A multi-channel magnetic resonance imaging method based on CMA-Net

Abstract

The present invention discloses a multi-channel magnetic resonance imaging method based on CMA-Net, which includes k-space data preprocessing, GRAPPA reconstruction, construction and training of a CMA-Net network model, data consistency replacement, and image reconstruction. The CMA-Net network model uses a complex multi-scale cascade attention module to improve the global feature extraction capability of the network, embeds a complex attention gate module into the fast connection between the encoding path and the decoding path, and improves the network's feature extraction capability for local region of interest information; utilizes the GRAPPA reconstruction results to construct residual connections, and combines the advantages of linear interpolation and nonlinear interpolation to further improve imaging quality; constructs multi-angle residual connections to effectively alleviate the gradient vanishing problem and improve network performance. Experimental results show that this method can effectively reduce the artifacts of multi-channel undersampled magnetic resonance reconstruction images and reconstruct high-quality magnetic resonance complex images.

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing, relates to magnetic resonance imaging, and particularly relates to a multi-channel magnetic resonance imaging method based on CMA-Net. Background Art

[0002] Magnetic resonance imaging (MRI) has the advantages of being radiation-free, having high soft tissue resolution, and being non-invasive, and is widely used in clinical medical diagnosis. However, in actual use, MRI has disadvantages such as long imaging times and the susceptibility to motion artifacts. To speed up MRI imaging, researchers have adopted methods such as parallel imaging and k-space undersampling, using multiple coils to under-acquire data to accelerate MRI data acquisition. These methods then use post-processing algorithms such as SENSE, GRAPPA, and compressed sensing to restore and reconstruct images. However, even at high acceleration, these methods still suffer from significant artifacts and suboptimal image reconstruction quality.

[0003] In recent years, with the rapid development of deep learning technology, magnetic resonance imaging based on convolutional neural networks (CNN) has become a research hotspot. However, most of the existing deep learning-based magnetic resonance imaging methods are based on real number operations, while the data acquired by magnetic resonance imaging is complex data, and the target after reconstruction is also a complex image. Therefore, the phase information in the complex data is very important in MRI applications such as magnetic susceptibility weighted imaging, and real number operations will lose phase information. In addition, in conventional convolutional neural networks, fixed-size convolution kernels are often used for feature extraction, but in actual applications, images usually contain objects of multiple scales.

[0004] In 2022, Dhengre et al. improved the cascade structure of U-Net, using multiple convolution paths with different convolution kernel sizes to form a multi-scale residual block, which was used on the encoder and decoder (Dhengre. Multiscale U-net-based accelerated magnetic resonance imaging reconstruction [J]. Signal, Image and Video Processing, 2022: 1-8.), enabling the model to extract the underlying features of different receptive fields, thereby performing more effective feature extraction. However, this method is only performed under the condition of single-coil imaging. Hossain et al. used a fully dense attention CNN and introduced an attention gate in each decoder layer to focus on the image features of the relevant magnetic resonance image, thereby improving the generalization ability of the network (Hossain, et al. De-aliasing and accelerated sparse magnetic resonance image reconstruction using fully dense CNN with attention gates [J]. Bioengineering, 2022, 10 (1): 22.). However, this model relies on the accuracy of MRI image feature extraction, especially the addition of the fully dense attention gate, which will amplify this error when the image feature extraction is not in place.

[0005] Prior Art 1 (201710689598.3) fuses feature maps from different convolutional layers through a multi-scale fusion unit, overcoming the flat layer structure of traditional convolutional neural networks, accelerating the convergence of the network, and reconstructing image details faster. However, this comes at the cost of the number of parameters. The importance of a large number of multi-scale features extracted by stacking convolutional layers varies, and processing all features equally will result in a waste of computing resources. Prior Art 2 (202110309274.9) proposes a recursive residual U-shaped convolutional neural network based on a complex attention mechanism. It uses an attention mechanism to increase the accuracy of model reconstruction and uses recursive residuals to control the number of parameters and prevent gradient disappearance. However, features in an image may exist at multiple scales, and a single attention mechanism may find it difficult to simultaneously capture features at these different scales, especially when these features differ significantly in importance. Summary of the Invention

[0006] To address the shortcomings of the existing technology, the present invention proposes a multi-channel magnetic resonance imaging method based on CMA-Net. A complex multi-scale cascaded attention module is used to replace the double convolution module of the traditional U-Net encoding part, and the complex attention gate module is embedded in the fast connection between the encoding path and the decoding path of the same layer. The GRAPPA reconstruction results are used to construct residual connections to alleviate the gradient vanishing problem and improve network performance, thereby balancing imaging speed and imaging quality.

[0007] A multi-channel magnetic resonance imaging method based on CMA-Net specifically includes the following steps:

[0008] Step 1: K-space data preprocessing

[0009] Define the undersampling template mask:

[0010]

[0011] Then the undersampled data S u for:

[0012] S u =mask.*S k [2]

[0013] Where “.*” represents dot product. k Represents fully sampled k-space complex multi-channel data.

[0014] The full sampling data S k With undersampled data S u Perform inverse Fourier transform (IDFT) respectively, and then perform complex normalization operation, that is, normalize the amplitude while retaining the complex data phase of each channel to obtain the reference image I ref With the undersampled image I u .

[0015] Step 2: GRAPPA reconstruction

[0016] For undersampled data S u Perform GRAPPA reconstruction to obtain k-space reconstruction data S GRAPPA :

[0017] S GRAPPA =GRAPPA(S u ) [3]

[0018] To S GRAPPA Perform inverse Fourier transform on each channel to obtain the GRAPPA reconstruction image I in the image domain GRAPPA .

[0019] Step 3: Build the CMA-Net network model

[0020] The CMA-Net network model includes a GRAPPA residual path and a complex convolutional network. The GRAPPA residual path is used to reconstruct FIG1 GRAPPA The complex convolution network adopts a symmetric encoding-decoding structure similar to U-Net. The CMA-Net network model adds the GRAPPA residual path and the output features of the complex convolution network as the final model output CMANet out :

[0021] CMANet out =I GRAPPA *ω+CNet(I u ) [4]

[0022] Where “*” represents complex convolution, ω represents a complex convolution kernel of size 1×1, and CNet(·) represents a complex convolutional network.

[0023] The complex convolutional network includes an encoder part and a decoder part. The input data first passes through four encoding layers, each of which includes a complex multi-scale cascaded attention module and a complex convolution downsampling module. The output feature map of the encoder part passes through an intermediate layer composed of a complex double convolution residual module before entering the decoder part. The decoder part includes four decoding layers, each of which includes a complex upsampling, a complex attention gate and a complex double convolution residual module. The input of the first decoding layer is the output of the intermediate layer, the input of the subsequent decoding layer is the output of the previous decoding layer, and the output of the last decoding layer passes through an output layer composed of complex point-by-point convolution to obtain the output of the complex convolution network.

[0024] s3.1, the complex multi-scale cascade attention module includes a parallel ordinary convolution path, a dilated convolution path and a residual connection path. The residual connection path is used to avoid the gradient vanishing phenomenon, and the other two paths are used to extract multi-scale features under different receptive fields. The input of the complex multi-scale cascade attention module in the first coding layer is the undersampled image I u , the input of the complex multi-scale cascade attention module in the subsequent encoding layer is the output of the complex convolution downsampling module in the previous encoding layer.

[0025] The ordinary convolution path includes three consecutive complex convolution modules, a feature splicing module, and a convolutional block attention module (CBAM). Each complex convolution module includes a complex convolution, a complex batch normalization, and a complex activation function. The feature splicing module is used to process the output G of the three complex convolution modules. 1out , G 2out , G 3outSplicing is performed on the channel dimension, and then input into the convolution block attention module to obtain the output G of the ordinary convolution path out :

[0026] G out =CBAM[G 1out , G 2out , G 3out ] [5]

[0027] G 1out =CModReLU(CBN(I in *ω G1 )) [6]

[0028] G 2out =CModReLU(CBN(G 1out *ω G2 )) [7]

[0029] G 3out =CModReLU(CBN(G 2out *ω G3 )) [8]

[0030] Among them, [·,·] represents the concatenation in the channel dimension, ω G1 、ω G2 、ω G3 They are the complex convolution kernels of three complex convolution modules, with a size of 3x3, CBAM represents the convolution block attention module, CBN represents the complex batch normalization, and CModReLU represents the complex activation function.

[0031] The dilated convolution path replaces the complex convolution in the ordinary convolution path with a complex dilated convolution, and its output D out for:

[0032] D out =CBAM[D 1out , D 2out , D 3out ] [9]

[0033] D 1out =CModReLU(CBN(I in *ω D1 ))

[10]

[0034] D 2out =CModReLU(CBN(D 1out *ω D2 ))

[11]

[0035] D 3out =CModReLU(CBN(D 2out *ω D3))

[12]

[0036] D 1out 、D 2out 、D 3out Represent the outputs of the three complex dilated convolution modules, ω D1 、ω D2 、ω D3 is a complex dilated convolution kernel with a size of 3x3.

[0037] The residual connection path consists of a layer of complex point-wise convolution and a complex batch normalization (CBN), whose R out for:

[0038] R out =CBN(I in *ω R )

[13]

[0039] where ω R Represents a complex convolution kernel of size 1×1, I in Represents the input of the multi-scale cascade attention module. The output of the multi-scale cascade attention module I out The outputs of the three paths are added together and passed through CModReLU to obtain:

[0040] I 0ut =CModReLU(G out +D out +R out )

[14]

[0041] s3.2, the complex double convolution residual module adds a layer of residual complex point-by-point convolution on the basis of the complex double convolution module to prevent the gradient from disappearing:

[0042] M out =CModReLU(CBN(M in *ω m )+CDconv(M in ))

[15]

[0043] Among them, M in 、M out are the input and output of the complex double convolution residual module, ω m represents a complex convolution kernel of size 1×1, and CDconv(·) represents five layers of calculation: complex convolution, complex batch normalization, CModReLU, complex convolution, and complex batch normalization.

[0044] s3.3. In each decoding layer, the input data is firstly upsampled by complex numbers, and then the upsampled result F is up The output F of the multi-scale cascade attention module of the same level encoding layerdown Input them into the complex attention gate together, and then the output CA of the complex attention gate out After being concatenated with the complex upsampling result, it is input into the complex double convolution residual module to obtain the output of the decoding layer.

[0045] The multiple attention gate is a grid-based gating that adjusts the image features output by the upper encoding layer in the jump route through the output feature information of the lower decoding layer, thereby enhancing the extraction of local area features:

[0046] μ=CRS(CSigmoid(ψ(CModReLU((F up *ω1)+(F dow n*ω2)))))

[16]

[0047] CA out =F down ×μ

[17]

[0048] Among them, μ is the calculated attention mechanism coefficient, ω1 and ω2 are both complex convolution kernels of size 1×1, Ψ represents complex linear transformation, CRS represents complex resampling, which is used to convert the size of the feature map; Csigmoid represents the complex activation function.

[0049] Step 4: CMA-Net network training

[0050] The undersampled image I processed in step 1 u Figure 1 of the GRAPPA reconstruction from step 2 GRAPPA As input sample, reference image I ref As the corresponding label for network training, the complex mean square error function is selected as the loss function of the network back propagation, and the loss value of the output layer is calculated:

[0051]

[0052] in, is the network output, T represents the size of the batch data, Re(·) represents the real part, Im(·) represents the imaginary part, They represent the input ξth undersampled image and GRAPPA reconstruction image respectively.

[0053] Step 5: Data consistency replacement and image reconstruction

[0054] Use the CMA-Net network model trained in step 4 to predict the undersampled image and GRAPPA reconstruction image:

[0055] I pre =CMANet((I GRAPPA , I u )|θ)

[19]

[0056] Among them, θ represents the saved network model parameters, I pre Represents the prediction result. pre Fourier transform into k-space and use the undersampled data S u Perform data replacement to obtain the multi-channel complex reconstructed image Recon:

[0057] Recon=IDFT(S u +DFT(I pre )·*(1-mask))

[20]

[0058] Then the virtual coil synthesis method (VCoil) is used to synthesize the multi-channel complex reconstructed image Recon into a single-channel complex image Resnlt:

[0059]

[0060] Among them, z represents the coil number, N z is the total number of coil channels.

[0061] As a preference, assume that the convolution kernel of the complex convolution layer is W = W R +iW I , the input data is h = a + ib, a and b are real vectors, then the calculation of complex convolution is expressed as:

[0062] W*h=(a*W R -b*W I )+i(a*W I +b*W R ) [twenty two]

[0063] The calculation process of complex batch normalization CBN is:

[0064]

[0065]

[0066] in, To calculate the intermediate value, γ is the scaling matrix, β is the shift parameter, x is the input of complex batch normalization, V is the covariance matrix of the input, and E[·] represents the mean.

[0067] The calculation process of the complex activation function CModReLU is:

[0068]

[0069] Where q is a trainable parameter, |·| is the magnitude of the complex number, y represents the input data, and δ is the phase of the input data y.

[0070] Preferably, the convolutional block attention module includes channel attention and spatial attention, which are used to perform adaptive feature extraction on input image features:

[0071] F=F in ×W C

[26]

[0072] F out =F×W S

[27]

[0073] Among them F in 、F ou t represents the input and output of the convolutional block attention module, F is the calculated intermediate value, and W C is the channel attention weight, W S is the spatial attention weight:

[0074] W C =σ(MLP(AvgPool(F in ))+MLP(MaxPool(F in )))

[28]

[0075] W S =σ(f 7×7 ([AvgPool(F),MaxPool(F)]))

[29]

[0076] Among them, AvgPool and MaxPool are global average pooling and global maximum pooling respectively, MLP is a multi-layer perceptron, including convolution-activation-convolution three-layer calculation, f 7×7 () represents a convolution operation of size 7×7, and σ is the Sigmoid function.

[0077] The present invention has the following beneficial effects:

[0078] 1. The CMA-Net network is constructed based on complex number operations, which preserves the geometric correlation between the real and imaginary parts of the complex magnetic resonance data and can reconstruct both amplitude and phase images.

[0079] 2. The use of multiple multi-scale cascaded attention modules helps to obtain image features under different receptive fields and enhance the network's feature extraction capabilities. At the same time, combined with multiple attention gates, attention weights are further assigned to the extracted multi-scale features, suppressing unimportant features such as the image background while highlighting important features of interest, so that the extracted multi-scale features can be more reasonably utilized.

[0080] 3. Residual connections are used to combine the linear mapping of GRAPPA with the nonlinear mapping of the CNet network to further improve the reconstruction quality of the CNet network. At the same time, residual connections are added to the multiple multi-scale cascade attention module and the multiple double convolution residual module. Combined with the GRAPPA residual path, multi-angle residual is constructed to minimize the gradient vanishing problem in network training. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 It is a CMA-Net structure diagram of the present invention;

[0082] Figure 2 This is a diagram of the structure of a multi-scale cascade attention module;

[0083] Figure 3 This is a diagram of the structure of a plural attention gate;

[0084] Figure 4 are the amplitude-phase contrast and error maps of the complex image reconstruction example. DETAILED DESCRIPTION

[0085] A multi-channel magnetic resonance imaging method based on CMA-Net combines the linear mapping of GRAPPA with the nonlinear mapping of a deep learning network. The reconstruction results of the traditional algorithm GRAPPA are used for residual training to further improve the reconstruction quality of the deep learning network. Multi-scale convolution and attention mechanisms are used to obtain image features under different receptive fields, making it easier for the network to focus computing power on key areas of the image, strengthening the network's feature extraction, and effectively reducing artifacts in undersampled magnetic resonance images. The addition of multi-angle residuals greatly alleviates the gradient vanishing problem that is prone to occur in network training, and can reconstruct high-quality complex magnetic resonance images. The present invention is further explained below with reference to the accompanying drawings.

[0086] First, fully sampled k-space complex multi-channel data were downloaded from the public database (https: / / fastmri.med.nyu.edu / ). Then, undersampling was simulated using an undersampling template that sampled one line every five lines and fully sampled the central 40 lines. The undersampling data S was obtained. u , the reference image I in the image domain is obtained through inverse discrete Fourier transform ref and the undersampled image I u .

[0087] Establish as Figure 1 The CMA-Net network model shown includes a GRAPPA residual path and a complex convolutional network. In this embodiment, the complex point-by-point convolution of the CMA-Net network model has a convolution kernel size of 1×1, a stride of 1, and padding of 0. The remaining complex convolutions, unless otherwise specified, default to a complex convolution kernel size of 3×3, a stride of 1, and a padding of 1.

[0088] The input of the GRAPPA residual path is the undersampled k-space data S u , the central 40 rows of data are used as ACS data for GRAPPA reconstruction, and the GRAPPA reconstruction image I is obtained after inverse Fourier transform. GRAPPA , then I GRAPPA Perform a complex point-by-point convolution and output.

[0089] The complex convolutional network includes an encoder part and a decoder part. The input data first passes through four encoding layers, each of which includes a complex multi-scale cascaded attention module and a complex convolution downsampling module. The convolution kernel size of the downsampling complex convolution is 3×3, the stride is 2, and the padding is 1. The output feature map of the encoder part passes through an intermediate layer composed of a complex double convolution residual module before entering the decoder part. The decoder part includes four decoding layers, each of which includes a complex upsampling, a complex attention gate, and a complex double convolution residual module. The input of the first decoding layer is the output of the intermediate layer, the input of the subsequent decoding layer is the output of the previous decoding layer, and the output of the last decoding layer passes through an output layer composed of complex point-by-point convolution to obtain the output of the complex convolution network.

[0090] like Figure 2 As shown in Figure 1, the complex multi-scale cascade attention module includes a parallel ordinary convolution path, an expanded convolution path, and a residual connection path. The convolution of the residual path is a complex point-by-point convolution. The convolution of the ordinary convolution path and the expanded convolution path is ω. G1 、ω G2 、ω G3 The number of the three convolution kernels is 1 / 8, 3 / 8, and 4 / 8 of the number of output channels of the complex multi-scale cascade attention module, respectively. D1 、ω D2 、ω D3 The number of the three dilated convolution kernels is 1 / 8, 3 / 8, and 4 / 8 of the number of output channels of the complex multi-scale cascade attention module, respectively. The dilation coefficients are 1, 2, and 3, respectively, and the padding is 1, 2, and 3.

[0091] The structure of the plural attention gate is as follows Figure 3 As shown, where F up is the feature after complex upsampling, F down is the output feature of the complex multi-scale cascade attention module in the same layer. The two are subjected to complex point-by-point convolution, the number of convolution kernels is halved, and then the two are added together and sequentially passed through ModReLU, complex linear transformation Ψ, CSigmoid and complex resampling to obtain the attention weight μ. Finally, μ is combined with F down Multiply and assign weights to get the output of this module.

[0092] In this example, the complex mean square error function is selected as the loss function, the Adam algorithm is selected as the network optimization algorithm, and the training round epoch is set to 100. The experimental environment is: Intel i5-4460 16G memory, NVIDIA GeForce GTX1080 8G video memory, Python3.8.11, Pytorch1.9.1, CUDA10.2. The comparative experimental results are shown in Figure 2. Figure 4 Figure 2 shows the amplitude and phase images of the reconstruction results from zero-filling reconstruction, GRAPPA, U-Net, and our method. Each amplitude and phase image is accompanied by a corresponding error map to the right and a zoomed-in image below. The amplitude error maps clearly show that our method produces reconstructed images with fewer artifacts and higher image quality.

[0093] Normalized mean square error (NMSE), peak signal-to-noise ratio (PSNR), and structural similarity (SSIM) were selected as objective quantitative indicators to evaluate the quality of 148 reconstructed images. The evaluation results are shown in the following table:

[0094] Zero-fill reconstruction GRAPPA U-Net CMA-Net SSIM 0.7429 0.8218 0.9146 0.9240 PSNR 23.37 24.19 26.85 28.12 NMSE 0.005089 0.004074 0.002399 0.001779

[0095] The data in the table are the mean values ​​of the quantitative indicators for 148 reconstructed images. As can be seen from the table, the images reconstructed by this method have the smallest NMSE value, the largest PSNR value, and an SSIM value closer to 1, objectively demonstrating that the reconstruction results of this method are superior to those of other reconstruction algorithms.

Claims

1. A multi-channel magnetic resonance imaging method based on CMA-Net, characterized by: The specific steps include: Step 1: K-space data preprocessing For the fully sampled k-space complex multi-channel data S k Perform undersampling to obtain undersampling data S u , respectively for the full sampling data S k With undersampled data S u Perform inverse Fourier transform and complex normalization to obtain the reference image I ref With the undersampled image I u ; Step 2: GRAPPA reconstruction For undersampled data S u Perform GRAPPA reconstruction to obtain k-space reconstruction data S GRAPPA , and then perform inverse Fourier transform according to the channel to obtain the GRAPPA reconstruction image I in the image domain GRAPPA ; Step 3: Build the CMA-Net network model The CMA-Net network model includes a GRAPPA residual path and a complex convolutional network; the GRAPPA residual path is used to reconstruct Figure 1 GRAPPA The input is a simple feature extraction layer of complex point-by-point convolution and then output; the complex convolution network adopts a symmetric encoding-decoding structure; the CMA-Net network model adds the GRAPPA residual path and the output features of the complex convolution network as the final model output CMANet out ; The complex convolutional network includes an encoder part and a decoder part. The input data first passes through four encoding layers, each of which includes a complex multi-scale cascaded attention module and a complex convolution downsampling module; the output feature map of the encoder part passes through an intermediate layer composed of a complex double convolution residual module, and then enters the decoder part; the decoder part includes four decoding layers, each of which includes a complex upsampling, a complex attention gate and a complex double convolution residual module, where the input of the first decoding layer is the output of the intermediate layer, and the input of the subsequent decoding layer is the output of the previous decoding layer. The complex attention gate calculates attention for the output features of the complex multi-scale cascaded attention module and the complex upsampling at the same level; The output of the last decoding layer passes through an output layer consisting of complex point-by-point convolution to obtain the output of the complex convolutional network; Step 4: CMA-Net network training The undersampled image I processed in step 1 u Figure 1 of the GRAPPA reconstruction from step 2 GRAPPA As input sample, reference image I ref Use the corresponding labels to train the network, select the complex mean square error function as the loss function of the network back propagation, and calculate the loss value of the output layer; Step 5: Data consistency replacement and image reconstruction Use the CMA-Net network model trained in step 4 to predict the undersampled image and GRAPPA reconstruction image; the prediction result I pre Fourier transform into k-space and use the undersampled data S u Data replacement is performed to obtain a multi-channel complex reconstructed image Recon; then the virtual coil synthesis method is used to synthesize the multi-channel complex reconstructed image Recon into a single-channel complex image Result to complete the image reconstruction.

2. The multi-channel magnetic resonance imaging method based on CMA-Net according to claim 1, characterized in that: Define the undersampling template mask: Then the undersampled data S u for: S u =mask.*S k [2] Where ".*" represents dot product; S k Represents fully sampled k-space complex multi-channel data.

3. The multi-channel magnetic resonance imaging method based on CMA-Net according to claim 1, characterized in that: The complex multi-scale cascade attention module includes a parallel ordinary convolution path, an expansion convolution path and a residual connection path; the input of the complex multi-scale cascade attention module in the first coding layer is the undersampled image I u , the input of the complex multi-scale cascade attention module in the subsequent encoding layer is the output of the complex convolution downsampling module in the previous encoding layer.

4. The multi-channel magnetic resonance imaging method based on CMA-Net according to claim 3, characterized in that: The ordinary convolution path includes three consecutive complex convolution modules, a feature splicing module, and a convolution block attention module. Each complex convolution module includes a complex convolution, a complex batch normalization, and a complex activation function. The feature splicing module performs the output G of the three complex convolution modules. 1out , G 2out , G 3out Splicing is performed on the channel dimension, and then input into the convolution block attention module to obtain the output G of the normal convolution path out : G out =CBAM[G 1out ,G 2out ,G 3out ] [3] MR 1out =CModReLU(CBN(I in *ω G1 )) [4] G 2out =CModReLU(CBN(G 1out *ω G2 )) [5] G 3out =CModReLU(CBN(G 2out *ω G3 )) [6] Among them, [·,·] represents the splicing in the channel dimension, ω G1 、ω G2 、ω G3 They are the complex convolution kernels of three complex convolution modules, with a size of 3x3; CBAM represents the convolution block attention module, CBN represents the complex batch normalization, and CModReLU represents the complex activation function; The dilated convolution path replaces the complex convolution in the ordinary convolution path with a complex dilated convolution, and its output D out for: D out =CBAM[D 1out ,D 2out ,D 3out ] [7] d 1out =CModReLU(CBN(i in *ω D1 )) [8] D 2out =CModReLU(CBN(D 1out *ω D2 )) [9] D 3out =CModReLU(CBN(d 2out *ω D3 )) [10] D 1out 、D 2out 、D 3out Represent the outputs of the three complex dilated convolution modules, ω D1 、ω D2 、ω D3 is a complex dilated convolution kernel of size 3x3; The residual connection path consists of a layer of complex point-wise convolution and a complex batch normalization (CBN), whose R out for: R out =CBN(I in *ω R ) [11] where ω R Represents a complex convolution kernel of size 1×1, I in represents the input of the multi-scale cascade attention module; the output of the multi-scale cascade attention module I out The outputs of the three paths are added together and passed through CModReLU to obtain: I out =CModReLU(G out +D out +R out ) [12]。 5. The multi-channel magnetic resonance imaging method based on CMA-Net according to claim 1, characterized in that: The complex double convolution residual module adds a layer of residual complex point-by-point convolution on the basis of the complex double convolution module: M out =CModReLU(CBN(M in *ω)+CDconv(M in )) [13] Among them, M in 、M out are the input and output of the complex double convolution residual module respectively, and CDconv(·) represents the five-layer calculation of complex convolution, complex batch normalization, CModReLU, complex convolution, and complex batch normalization.

6. The multi-channel magnetic resonance imaging method based on CMA-Net according to claim 1, characterized in that: In each decoding layer, the input data is first complex upsampled, and then the upsampled result F up The output F of the multi-scale cascade attention module of the same level encoding layer down Input them into the complex attention gate together, and then the output CA of the complex attention gate out After concatenating with the complex upsampling result, it is input into the complex double convolution residual module to obtain the output of the decoding layer; The multiple attention gates adjust the image features output by the upper encoding layer in the jump route through the output feature information of the lower decoding layer: μ=CRS(CSigmoid(Ψ(CModReLU((F up *ω1)+(F down *ω2))))) [14] THAT out =F down ×μ [15] Among them, μ is the calculated attention mechanism coefficient, ω1 and ω2 are both complex convolution kernels of size 1×1, Ψ represents complex linear transformation, CRS represents complex resampling, which is used to convert the size of the feature map; Csigmoid represents the complex activation function.

7. The multi-channel magnetic resonance imaging method based on CMA-Net according to any one of claims 3 to 6, characterized in that: For the convolution kernel, W = W R +iW I The complex convolution layer, the input data of h = a + ib, the calculation of complex convolution is expressed as: W*h=(a*W R -b*W I )+i(a*W I +b*W R ) [16] Where a and b are real vectors; The calculation process of complex batch normalization CBN is: in, To calculate the intermediate value, γ is the scaling matrix, β is the shift parameter, x is the input of complex batch normalization, V is the covariance matrix of the input, and E[·] represents the mean; The calculation process of the complex activation function CModReLU is: Where q is a trainable parameter, |·| is the magnitude of the complex number, y represents the input data, and δ is the phase of the input data y.

8. The multi-channel magnetic resonance imaging method based on CMA-Net according to claim 1, characterized in that: The complex mean square error function is: in, is the network output, T represents the size of the batch data, Re(·) represents the real part, Im(·) represents the imaginary part, They represent the input ξth undersampled image and GRAPPA reconstruction image respectively.

9. The multi-channel magnetic resonance imaging method based on CMA-Net according to claim 4, characterized in that: The convolutional block attention module includes channel attention and spatial attention, which are used to perform adaptive feature extraction on input image features: F =F in ×W C [21] F out =F×W S [22] Among them F in 、F out Represent the input and output of the convolution block attention module respectively, F is the calculated intermediate value, W C is the channel attention weight, W S is the spatial attention weight: W C =σ(MLP(AvgPool(F in ))+MLP(MaxPool(F in ))) [23] W S =σ(f 7×7 ([AvgPool(F),MaxPool(F)])) [24] Among them, AvgPool and MaxPool are global average pooling and global maximum pooling respectively, MLP is a multi-layer perceptron, including convolution-activation-convolution three-layer calculation, f 7×7 () represents a convolution operation of size 7×7, and σ is the Sigmoid function.

10. A computer-readable storage medium having a computer program stored thereon, which, when executed in a computer, causes the computer to execute the method according to any one of claims 1 to 6, 8, and 9.

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