering branch and the hybrid domain coding feature enhancement branch of the gated hybrid domain adaptive Fourier convolution module, respectively. Among them, the hybrid domain coding feature enhancement branch decomposes the input modal k-space data into a series of one-dimensional k-space data in the corresponding direction, and each one-dimensional k-space data is input into the frequency domain branch and the time domain branch of the hybrid domain coding feature enhancement branch respectively. The one-dimensional k-space data input to the frequency domain branch is sequentially processed through a one-dimensional Fourier convolution and a sigmoid activation function in the weight branch of the frequency domain branch to obtain the corresponding weights. At the same time, the one-dimensional k-space data input to the frequency domain branch is also processed through a one-dimensional Fourier convolution in the feature extraction branch of the frequency domain branch to obtain the corresponding features. The weights output by the weight branch of the frequency domain branch and the features output by the feature extraction branch of the frequency domain branch are multiplied together to obtain the frequency domain filtered features. The one-dimensional k-space data input to the time-domain branch is first subjected to a one-dimensional inverse Fourier transform to obtain the time-domain data. The time-domain data is then subjected to a one-dimensional Fourier convolution in the feature extraction branch of the time-domain branch to obtain the corresponding features. Simultaneously, the time-domain data is subjected to a one-dimensional Fourier convolution and a sigmoid activation function in the weight branch of the time-domain branch to obtain the corresponding weights. The weights output from the weight branch and the features output from the feature extraction branch of the time-domain branch are multiplied together and then subjected to a one-dimensional inverse Fourier transform to obtain the time-domain filtered features. Each one-dimensional k-space data, the frequency domain filtering feature and the time domain filtering feature of the one-dimensional k-space data are added together to obtain the corresponding mixed domain feature. The mixed domain features of all one-dimensional k-space data are concatted in the corresponding directions to obtain the concatenated mixed domain feature. The full receptive field frequency domain adaptive filtering branch performs a full receptive field two-dimensional Fourier convolution on the corresponding input mode k-space data and then passes it through a sigmoid activation function to obtain the full receptive field filtering weights. The output of the corresponding gated hybrid domain adaptive Fourier convolution module is obtained by multiplying the full receptive field filtering weights with the concatenated hybrid domain features; For the vertically gated hybrid domain adaptive Fourier convolution module: the corresponding input modality k-space data is decomposed vertically into a series of one-dimensional k-space data of size 1×w, and the corresponding one-dimensional Fourier convolution kernel size is 1×w', outputting phase-encoded features; w is the horizontal length of the data matrix of the input modality k-space data; For the horizontally gated hybrid domain adaptive Fourier convolution module: the corresponding input modality k-space data is horizontally decomposed into a series of one-dimensional k-space data of size h×1. The corresponding one-dimensional Fourier convolution kernel size is h'×1, which is used to output frequency coding features; h is the vertical length of the data matrix of the input modality k-space data.

[0011] Each encoder as described above includes multiple cascaded transformer blocks, and each transformer block sequentially includes a corresponding position coding layer, a linear mapping layer, a first normalization layer, a frequency domain attention mechanism layer, a second normalization layer, and a fully connected layer. The features input to the frequency domain attention mechanism layer are separated into vectors through a reshape operation. ,vector sum vector In the frequency domain attention mechanism layer, vector ,vector sum vector Each vector is transformed into a frequency domain vector by a one-dimensional Fourier transform. Frequency domain vector and frequency domain vector Frequency domain vector Frequency domain vector Frequency domain vector The features are obtained through the following calculations. : , in, This represents the number of heads in the frequency domain attention mechanism layer. The normalized dimension of the middle layer in the frequency domain attention mechanism layer. It is a normalized exponential function; feature After sequentially undergoing one-dimensional inverse Fourier transform, taking absolute value, and linear mapping, the input features of the frequency domain attention mechanism layer are added together with the residual connection to obtain the output features of the frequency domain attention mechanism layer.

[0012] As mentioned above, the number of transformer blocks included in the encoder increases with the sequence number of the cascaded encoders.

[0013] Each frequency domain cross-attention encoder as described above includes a target mode branch cross-attention layer and an auxiliary mode branch cross-attention layer. Each branch cross-attention layer sequentially includes a corresponding position coding layer, a linear mapping layer, a first normalization layer, a frequency domain cross-attention mechanism layer, a second normalization layer, and a fully connected layer. For each frequency domain cross-attention encoder: The features corresponding to the input target modality enter the position encoding layer in the target modality branch cross attention layer, add the position information vector, and then pass through the corresponding linear mapping layer and the first normalization layer in sequence. They are then simultaneously input into the frequency domain cross attention mechanism layer in the target modality branch cross attention layer and the frequency domain cross attention mechanism layer in the auxiliary modality branch cross attention layer of the same frequency domain cross attention encoder. The features corresponding to the input auxiliary modality enter the position encoding layer in the auxiliary modality branch cross attention layer, add the position information vector, and then pass through the corresponding linear mapping layer and the first normalization layer in sequence; then they are simultaneously input into the frequency domain cross attention mechanism layer in the target modality branch cross attention layer and the frequency domain cross attention mechanism layer in the auxiliary modality branch cross attention layer of the same frequency domain cross attention encoder. The features of the target mode and the features of the auxiliary mode, which are input into the frequency domain cross-attention mechanism layer of the target mode branch cross-attention layer, are respectively used as the first mode feature and the second mode feature of the frequency domain cross-attention mechanism layer of the target mode branch cross-attention layer. The features of the auxiliary mode and the features of the target mode, which are input into the frequency domain cross-attention mechanism layer of the auxiliary mode branch cross-attention layer, are respectively used as the first mode feature and the second mode feature of the frequency domain cross-attention mechanism layer of the auxiliary mode branch cross-attention layer. In the frequency domain cross-attention mechanism layer: The features corresponding to the first mode are converted into vectors after a reshape operation. The second modality feature block is converted into a vector after the reshape operation. sum vector Then vector , and Each vector is transformed into a frequency domain vector using a one-dimensional Fourier transform. Frequency domain vector and frequency domain vector Frequency domain vector Frequency domain vector and frequency domain vector The output features are obtained through the following calculations. : , in This represents the number of heads in the frequency domain cross-attention mechanism layer. It is the normalized dimension of the middle layer in the frequency domain cross-attention mechanism layer. It is a normalized exponential function; feature After sequentially undergoing one-dimensional inverse Fourier transform, absolute value taking, and linear mapping, the features corresponding to the first mode of the input frequency domain cross-attention mechanism layer are added together through residual connection to obtain the output features of the corresponding frequency domain cross-attention mechanism layer.

[0014] As described above, the decoding and reconstruction network consists of an input layer, multiple convolutional layers, and an output layer. The output layer of the decoding and reconstruction network has two channels, which represent the real and imaginary parts of the output result, respectively. The complex result composed of the two channels output by the output layer is the final target modality reconstruction image output by the decoding and reconstruction network.

[0015] The loss function is as described above: , in, Represents the total loss function. Let be the error function. It is 2D fully sampled target modal k-space data. It is 2D undersampled target mode k-space data. Represents 2D fully sampled auxiliary modal k-space data; The parameter is The entire hybrid domain Transformer reconstruction network, This represents the target modality reconstruction image output by a hybrid domain Transformer reconstruction network, using 2D fully sampled auxiliary modality k-space data and 2D undersampled target modality k-space data. For inverse Fourier transform, For 2D fully sampled target modal images, The target mode reconstruction image is obtained by performing a two-dimensional inverse Fourier transform on the target mode reconstruction k-space data.

[0016] A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement steps 2 to 5 of the reconstruction method described in any one of the claims.

[0017] Compared with the prior art, the present invention has the following advantages: The hybrid-domain Transformer reconstruction network provided by this invention is based on the frequency domain Transformer and integrates... 23 NaMRI and 1 The complementary information from H MRI, and the innovative realization of global, semantic-level cross-modal feature fusion and compensation within the hybrid domain, are specifically reflected in: 1. A hybrid domain Transformer reconstruction network was constructed, which utilizes full sampling... 1 H MRI k-space data to enhance 23 The reconstruction effect of the target modality on Na MRI. Although 1 h MRI provides limited information on the distribution of sodium ions in the brain, leading to the generation of... 23 While there are some discrepancies between the MRI images and the actual images, the hybrid domain Transformer reconstruction network can still effectively restore the images. 1 Key regions identifiable in 1H MRI images, such as the cerebral cortex and white matter. This provides... 23 Accelerated acquisition and reconstruction of Na MRI provides prior information, especially details about brain structure and sodium ion distribution, which is of great significance for improving image reconstruction quality and enhancing image detail features.

[0018] 2. Precise k-space global information compensation: Through the frequency domain cross-attention encoder, the network can dynamically analyze the frequency domain feature correlation between the target mode and the auxiliary mode with the global receptive field, thereby making full use of frequency domain information and spatial information to accurately locate the key frequency components in the auxiliary mode that can be used to fill the missing points in the k-space of the target mode, realizing targeted and intelligent k-space data completion, effectively suppressing aliasing artifacts; and it is faster and extracts features more fully. 3. Multimodal semantic collaboration and redundancy elimination: The frequency domain-based Transformer mechanism in the hybrid domain Transformer reconstruction network realizes deep interaction between different modalities at the frequency domain feature level, which can mine and enhance their shared semantic information in anatomical structure, while filtering modality-specific noise and redundant features, significantly improving the utilization efficiency of multimodal data. 4. Excellent detail preservation and texture restoration capabilities: The hierarchical coding structure of the frequency domain Transformer can progressively extract and integrate multi-scale frequency domain features, ensuring the effective capture and restoration of high-order frequency information such as fine textures and edges, and significantly improving the visual quality of the reconstructed image.

[0019] Furthermore, in the hybrid domain Transformer reconstruction network of this invention, the gated hybrid domain adaptive Fourier convolution module of the Patch Embedding block includes two complementary branches: a full receptive field frequency domain adaptive filtering branch and a hybrid domain coding feature enhancement branch. Combined with one-dimensional Fourier convolutions in different directions, it can fully exploit the coding characteristics of k-space from two levels. Compared with the traditional Patch Embedding block, the gated hybrid domain adaptive Fourier convolution module proposed in this paper enables the Patch Embedding block to simultaneously fuse local and global k-space frequency and phase coding features, making it more suitable for MRI reconstruction tasks and thus significantly improving the accuracy and quality of the reconstructed images. Attached Figure Description

[0020] Figure 1 Multi-kernel based on image generation 23 Flowchart of Na MRI artificial intelligence reconstruction method; Figure 2 Undersampled mask image; Figure 3 This is a schematic diagram of the overall structure of the hybrid domain Transformer reconstruction network; Patch Embedding represents the Patch Embedding block. Indicates channel splicing; Figure 4Here are schematic diagrams of the Patch Embedding block structure; where (a) is a schematic diagram of the Patch Embedding block structure in the branch network corresponding to the target mode, and (b) is a schematic diagram of the Patch Embedding block structure in the branch network corresponding to the auxiliary mode; Abs represents the function for obtaining the absolute value; Figure 5 This is a gated hybrid domain adaptive Fourier convolution module structure; This indicates multiplication; w is the horizontal length of the data matrix containing the input modality k-space data; h is the vertical length of the data matrix containing the input modality k-space data. Figure 6 Here are schematic diagrams of the encoder structure; where (a) is a schematic diagram of the encoder structure in the branch network corresponding to the target mode, and (b) is a schematic diagram of the encoder structure in the branch network corresponding to the auxiliary mode. Figure 7 This is a schematic diagram of the frequency domain attention mechanism layer structure; This is represented as a reshape operation, used to separate vectors Q, K, and V; Figure 8 This is a schematic diagram of the structure of a frequency domain cross-attention encoder; Figure 9 Here are schematic diagrams of the frequency domain cross-attention mechanism layer, where (a) is a schematic diagram of the frequency domain cross-attention mechanism layer in the target modality branch cross-attention layer, and (b) is a schematic diagram of the frequency domain cross-attention mechanism layer in the auxiliary modality branch cross-attention layer. Figure 10 This is a schematic diagram of the network structure for decoding and reconstruction. Figure 11 It is test set reconstruction 23 Comparison of Na MRI image results, where (a) is 2D full sampling. 23 Na MRI image, (b) is zero-filled 23 Na MRI image, (c) is the final reconstruction 23 Na MRI image. Detailed Implementation

[0021] To facilitate understanding and implementation of the present invention by those skilled in the art, the present invention will be further described in detail below with reference to embodiments. The embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0022] Enhanced based on hybrid domain coding 23 Na multinucleus MRI reconstruction methods, such as Figure 1As shown, multiple MRI modalities are selected for joint reconstruction. Each MRI modality can reflect similar brain anatomical structures, and the information provided by each MRI modality can complement each other (in this embodiment, the MRI modality selected is...). 1 H MRI and 23 Na MRI, in which 1 H MRI is an auxiliary modality. 23 Na MRI (target modality) specifically includes the following steps: Step 1: Obtain the training set and test set. Both the training set and test set include multiple sample groups. Each sample group includes 2D fully sampled auxiliary modality k-space data, 2D fully sampled target modality k-space data and corresponding 2D fully sampled target modality image and 2D undersampled target modality k-space data of the same subject. The auxiliary modality and the target modality represent MRI results of two different elements. In this embodiment, the auxiliary modality is... 1 H MRI, target modality is 23 Na MRI, each sample group includes: 2D full sampling 1 H MRI k-space data, 2D full sampling 23 Na MRI k-space data, 2D full sampling 23 Na MRI images, 2D full sampling 23 2D undersampling of Na MRI k-space data 23 Na MRI k-space data. T2-weighted data from the IXI public dataset are used in this example. 1 H-mode magnetic resonance imaging was used to simulate the target mode 5.0 T. 23 Experiments were conducted using Na magnetic resonance images, weighted using the IXI public dataset T1. 1 H-MRI images were used as auxiliary modality images, with 1000 images for each modality included in the training set and 300 images included in the test set. In practical applications, images acquired in-house can also be used. 23 Na MRI data and 1 H MRI data.

[0023] The specific method for step 1 is as follows: Step 1.1: Scan multiple subjects to obtain 3D full-sample auxiliary modality k-space data and 3D full-sample target modality k-space data for each subject; This embodiment scans multiple subjects to obtain corresponding 3D full samples. 1 H MRI k-space data, and 3D full sampling 23 Na MRI k-space data.

[0024] Step 1.2: Extract 3D fully sampled auxiliary modal k-space data layer by layer to obtain the corresponding 2D fully sampled auxiliary modal k-space data; extract 3D fully sampled target modal k-space data layer by layer to obtain the corresponding 2D fully sampled target modal k-space data; undersample the 2D fully sampled target modal k-space data according to the undersampled sampling matrix to obtain the corresponding 2D undersampled target modal k-space data; in this embodiment, the sampling mask corresponding to the undersampled sampling matrix is ​​as follows: Figure 2 As shown; This embodiment extracts 3D full sampling layer by layer. 1 H MRI k-space data, to obtain the corresponding 2D full sampling 1 H MRI k-space data; layer-by-layer extraction of 3D full sampling 23 Na MRI k-space data, to obtain the corresponding 2D full sampling 23 Na MRI k-space data; 2D full sampling based on undersampled sampling matrix 23 Na MRI k-space data is undersampled to obtain the corresponding 2D undersampling. 23 Na MRI k-space data.

[0025] Step 1.3: Perform a two-dimensional inverse Fourier transform on the 2D fully sampled target modal k-space data to obtain the 2D fully sampled target modal image.

[0026] This embodiment uses 2D full sampling. 23 Two-dimensional inverse Fourier transform was performed on Na MRI k-space data to obtain 2D full sampling. 23 Na MRI image.

[0027] Step 1.4: Take a subject's 2D fully sampled auxiliary modality k-space data, 2D fully sampled target modality k-space data, 2D undersampled target modality k-space data, and 2D fully sampled target modality image as a sample group, and divide all sample groups into training set and test set. Both training set and test set include multiple sample groups.

[0028] This embodiment uses a 2D full sample of a subject. 1 H MRI k-space data, 2D full sampling 23 Na MRI k-space data, 2D undersampling 23 Na MRI k-space data, and 2D full sampling 23 Na MRI images are treated as a sample group, and all sample groups are divided into training and test sets, each of which includes multiple sample groups.

[0029] Step 2: Construct a hybrid domain Transformer reconstruction network. This network consists of a hybrid domain feature extraction network and a decoding and reconstruction network, as follows: Figure 3 As shown.

[0030] The 2D fully sampled auxiliary modal k-space data and the corresponding 2D undersampled target modal k-space data of the sample group are input into the hybrid domain feature extraction network to extract the corresponding features and perform channel stitching. Then, they are input into the decoding and reconstruction network to obtain the corresponding target modal reconstruction image.

[0031] (1) Hybrid Domain Feature Extraction Network The hybrid domain feature extraction network consists of two branches (corresponding to the auxiliary mode and the target mode, respectively). Each branch includes a patch embedding block and multiple encoders. Multiple frequency domain cross-attention encoders are set between the two branches. The specific settings of the hybrid domain feature extraction network are as follows: 2D fully sampled auxiliary mode k-space data and 2D undersampled target mode k-space data are used as input mode k-space data, respectively, and are input to the Patch Embedding block of the corresponding branch network. Each Patch Embedding block extracts the frequency coding features and phase coding features of the corresponding input mode k-space data, fuses them, and then inputs them into the first layer encoder of the same branch network for further feature extraction. The features output from the first layer encoder of each of the two branch networks are simultaneously input into the first layer frequency domain cross-attention encoder. After interactive learning, the features corresponding to the 2D fully sampled auxiliary modality k-space data and the 2D undersampled target modality k-space data are sequentially input into the second layer encoder and the second layer frequency domain cross-attention encoder of the corresponding branch networks, respectively, to continue the mixed domain feature extraction. This process is repeated layer by layer through the encoder and the frequency domain cross-attention encoder for feature extraction until the last layer frequency domain cross-attention encoder outputs the features corresponding to the 2D fully sampled auxiliary modality k-space data and the 2D undersampled target modality k-space data. These features are then concatenated and input into the decoding and reconstruction network. The frequency domain cross-attention encoder helps subsequent networks learn image features more easily.

[0032] (1.1) The specific structure of the Patch Embedding block is as follows: Each Patch Embedding block includes two gated hybrid domain adaptive Fourier convolutional modules (i.e., a vertically gated hybrid domain adaptive Fourier convolutional module and a horizontally gated hybrid domain adaptive Fourier convolutional module) and a two-dimensional inverse Fourier transform layer. Each gated hybrid domain adaptive Fourier convolutional module includes a full receptive field frequency domain adaptive filtering branch and a hybrid domain coding feature enhancement branch. The specific settings of the Patch Embedding block are as follows: The input modality k-space data is fed into the vertically gated hybrid domain adaptive Fourier convolution module of the corresponding Patch Embedding block to obtain the corresponding phase-coded features. Simultaneously, the input modality k-space data is fed into the horizontally gated hybrid domain adaptive Fourier convolution module of the corresponding Patch Embedding block to obtain the corresponding frequency-coded features. The phase-coded and frequency-coded features are concatenated and then sequentially passed through a two-dimensional inverse Fourier transform layer and an absolute value function to obtain the feature output of the corresponding input modality k-space data, such as... Figure 4 As shown.

[0033] Each gated hybrid-domain adaptive Fourier convolutional module includes two branches: a full-receptive-field frequency-domain adaptive filtering branch and a hybrid-domain coding feature enhancement branch, such as... Figure 5 As shown, the hybrid domain coding feature enhancement branch includes a frequency domain branch and a time domain branch. The frequency domain branch includes a feature extraction branch and a weighting branch. The time domain branch has a one-dimensional Fourier transform and a one-dimensional inverse Fourier transform. Between the one-dimensional Fourier transform and the one-dimensional inverse Fourier transform in the time domain branch, there is a feature extraction branch and a weighting branch, specifically configured as follows: The input modal k-space data are fed into the full receptive field frequency domain adaptive filtering branch and the hybrid domain coding feature enhancement branch, respectively.

[0034] Among them, the hybrid domain coding feature enhancement branch decomposes the input modal k-space data into a series of one-dimensional k-space data in the corresponding direction, and each one-dimensional k-space data is input into the frequency domain branch and the time domain branch of the hybrid domain coding feature enhancement branch respectively.

[0035] The one-dimensional k-space data input to the frequency domain branch is sequentially processed through a one-dimensional Fourier convolution and a sigmoid activation function in the weight branch of the frequency domain branch to obtain the corresponding weights. At the same time, the one-dimensional k-space data input to the frequency domain branch is also processed through a one-dimensional Fourier convolution in the feature extraction branch of the frequency domain branch to obtain the corresponding features. The weights output by the weight branch of the frequency domain branch and the features output by the feature extraction branch of the frequency domain branch are multiplied together to obtain the frequency domain filtered features.

[0036] The one-dimensional k-space data input to the time-domain branch is first subjected to a one-dimensional inverse Fourier transform to obtain the time-domain data. The time-domain data is then subjected to a one-dimensional Fourier convolution in the feature extraction branch of the time-domain branch to obtain the corresponding features. At the same time, the time-domain data is subjected to a one-dimensional Fourier convolution and a sigmoid activation function in the weight branch of the time-domain branch to obtain the corresponding weights. The weights output by the weight branch in the frequency-domain branch and the features output by the feature extraction branch in the frequency-domain branch are multiplied together and then subjected to a one-dimensional inverse Fourier transform to obtain the time-domain filtered features.

[0037] Each one-dimensional k-space data point, the frequency domain filtering feature and the time domain filtering feature of the one-dimensional k-space data are added together to obtain the corresponding mixed domain feature. The mixed domain features of all one-dimensional k-space data are concatted in the corresponding directions to obtain the concatenated mixed domain feature.

[0038] The full receptive field frequency domain adaptive filtering branch performs a full receptive field two-dimensional Fourier convolution on the corresponding input mode k-space data and then passes it through a sigmoid activation function to obtain the full receptive field filtering weights. The output of the corresponding gated hybrid domain adaptive Fourier convolution module is obtained by multiplying the full receptive field filtering weights with the concatenated hybrid domain features.

[0039] For the vertically gated hybrid domain adaptive Fourier convolution module: the corresponding input modality k-space data is decomposed vertically into a series of one-dimensional k-space data of size 1×w, and the corresponding one-dimensional Fourier convolution kernel size is 1×w', outputting phase-encoded features; w is the horizontal length of the data matrix of the input modality k-space data; For the horizontally gated hybrid domain adaptive Fourier convolution module: the corresponding input modality k-space data is horizontally decomposed into a series of one-dimensional k-space data of size h×1. The corresponding one-dimensional Fourier convolution kernel size is h'×1, which is used to output frequency coding features; h is the vertical length of the data matrix of the input modality k-space data.

[0040] The gated hybrid-domain adaptive Fourier convolution module structure designed in this invention includes two complementary branches: a full-receptive-field frequency-domain adaptive filtering branch and a hybrid-domain coding feature enhancement branch, which can fully explore the coding characteristics of k-space from two levels. In the hybrid-domain coding feature enhancement branch, a one-dimensional full-receptive-field Fourier convolution is used to extract features in both the frequency coding direction and the phase coding direction, thereby fully learning important features in different phase coding directions. In this branch, the temporal component provides image priors (details and edge information), while the frequency-domain component imposes data consistency constraints (k-space completion). The fusion of these two components effectively ensures the physical correctness of the reconstruction result. On the other hand, the full-receptive-field frequency-domain adaptive filtering branch uses a two-dimensional global receptive-field Fourier convolution, which can directly explore the interrelationships between coding features at the global level of the entire k-space, identifying key frequency coding features and phase coding features. The outputs of the two branches are adaptively selected by weights constructed through convolution and the sigmoid activation function, and then fused to form a fused representation that combines local and global features. In summary, compared with traditional Patch Embedding blocks, the gated hybrid domain adaptive Fourier convolution module proposed in this paper enables Patch Embedding blocks to simultaneously fuse local and global k-space frequency and phase coding features, making it more suitable for MRI reconstruction tasks and thus significantly improving the accuracy and quality of reconstructed images.

[0041] (1.2) The specific structure of the encoder is as follows: Each encoder comprises multiple cascaded transformer blocks. Each transformer block sequentially includes a positional coding layer, a linear mapping layer, a first normalization layer, a frequency domain attention mechanism layer, a second normalization layer, and a fully connected layer, as shown below. Figure 6 As shown. The number of transformer blocks included in the encoder increases with the sequence number of the cascaded encoders (i.e., with the depth).

[0042] In this embodiment, five encoders and five frequency-domain cross-attention encoders are provided. The encoders include 2, 3, 3, and 4 transformer blocks respectively as the depth increases.

[0043] The features input to each transformer block are sequentially processed through positional encoding, linear mapping, and the first normalization layer before being input to the corresponding frequency domain attention mechanism layer; the frequency domain attention mechanism layer includes three vectors. , , ,like Figure 7 : The features input to the frequency domain attention mechanism layer are separated into vectors through a reshape operation. ,vector sum vector In the frequency domain attention mechanism layer, vector ,vector sum vector Each vector is transformed into a frequency domain vector by a one-dimensional Fourier transform. Frequency domain vector and frequency domain vector Frequency domain vector Frequency domain vector Frequency domain vector The features are obtained through the following calculations. : , in, This represents the number of heads in the frequency domain attention mechanism layer. The normalized dimension of the middle layer in the frequency domain attention mechanism layer. It is a normalized exponential function; feature After sequentially undergoing one-dimensional inverse Fourier transform, absolute value taking, and linear mapping, the input features of the frequency domain attention mechanism layer are added to the output features of the frequency domain attention mechanism layer through residual connections. The output features of the frequency domain attention mechanism layer are then input to the second normalization layer and the fully connected layer of the transformer block to obtain the output features of the current transformer block.

[0044] (1.3) The specific structure of the frequency domain cross-attention encoder is as follows: Each frequency domain cross-attention encoder, such as Figure 8 As shown, it includes two branch cross attention layers, namely the target mode branch cross attention layer and the auxiliary mode branch cross attention layer. Each branch cross attention layer includes, in sequence, a corresponding position coding layer, a linear mapping layer, a first normalization layer, a frequency domain cross attention mechanism layer, a second normalization layer, and a fully connected layer. For each frequency domain cross-attention encoder: The features corresponding to the input target modality enter the position encoding layer in the target modality branch cross attention layer, add the position information vector, and then pass through the corresponding linear mapping layer and the first normalization layer in sequence. They are then simultaneously input into the frequency domain cross attention mechanism layer in the target modality branch cross attention layer and the frequency domain cross attention mechanism layer in the auxiliary modality branch cross attention layer of the same frequency domain cross attention encoder. The features corresponding to the input auxiliary modality enter the position encoding layer in the auxiliary modality branch cross attention layer, add the position information vector, and then pass through the corresponding linear mapping layer and the first normalization layer in sequence; then they are simultaneously input into the frequency domain cross attention mechanism layer in the target modality branch cross attention layer and the frequency domain cross attention mechanism layer in the auxiliary modality branch cross attention layer of the same frequency domain cross attention encoder. The features of the target mode and the features of the auxiliary mode, which are input into the frequency domain cross-attention mechanism layer of the target mode branch cross-attention layer, are respectively used as the first mode feature and the second mode feature of the frequency domain cross-attention mechanism layer of the target mode branch cross-attention layer. The features of the auxiliary mode and the features of the target mode, which are input into the frequency domain cross-attention mechanism layer of the auxiliary mode branch cross-attention layer, are respectively used as the first mode feature and the second mode feature of the frequency domain cross-attention mechanism layer of the auxiliary mode branch cross-attention layer. In the frequency domain cross-attention mechanism layer (structure as follows) Figure 9 As shown in the figure: The features corresponding to the first mode are converted into vectors after a reshape operation. The second modality feature block is converted into a vector after the reshape operation. sum vector Then vector , and Each vector is transformed into a frequency domain vector using a one-dimensional Fourier transform. Frequency domain vector and frequency domain vector Frequency domain vector Frequency domain vector and frequency domain vector The output features are obtained through the following calculations. : , in This represents the number of heads in the frequency domain cross-attention mechanism layer. It is the normalized dimension of the middle layer in the frequency domain cross-attention mechanism layer. It is a normalized exponential function; feature After passing through a one-dimensional inverse Fourier transform, taking the absolute value, and linear mapping, the features corresponding to the first mode of the input frequency domain cross-attention mechanism layer are added through residual connections to obtain the output features of the corresponding frequency domain cross-attention mechanism layer. The output features of the frequency domain cross-attention mechanism layer then pass through the second normalization layer and the fully connected layer of the same branch cross-attention layer to obtain the output features of the current branch cross-attention layer.

[0045] (2) Decoding and reconstructing the network The decoding and reconstruction network consists of an input layer, multiple convolutional layers, and an output layer, as follows: Figure 10 As shown.

[0046] The number of channels in the input layer of the decoding and reconstruction network is the same as the number of channels in the stitched output of the hybrid domain feature extraction network. The number of channels in the output layer of the decoding and reconstruction network is 2, representing the real and imaginary parts of the output result. The complex result composed of the two channels output by the output layer is the final target modality reconstructed image output by the decoding and reconstruction network.

[0047] In this example, the decoding and reconstruction network has 5 convolutional layers, each with a 3×3 kernel, and each convolutional layer is supplemented with a ReLU activation layer.

[0048] Step 3: Define the total loss function.

[0049] The total loss function includes a pixel loss function and a frequency domain loss function; wherein, the pixel loss function is the error between the predicted target modality reconstruction image and the 2D fully sampled target modality image in step 1; the frequency domain loss function is the error between the target modality reconstruction k-space data of the target modality reconstruction image reconstructed by the hybrid domain Transformer reconstruction network after two-dimensional inverse Fourier transform and the 2D fully sampled target modality k-space data in step 1.

[0050] In this example, the pixel loss function is the mean square error between the predicted target modality reconstructed image and the corresponding 2D fully sampled target modality image; the frequency domain loss function is the mean square error between the target modality reconstructed k-space corresponding to the predicted target modality reconstructed image and the corresponding 2D fully sampled target modality k-space data.

[0051] Total loss function Set as: , in, Represents the total loss function. Let be the error function; in this example, the error function is... Choose to calculate the mean square error value. It is 2D fully sampled target modal k-space data. It is 2D undersampled target mode k-space data. Represents 2D fully sampled auxiliary modal k-space data; The parameter is The entire hybrid domain Transformer reconstruction network, This represents the target modality reconstruction image output by a hybrid domain Transformer reconstruction network, using 2D fully sampled auxiliary modality k-space data and 2D undersampled target modality k-space data. For inverse Fourier transform, That is, a 2D fully sampled target modal image. The target mode reconstruction image is obtained by performing a two-dimensional inverse Fourier transform on the target mode reconstruction k-space data.

[0052] Step 4: Based on the total loss function set in Step 3, use the training set generated in Step 1 to perform end-to-end training on the hybrid domain Transformer reconstruction network constructed in Step 2, and save the parameters of the frequency domain Transformer network.

[0053] The 2D fully sampled auxiliary modal k-space data and the corresponding 2D undersampled target modal k-space data in the training set generated in step 1 are input into the hybrid domain feature extraction network to extract the corresponding features and perform channel stitching. Then, they are input into the decoding and reconstruction network to obtain the corresponding target modal reconstruction image. In this embodiment, based on the hybrid domain Transformer reconstruction network built in step 2, the network learning rate is initialized to 0.0001, the batch size is set to 8, and the network is trained on the PyTorch platform using the Adam optimizer. The 2D undersampled target modality k-space data and 2D fully sampled auxiliary modality k-space data from the training set generated in step 1 are input into the hybrid domain Transformer reconstruction network to obtain the predicted target modality reconstructed image, and the network is trained according to the total loss function set in step 4. Training is stopped after the total number of iterations reaches 200, and the parameters of the corresponding hybrid domain Transformer reconstruction network are saved.

[0054] Step 5: Input the 2D fully sampled auxiliary modal k-space data and the 2D undersampled target modal k-space data to be reconstructed into the hybrid domain Transformer reconstruction network trained in Step 4 to obtain the corresponding target modal reconstruction image.

[0055] In this example, the 2D undersampling to be reconstructed in the test set generated in step 1 is utilized. 23 Na MRI k-space data and 2D full sampling 1 The H MRI k-space data is input into the hybrid domain Transformer reconstruction network trained in step 4 to obtain the corresponding target modality reconstruction image.

[0056] The target modality reconstruction image obtained in step 5 is compared with the 2D full sample corresponding to the test set. 23Na MRI images were compared, and the peak signal-to-noise ratio (PSNR) and structural similarity index between the two were calculated.

[0057] Figure 11 This demonstrates an example of 2D undersampling in the test set. 23 Reconstruction results of Na MRI k-space data, with PSNR / SSIM values ​​labeled at the bottom of the image. (a) shows 2D full sampling. 23 Na MRI image, (b) is zero-filled 23 Na MRI image, (c) is the final reconstruction obtained using the method of the present invention. 23 Na MRI images. As can be seen from the results, the hybrid domain coding enhancement method provided by this invention... 23 Na multinucleus MRI reconstruction methods can extract data from high-magnification undersampled 2D images. 23 High-quality reconstruction from Na MRI k-space data 23 Na MRI image.

[0058] Example 2 Enhanced based on hybrid domain coding 23 A multinucleus MRI reconstruction device for implementing the hybrid domain coding enhancement described in Example 1. 23 Na multinucleus MRI reconstruction methods include: The model building module is used to implement step 2 in Example 1; The total loss function construction module is used to implement step 3 in Example 1; The training module is used to implement step 4 in Example 1; The application module is used to implement step 5 in embodiment 1.

[0059] Example 3 A computer device includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to perform steps 2 to 5 of the above embodiment 1.

[0060] Example 4 A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements steps 2 to 5 of Embodiment 1 above.

[0061] Example 5 A computer program product includes a computer program that, when executed by a processor, implements steps 2 to 5 of embodiment 1 described above.

[0062] The specific embodiments described herein are merely illustrative of the spirit of the invention. Those skilled in the art to which this invention pertains may make various modifications or additions to the described specific embodiments or use similar methods to substitute them, without departing from the spirit of the invention or exceeding the scope defined by the appended claims.

Claims

1. Enhanced based on hybrid domain coding 23 The Na multinucleus MRI reconstruction method is characterized by... Includes the following steps: Step 1: Obtain the training set. The training set includes multiple sample groups. Each sample group includes 2D fully sampled auxiliary modality k-space data, 2D fully sampled target modality k-space data, 2D fully sampled target modality image, and 2D undersampled target modality k-space data of the same subject. Step 2: Construct a hybrid domain Transformer reconstruction network, which includes a hybrid domain feature extraction network and a decoding and reconstruction network. The 2D fully sampled auxiliary modal k-space data and the corresponding 2D undersampled target modal k-space data are input into the hybrid domain feature extraction network to extract the corresponding features and then perform channel stitching. The results are then input into the decoding and reconstruction network to obtain the corresponding target modal reconstruction image. Step 3: Define the total loss function; Step 4: Train the hybrid domain Transformer reconstruction network according to the total loss function set in Step 3; Step 5: Input the 2D fully sampled auxiliary modal k-space data to be processed and the corresponding 2D undersampled target modal k-space data into the hybrid domain Transformer reconstruction network trained in Step 4 to obtain the corresponding final reconstructed target modal image.

2. The hybrid domain coding enhancement method according to claim 1 23 The Na multinucleus MRI reconstruction method is characterized by... The hybrid domain feature extraction network includes two branch networks, each branch network including a patch embedding block and multiple encoders, and multiple frequency domain cross-attention encoders are set between the two branch networks: 2D fully sampled auxiliary mode k-space data and 2D undersampled target mode k-space data are used as input mode k-space data, respectively, and are input to the Patch Embedding block of the corresponding branch network. Each Patch Embedding block extracts the frequency coding features and phase coding features of the corresponding input mode k-space data, fuses them, and then inputs them into the first layer encoder of the same branch network for further feature extraction. The features output from the first layer encoders of the two branch networks are simultaneously input into the first layer frequency domain cross-attention encoder. After interactive learning, the features corresponding to the 2D fully sampled auxiliary mode k-space data and the features corresponding to the 2D undersampled target mode k-space data are sequentially input into the second layer encoder and the second layer frequency domain cross-attention encoder of the corresponding branch networks, respectively, to continue the mixed domain feature extraction. This process is repeated layer by layer through the encoder and the frequency domain cross-attention encoder for feature extraction until the last layer frequency domain cross-attention encoder outputs the features corresponding to the 2D fully sampled auxiliary mode k-space data and the features corresponding to the 2D undersampled target mode k-space data, which are then concatenated and input into the decoding and reconstruction network.

3. The hybrid domain coding enhancement method according to claim 2 23 The Na multinucleus MRI reconstruction method is characterized by... The Patch Embedding block includes a vertically gated hybrid domain adaptive Fourier convolution module, a horizontally gated hybrid domain adaptive Fourier convolution module, and a two-dimensional inverse Fourier transform layer: The input modal k-space data is fed into the vertical gated hybrid domain adaptive Fourier convolution module of the corresponding Patch Embedding block to obtain the corresponding phase coding features. At the same time, the input modal k-space data is fed into the horizontal gated hybrid domain adaptive Fourier convolution module of the corresponding Patch Embedding block to obtain the corresponding frequency coding features. After the phase-coded features and frequency-coded features are concatenated, they are sequentially passed through a two-dimensional inverse Fourier transform layer and an absolute value function to obtain the feature output of the corresponding input mode k-space data.

4. The hybrid domain coding enhancement method according to claim 3 23 The Na multinucleus MRI reconstruction method is characterized by... For each gated hybrid domain adaptive Fourier convolution module The input modal k-space data are fed into the full receptive field frequency domain adaptive filtering branch and the hybrid domain coding feature enhancement branch of the gated hybrid domain adaptive Fourier convolution module, respectively. Among them, the hybrid domain coding feature enhancement branch decomposes the input modal k-space data into a series of one-dimensional k-space data in the corresponding direction, and each one-dimensional k-space data is input into the frequency domain branch and the time domain branch of the hybrid domain coding feature enhancement branch respectively. The one-dimensional k-space data input to the frequency domain branch is sequentially processed through a one-dimensional Fourier convolution and a sigmoid activation function in the weight branch of the frequency domain branch to obtain the corresponding weights. At the same time, the one-dimensional k-space data input to the frequency domain branch is also processed through a one-dimensional Fourier convolution in the feature extraction branch of the frequency domain branch to obtain the corresponding features. The weights output by the weight branch of the frequency domain branch and the features output by the feature extraction branch of the frequency domain branch are multiplied together to obtain the frequency domain filtered features. The one-dimensional k-space data input to the time-domain branch is first subjected to a one-dimensional inverse Fourier transform to obtain the time-domain data. The time-domain data is then subjected to a one-dimensional Fourier convolution in the feature extraction branch of the time-domain branch to obtain the corresponding features. Simultaneously, the time-domain data is subjected to a one-dimensional Fourier convolution and a sigmoid activation function in the weight branch of the time-domain branch to obtain the corresponding weights. The weights output from the weight branch and the features output from the feature extraction branch of the time-domain branch are multiplied together and then subjected to a one-dimensional inverse Fourier transform to obtain the time-domain filtered features. Each one-dimensional k-space data, the frequency domain filtering feature and the time domain filtering feature of the one-dimensional k-space data are added together to obtain the corresponding mixed domain feature. The mixed domain features of all one-dimensional k-space data are concatted in the corresponding directions to obtain the concatenated mixed domain feature. The full receptive field frequency domain adaptive filtering branch performs a full receptive field two-dimensional Fourier convolution on the corresponding input mode k-space data and then passes it through a sigmoid activation function to obtain the full receptive field filtering weights. The output of the corresponding gated hybrid domain adaptive Fourier convolution module is obtained by multiplying the full receptive field filtering weights with the concatenated hybrid domain features; For the vertically gated hybrid domain adaptive Fourier convolution module: the corresponding input modality k-space data is decomposed vertically into a series of one-dimensional k-space data of size 1×w, and the corresponding one-dimensional Fourier convolution kernel size is 1×w', outputting phase-encoded features; w is the horizontal length of the data matrix of the input modality k-space data; For the horizontally gated hybrid domain adaptive Fourier convolution module: the corresponding input modality k-space data is horizontally decomposed into a series of one-dimensional k-space data of size h×1. The corresponding one-dimensional Fourier convolution kernel size is h'×1, which is used to output frequency coding features; h is the vertical length of the data matrix of the input modality k-space data.

5. The hybrid domain coding enhancement method according to claim 4 23 The Na multinucleus MRI reconstruction method is characterized by... Each encoder includes multiple cascaded transformer blocks, and each transformer block sequentially includes a position coding layer, a linear mapping layer, a first normalization layer, a frequency domain attention mechanism layer, a second normalization layer, and a fully connected layer. The features input to the frequency domain attention mechanism layer are separated into vectors through a reshape operation. ,vector sum vector In the frequency domain attention mechanism layer, vector ,vector sum vector Each vector is transformed into a frequency domain vector by a one-dimensional Fourier transform. Frequency domain vector and frequency domain vector Frequency domain vector Frequency domain vector Frequency domain vector The features are obtained through the following calculations. : ， in, This represents the number of heads in the frequency domain attention mechanism layer. The normalized dimension of the middle layer in the frequency domain attention mechanism layer. It is a normalized exponential function; feature After sequentially undergoing one-dimensional inverse Fourier transform, taking absolute value, and linear mapping, the input features of the frequency domain attention mechanism layer are added together with the residual connection to obtain the output features of the frequency domain attention mechanism layer.

6. The hybrid domain coding enhancement method according to claim 5 23 The Na multinucleus MRI reconstruction method is characterized by... The number of transformer blocks included in the encoder increases as the sequence number of the cascaded encoders increases.

7. The hybrid domain coding enhancement method according to claim 3 23 The Na multinucleus MRI reconstruction method is characterized by... Each frequency domain cross-attention encoder includes a target mode branch cross-attention layer and an auxiliary mode branch cross-attention layer. Each branch cross-attention layer sequentially includes a corresponding position coding layer, a linear mapping layer, a first normalization layer, a frequency domain cross-attention mechanism layer, a second normalization layer, and a fully connected layer. For each frequency domain cross-attention encoder: The features corresponding to the input target modality enter the position encoding layer in the target modality branch cross attention layer, add the position information vector, and then pass through the corresponding linear mapping layer and the first normalization layer in sequence. They are then simultaneously input into the frequency domain cross attention mechanism layer in the target modality branch cross attention layer and the frequency domain cross attention mechanism layer in the auxiliary modality branch cross attention layer of the same frequency domain cross attention encoder. The features corresponding to the input auxiliary modality enter the position encoding layer in the auxiliary modality branch cross attention layer, add the position information vector, and then pass through the corresponding linear mapping layer and the first normalization layer in sequence; then they are simultaneously input into the frequency domain cross attention mechanism layer in the target modality branch cross attention layer and the frequency domain cross attention mechanism layer in the auxiliary modality branch cross attention layer of the same frequency domain cross attention encoder. The features of the target mode and the features of the auxiliary mode, which are input into the frequency domain cross-attention mechanism layer of the target mode branch cross-attention layer, are respectively used as the first mode feature and the second mode feature of the frequency domain cross-attention mechanism layer of the target mode branch cross-attention layer. The features of the auxiliary mode and the features of the target mode, which are input into the frequency domain cross-attention mechanism layer of the auxiliary mode branch cross-attention layer, are respectively used as the first mode feature and the second mode feature of the frequency domain cross-attention mechanism layer in the auxiliary mode branch cross-attention layer. In the frequency domain cross-attention mechanism layer: The features corresponding to the first mode are converted into vectors after a reshape operation. The second modality feature block is converted into a vector after the reshape operation. sum vector Then vector , and Each vector is transformed into a frequency domain vector using a one-dimensional Fourier transform. Frequency domain vector and frequency domain vector Frequency domain vector Frequency domain vector and frequency domain vector The output features are obtained through the following calculations. : ， in This represents the number of heads in the frequency domain cross-attention mechanism layer. It is the normalized dimension of the middle layer in the frequency domain cross-attention mechanism layer. It is a normalized exponential function; feature After sequentially undergoing one-dimensional inverse Fourier transform, absolute value taking, and linear mapping, the features corresponding to the first mode of the input frequency domain cross-attention mechanism layer are added together through residual connection to obtain the output features of the corresponding frequency domain cross-attention mechanism layer.

8. The hybrid domain coding enhancement method according to claim 1 23 The Na multinucleus MRI reconstruction method is characterized by... The decoding and reconstruction network consists of an input layer, multiple convolutional layers, and an output layer. The output layer of the decoding and reconstruction network has two channels, which represent the real and imaginary parts of the output result, respectively. The complex result composed of the two channels output by the output layer is the final target modality reconstruction image output by the decoding and reconstruction network.

9. The hybrid domain coding enhancement method according to claim 1 23 The Na multinucleus MRI reconstruction method is characterized by... The loss function is: ， in, Represents the total loss function. Let be the error function. It is 2D fully sampled target modal k-space data. It is 2D undersampled target mode k-space data. Represents 2D fully sampled auxiliary modal k-space data; The parameter is The entire hybrid domain Transformer reconstruction network, This represents the target modality reconstruction image output by a hybrid domain Transformer reconstruction network, using 2D fully sampled auxiliary modality k-space data and 2D undersampled target modality k-space data. For inverse Fourier transform, For 2D fully sampled target modal images, The target mode reconstruction image is obtained by performing a two-dimensional inverse Fourier transform on the target mode reconstruction k-space data.

10. A computer device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements steps 2 to 5 of the reconstruction method according to any one of claims 1-9.

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