Intelligent reconstruction method for high-fidelity magnetic resonance sampling signals

Abstract

The application discloses an intelligent reconstruction method for high-fidelity magnetic resonance sampling signals, and comprises the following steps: firstly, collecting magnetic resonance sampling signals; constructing a training set composed of undersampled one-dimensional magnetic resonance sampling signals, corresponding one-dimensional undersampling templates and fully sampled one-dimensional magnetic resonance sampling signals according to signal characteristics, undersampling, Fourier transform and other operations; taking the former two as inputs of a network model and the latter as a label; designing a deep learning neural network structure by using an optimization algorithm for iteratively solving a low-rank model; alternately iterating the neural network structure and the optimization algorithm to form a final network structure; solving optimization parameters of the network by using the training set to form a reconstruction model; and finally inputting undersampled magnetic resonance sampling signals to be reconstructed into the trained network model to reconstruct the magnetic resonance sampling signals.

Description

TECHNICAL FIELD

[0001] The present application relates to a reconstruction method of magnetic resonance sampling signals, and in particular to a high-fidelity magnetic resonance sampling signal intelligent reconstruction method based on an alternating iterative deep learning network of a low-rank model. BACKGROUND

[0002] Magnetic resonance technology plays an indispensable role in modern life science, including magnetic resonance spectroscopy and magnetic resonance imaging. It is a non-invasive and non-radioactive imaging technology that provides high-quality images. Magnetic resonance spectroscopy is used to analyze the structure of chemical substances, and magnetic resonance imaging is used to display anatomical structure and physiological function. However, the sampling time of the magnetic resonance signal is relatively long, which restricts the further development of the technology. Sparse sampling shortens the scanning time by undersampling the space, but introduces strong artifacts. Therefore, high-fidelity reconstruction of undersampled magnetic resonance data containing strong artifacts is an important direction in fast magnetic resonance technology.

[0003] In the past 20 years, many methods based on optimization algorithms have been proposed for reconstructing magnetic resonance (MR) sampling signals, including 1) methods that impose sparsity constraints on the Fourier-transformed MR sampling signals (Xiaobo Qu, Xue Cao, Di Guo, and Zhong Chen, “Compressed sensing for sparse magnetic resonance spectroscopy,” in Proceedings of the International Society for Magnetic Resonance in Medicine Scientific Meeting, 2010, p. 3371) to improve the reconstruction performance. However, such methods are difficult to obtain good reconstruction results once the data after sparse transformation does not have significant sparsity. 2) methods that impose low-rank constraints directly on the MR sampling signals (Xiaobo Qu, Maxim Mayzel, Jian-Feng Cai, Zhong Chen, and Vladislav Orekhov, “Accelerated NMR spectroscopy with low-rank reconstruction,” Angewandte Chemie-International Edition, vol. 54, no. 3, pp. 852-854, 2015; Xinlin Zhang, Hengfa Lu, Di Guo, Zongying Lai, Huihui Ye, Xi Peng, Bo Zhao, and Xiaobo Qu, “Accelerated MRI reconstruction with separable and enhanced low-rank Hankel regularization,” IEEE Transactions on Medical Imaging, vol. 41, no. 9, pp. 2486-2498, 2022), which, although improving the quality of reconstruction, usually need to rely on time-consuming singular value decomposition, resulting in too long reconstruction time.Although it can be accelerated by matrix decomposition method (Di Guo, Hengfa Lu, and Xiaobo Qu, "A fast low rank Hankel matrix factorization reconstruction method for non-uniformly sampled magnetic resonance spectroscopy," IEEE Access, vol. 5, pp. 16033-16039, 2017), it still cannot be reconstructed in real time. At the same time, like the above method, the parameter selection of its algorithm is very dependent on the experience of the user.

[0004] Recently, deep learning has shown strong capability in the reconstruction of fast magnetic resonance sampling signals by using convolutional neural networks (Xiaobo Qu, Yihui Huang, Hengfa Lu, Tianyu Qiu, Di Guo, Tatiana Agback, Vladislav Orekhov, and Zhong Chen, "Accelerated nuclear magnetic resonance spectroscopy with deep learning," Angewandte Chemie-International Edition, vol. 59, no. 26, pp. 10297-10300, 2020; Yihui Huang, Jinkui Zhao, Zi Wang, Vladislav Orekhov, Di Guo, and Xiaobo Qu, "Exponential signal reconstruction with deep Hankel matrix factorization," IEEE Transactions on Neural Networks and Learning Systems, 2021, doi:10.1109 / TNNLS.2021.3134717; Zi Wang, Chen Qian, Di Guo, Hongwei Sun, Rushuai Li, Bo Zhao, and Xiaobo Qu, "One-dimensional deep low-rank and sparse network for accelerated MRI," IEEE Transactions on Medical Imaging, 2022, doi:10.1109 / TMI.2022.3203312). However, the parameter learning process of the neural network model is heavily dependent on the characteristics and distribution of the training data. When using a trained neural network model to reconstruct data different from the characteristics of the training data, its reconstruction capability is greatly reduced.

[0005] In summary, in the reconstruction of magnetic resonance sampling signals, the reconstruction quality and generalization performance of existing reconstruction methods need to be improved, and there is no simultaneous use of deep learning and optimization algorithm to establish an alternating iterative deep learning network based on a low-rank model to realize an intelligent reconstruction method of fast, high-fidelity and good generalization of magnetic resonance sampling signals. SUMMARY

[0006] The application aims to provide a high-fidelity magnetic resonance sampling signal intelligent reconstruction method with rapidness and good generalization.

[0007] The application comprises the following steps:

[0008] 1) obtaining a full-sampling one-dimensional magnetic resonance sampling signal, i.e. time-domain data of a simulated one-dimensional magnetic resonance spectrum or k-space data of a real-sampling one-dimensional multi-channel magnetic resonance imaging;

[0009] 2) performing a zero-filling operation on the uncollected data positions according to an actual undersampling template to generate a zero-filled one-dimensional magnetic resonance sampling signal;

[0010] 3) taking the full-sampling signal in step 1) as an artificial intelligence network output, taking the undersampling signal and undersampling template in step 2) as network inputs to form a training set;

[0011] 4) designing an alternating iterative deep learning network model based on a low-rank model, a loss function and a network feedback function;

[0012] 5) solving a set of learnable parameters of the alternating iterative deep learning network based on the low-rank model by using the training set obtained in step 3) to complete neural network training;

[0013] 6) inputting an undersampling signal of a magnetic resonance to be reconstructed into the trained network to reconstruct a complete magnetic resonance signal.

[0014] In step 1), the full-sampling one-dimensional magnetic resonance sampling signal, i.e. time-domain data of a simulated one-dimensional magnetic resonance spectrum or k-space data of a real-sampling one-dimensional multi-channel magnetic resonance imaging, is obtained, and the specific method is as follows:

[0015] For obtaining time-domain data of a simulated one-dimensional magnetic resonance spectrum, full-sampling one-dimensional magnetic resonance spectrum time-domain data can be simulated and generated according to an exponential function model The expression is as follows:

[0016]

[0017] wherein, represents a complex vector with a length of N, J represents the number of exponential functions, j=1,…,J represents the index of the number of exponential functions, n=0,…,N-1 represents the index of the sampling point number of the one-dimensional magnetic resonance spectrum time-domain data x, Δt represents a time interval, A j , φ j , τ j and f j respectively represent the amplitude, phase, attenuation factor and normalized frequency of the jth exponential function;

[0018] For acquiring the k-space data of the full-sampling one-dimensional multi-channel magnetic resonance imaging, first, the k-space data of the full-sampling multi-coil magnetic resonance imaging is obtained from a magnetic resonance imaging scanner wherein M, Z and C represent the length of the frequency encoding dimension, the length of the phase encoding dimension and the number of channels respectively; performing one-dimensional inverse Fourier transform along the frequency encoding dimension to obtain the multi-channel magnetic resonance imaging hybrid spatial data wherein represents the one-dimensional multi-channel magnetic resonance imaging hybrid spatial data of the mth row; the multi-channel magnetic resonance imaging hybrid spatial data E is split into M pieces of the k-space data of the full-sampling one-dimensional multi-channel magnetic resonance imaging along the frequency encoding dimension

[0019] The time-domain data x of the full-sampling one-dimensional magnetic resonance spectrum and the k-space data K of the full-sampling one-dimensional multi-channel magnetic resonance imaging are collectively referred to as the full-sampling one-dimensional magnetic resonance sampling signal

[0020] In step 2), the zero-filling operation is performed on the unacquired data positions according to the actual undersampling template to generate the zero-filled one-dimensional magnetic resonance sampling signal, specifically:

[0021] The undersampling operation is performed on the magnetic resonance sampling signal to obtain the undersampling one-dimensional magnetic resonance sampling signal Specifically, the time-domain data x of the undersampling one-dimensional magnetic resonance spectrum or the k-space data K of the undersampling one-dimensional multi-channel magnetic resonance imaging

[0022] In step 3), the full-sampling signal of step 1) is taken as the artificial intelligence network output, and the undersampling signal and the undersampling template in step 2) are taken as the network input to constitute a training set, specifically the training set is composed of the full-sampling one-dimensional magnetic resonance sampling signal the undersampling operation and the undersampling one-dimensional magnetic resonance sampling signal .

[0023] In step 4), the alternating iterative deep learning network model based on the low-rank model is composed of iteration blocks, and a plurality of iteration blocks are stacked in series as the entire network structure, each iteration block is composed of a sub-block P, a sub-block Q, a sub-block S and a sub-block O, and the variables P k+1 , Q k+1 , are updated in turn, wherein the sub-block P, the sub-block Q and the sub-block S constitute a deep learning module, and the sub-block O is referred to as an optimization module; as shown by taking the kth iteration block as an example:

[0024] a) Sub-block P is used to update the network variable solved based on low-rank priori It is composed of L layers of dense two-dimensional convolutional neural networks, and the size of the convolution kernel is SxS, which is used to learn the nonlinear mapping function The input variable of each layer is sequentially input into a two-dimensional convolution module and a linear rectifier function, and finally input into the next layer; the input of the first layer is Wherein Hankel operator, which converts one-dimensional magnetic resonance sampling signals into a Hankel matrix; Q k are the output variables of the previous iteration block. The set of historical information of matrix P is represented by P. The output of the dense two-dimensional convolutional neural network is added to the updated variable P k of the previous iteration block, and the final output of the entire sub-block P is obtained. The complete sub-block P is represented by the following nonlinear mapping function:

[0025]

[0026] Wherein, represents the nonlinear mapping function trained by the dense two-dimensional convolutional neural network in the sub-block P in the kth iteration block, represents the parameter set of the neural network;

[0027] b) Sub-block Q is used to update the network variable solved based on low-rank priori The structure is similar to sub-block P and is composed of L layers of dense two-dimensional convolutional neural networks, and the size of the convolution kernel is SxS, which is used to learn the nonlinear mapping function The input variable of each layer is sequentially input into a two-dimensional convolution module and a linear rectifier function, and finally input into the next layer; the input of the first layer is Wherein the superscript H represents the complex conjugate operation, is the output variable of the sub-block P of the iteration block; The set of historical information of matrix Q is represented by Q. The output of the dense two-dimensional convolutional neural network is added to the updated variable Q k of the previous iteration block, and the final output of the entire sub-block Q is obtained. The complete sub-block Q is represented by the following nonlinear mapping function:

[0028]

[0029] Wherein, represents the nonlinear mapping function trained by the dense two-dimensional convolutional neural network in the sub-block Q in the kth iteration block, represents the parameter set of the neural network;

[0030] c) Sub-block S is used to update the network variable solved based on data checking operation Data check operation is used to keep intermediate variables and undersampled one-dimensional magnetic resonance sampling signals consistency, wherein represents an inverse Hankel operator, which converts the matrix into one-dimensional magnetic resonance sampling signals, represents a zero padding operation. represents a trainable regularization parameter in the data check operation, whose mapping function is represented as:

[0031]

[0032] wherein the mapping function at the index value n is specifically:

[0033]

[0034] d) Sub-block O is used to update the network variable P solved by the low-rank optimization solver k+1 , Q k+1 , The input variables of which include the output variables of the sub-block Q in the current iteration block the output variables of the sub-block S and undersampled one-dimensional magnetic resonance sampling signals variable β k and λ k is a trainable regularization parameter, whose mapping function is represented as:

[0035]

[0036] The specific form of which is:

[0037]

[0038] wherein I represents a unit matrix, (·) -1 represents an inverse operation on the matrix;

[0039] In summary, the above four sub-blocks P, Q, S and O are cascaded, and then a single iteration block can be represented by the following nonlinear mapping function:

[0040]

[0041] wherein θ k represents the parameter set of all sub-blocks of the kth iteration block; f represents the input variable P k , Q k , to the output variable Pk+1 Q k+1 , The nonlinear mapping function is a combination of function mappings of sub-blocks P, Q, S and O, and C(·) represents the cascading operation of the sub-blocks.

[0042] The initial input variables of the designed alternating iterative deep learning network model based on a low-rank model are obtained by Singular Value Decomposition (SVD):

[0043]

[0044] P 1 =U∑ 0.5

[0045] Q 1 =V H ∑ 0.5

[0046]

[0047] Finally, from the undersampled one-dimensional magnetic resonance sampling signal The entire network model, consisting of K iteration blocks, outputs the reconstructed one-dimensional magnetic resonance sampling signal. It can be represented as:

[0048]

[0049] Where F(·) represents the nonlinear mapping function of the network model consisting of all cascaded iterative blocks, and θ represents the parameter set of the entire network model.

[0050] The loss function of the network consists of the loss functions of each of the K iteration blocks. and constitute:

[0051]

[0052] Specifically, it is expressed as follows:

[0053]

[0054]

[0055] Where ∑ represents the summation operation, k represents the k-th iteration block, k = 1, 2, ..., K, ||·||2 represents the L2 norm term, and α is the regularization parameter.

[0056] The feedback function of the network is an important process to solve the parameter set of the network model. In the process of constructing the network model, according to the loss function of the network, the reconstructed one-dimensional magnetic resonance sampling signal output by the network model Compared with the full-sampling one-dimensional magnetic resonance sampling signal The feedback gradient is updated to update all parameters of the iteration block, so that the output value of the network model gradually approaches the full-sampling one-dimensional magnetic resonance sampling signal.

[0057] In step 5), the solved low-rank model-based alternating iterative deep learning network learning parameter set is trained by using the training set obtained in step 3) by using the Adam optimizer which performs well in deep learning, and the loss function in step 4) is minimized To get the optimal learning parameter set That is, the trained network model is obtained.

[0058] In step 6), the undersampled magnetic resonance sampling signal to be reconstructed is input into the trained network model for magnetic resonance sampling signal reconstruction, and the specific method is as follows:

[0059] a) Separate the undersampled magnetic resonance sampling signal to be reconstructed into a plurality of rows of undersampled one-dimensional magnetic resonance sampling signals to be reconstructed, as follows:

[0060] For the time-domain data of the undersampled magnetic resonance spectrum to be reconstructed, the length of the direct dimension and the indirect dimension is A and B respectively The Fourier transform is performed along the direct dimension to obtain the magnetic resonance spectrum mixed space data, and the undersampled one-dimensional magnetic resonance spectrum time-domain data is separated along the direct dimension

[0061] For the k-space data of the undersampled multi-coil magnetic resonance imaging to be reconstructed, the length of the frequency encoding dimension, the phase encoding dimension and the channel number is C, D and E respectively Inverse Fourier transform is performed along the frequency encoding dimension to obtain multi-channel magnetic resonance imaging mixed space data, and C rows of undersampled one-dimensional multi-channel magnetic resonance imaging k-space data are separated along the frequency encoding dimension

[0062] The undersampled one-dimensional magnetic resonance spectrum time-domain data to be reconstructed And the undersampled one-dimensional multi-channel magnetic resonance imaging k-space data to be reconstructed are collectively referred to as undersampled one-dimensional magnetic resonance sampling signals to be reconstructed

[0063] b) Each row of undersampled one-dimensional magnetic resonance sampling signals to be reconstructed input the network model F(·) constructed in step 2) and use the set of learnable parameters obtained in step 3) output the reconstructed one-dimensional magnetic resonance sampling signal The process is represented as

[0064]

[0065] c) splice each row of the reconstructed one-dimensional magnetic resonance sampling signal into a complete reconstructed magnetic resonance mixed space data and convert into the required data form. Specifically, a Fourier transform along the indirect dimension on the complete reconstructed magnetic resonance spectral mixed space data can obtain complete reconstructed magnetic resonance spectral frequency domain data, and an inverse Fourier transform along the phase encoding dimension on the complete reconstructed multi-channel magnetic resonance imaging mixed space data can obtain complete reconstructed multi-channel magnetic resonance imaging data.

[0066] The present application proposes an intelligent reconstruction method of high-fidelity magnetic resonance sampling signal. First, the magnetic resonance sampling signal is collected, and according to the signal characteristics, the operations such as undersampling and Fourier transform are performed to construct a training set composed of undersampled one-dimensional magnetic resonance sampling signal, corresponding one-dimensional undersampling template and fully sampled one-dimensional magnetic resonance sampling signal. The former two are the input of the network model, and the latter is the label; the optimization algorithm of the low-rank model iterative solution designs a deep learning neural network structure, alternately iterates the neural network structure and the optimization algorithm, constructs the final network structure, and solves the optimization parameters of the network with the above training set to construct the reconstruction model; finally, the undersampled magnetic resonance sampling signal to be reconstructed is input into the trained network model to reconstruct the magnetic resonance sampling signal.

[0067] The present application combines the advantages of deep learning and traditional optimization algorithm, not only retains the former fast reconstruction time performance, but also has the reliable theoretical support of the latter, and has better results than the leading deep learning algorithm (Yihui Huang, Jinkui Zhao, Zi Wang, Vladislav Orekhov, Di Guo, and Xiaobo Qu, "Exponential signal reconstruction with deep Hankel matrix factorization," IEEE Transactions on Neural Networks and Learning Systems, 2021, doi: 10.1109 / TNNLS.2021.3134717; Zi Wang, Chen Qian, Di Guo, Hongwei Sun, Rushuai Li, Bo Zhao, and Xiaobo Qu, "One-dimensional deep low-rank and sparse network for accelerated MRI," IEEE Transactions on Medical Imaging, 2022, doi: 10.1109 / TMI.2022.3203312) in reconstruction quality, and improves the generalization. The present application designs an alternating iterative deep learning and optimization algorithm network model by constraining the low rank of the magnetic resonance sampling signal, which has the characteristics of fast reconstruction, high quality and strong generalization. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 It is an alternating iterative deep learning network model based on a low rank model. Wherein, (a) is the overall framework of the present application; (b) is the structural block diagram of the deep learning module, including sub-blocks P, Q and S; (c) is a dense two-dimensional convolutional neural network.

[0069] Figure 2Reconstructed spectra of the two-dimensional magnetic resonance full-sampling tag spectra and the model trained using the training set of 25% sampling rate at 50% sampling rate. Among them, (a) is the full-sampling tag spectrum, (b) is the under-sampling template of 50% sampling rate used in the reconstruction of the magnetic resonance spectrum, (c) is the reconstructed spectrum of the state-of-the-art deep learning algorithm (Yihui Huang, Jinkui Zhao, Zi Wang, Vladislav Orekhov, Di Guo, and Xiaobo Qu, "Exponential signal reconstruction with deep Hankel matrix factorization," IEEE Transactions on Neural Networks and Learning Systems, 2021, doi:10.1109 / TNNLS.2021.3134717), and (d) is the reconstructed spectrum of the present application.

[0070] Figure 3 Brain reconstructed images of the two-dimensional magnetic resonance full-sampling tag images and the model trained using the training set of 25% sampling rate of the knee at 25% sampling rate. Among them, (a) is the full-sampling tag image, (d) is the under-sampling template of 25% sampling rate used in the reconstruction of the magnetic resonance imaging, (b) and (e) are the reconstructed images and the corresponding five-fold magnification error maps of the state-of-the-art deep learning algorithm (Zi Wang, Chen Qian, Di Guo, Hongwei Sun, Rushuai Li, Bo Zhao, and Xiaobo Qu, "One-dimensional deep low-rank and sparse network for accelerated MRI," IEEE Transactions on Medical Imaging, 2022, doi:10.1109 / TMI.2022.3203312), and (c) and (f) are the reconstructed images and the corresponding five-fold magnification error maps of the present application. DETAILED DESCRIPTION

[0071] The following embodiments will further illustrate the present application in conjunction with the accompanying drawings. The embodiments of the present application construct a training set using magnetic resonance sampling signals, obtain an optimal set of network parameters through several iterations of training, and finally input the under-sampled magnetic resonance sampling signals to be reconstructed into the trained deep learning network model to obtain the reconstructed magnetic resonance sampling signals.

[0072] The following gives specific embodiments according to the reconstruction of the time-domain data of the magnetic resonance spectrum and the reconstruction of the k-space data of the multi-coil magnetic resonance imaging.

[0073] The embodiment for reconstruction of time-domain data of magnetic resonance spectrum includes the following steps:

[0074] First step: obtaining full-sampling one-dimensional magnetic resonance spectrum time-domain data;

[0075] The embodiment uses an exponential function model to simulate one-dimensional magnetic resonance spectrum time-domain data. For each full-sampling one-dimensional magnetic resonance spectrum time-domain data, the expression is:

[0076]

[0077] In the embodiment, for each one-dimensional magnetic resonance spectrum time-domain data x, n=0,…,N-1 represents the index of the sampling point number of the one-dimensional magnetic resonance spectrum time-domain data x, and j=1,…,J represents the index of the number of exponential functions. The specific parameters are: data length N=255, time interval Δt=1. For the jth exponential function, the amplitude A j ∈(0.05,1], the phase φ j ∈(0,2π], the attenuation factor τ j ∈(10,180], and the normalized frequency f j ∈(0,1], and are randomly generated according to a uniform probability distribution. For each exponential number J, 4000 one-dimensional magnetic resonance spectrum time-domain data are generated. The embodiment uses a total of J=1,…,10 exponential numbers, and a total of 40000 one-dimensional magnetic resonance spectrum time-domain data are generated.

[0078] Second step: performing a zero-filling operation on the uncollected data positions according to the actual undersampling template to generate zero-filled one-dimensional magnetic resonance spectrum time-domain data;

[0079] The one-dimensional magnetic resonance spectrum time-domain data is subjected to an undersampling operation with a sampling rate of 25% to obtain the undersampling one-dimensional magnetic resonance spectrum time-domain data

[0080] Third step: taking the full-sampling magnetic resonance spectrum time-domain data of the first step as the artificial intelligence network output, taking the undersampling magnetic resonance spectrum time-domain data and the undersampling template in the second step as the network input, and constituting a training set:

[0081] The training set is composed of 40000 full-sampling one-dimensional magnetic resonance spectrum time-domain data x, corresponding undersampling operations and undersampling one-dimensional magnetic resonance spectrum time-domain data y.

[0082] Fourth step: designing an alternating iterative deep learning network model based on a low-rank model, a loss function, and a network feedback function.

[0083] The deep learning model is composed of iterative blocks, and each iterative block is composed of sub-block P, sub-block Q, sub-block S and sub-block O by stacking several iterative blocks in series as the whole network structure, and the variables are updated in turn P k+1 , Q k+1 , x k+1 . Wherein the sub-block P, the sub-block Q and the sub-block S constitute a deep learning module, and the sub-block O is called an optimization module. Taking the kth iterative block as an example:

[0084] a) Sub-block P is used to update the network variable solved based on low-rank priori It is composed of 4 layers of dense two-dimensional convolutional neural network, and the size of the convolution kernel is 3*3, which is used to learn the nonlinear mapping function The input variable of each layer is sequentially input into a two-dimensional convolution module and a linear rectifier function, and finally input into the next layer. The input of the first layer is Wherein represents the Hankel operator, which converts the time domain data of one-dimensional magnetic resonance spectrum into a Hankel matrix. x k , Q k are the output variables of the previous iterative block. represents the set of historical information of matrix P. The output of the dense two-dimensional convolutional neural network is added to the updated variable P k of the previous iterative block, that is, the final output of the whole sub-block P is obtained. The complete sub-block P is represented by the following nonlinear mapping function:

[0085]

[0086] Wherein, represents the nonlinear mapping function trained by the dense two-dimensional convolutional neural network in the sub-block P in the kth iterative block, represents the parameter set of the neural network.

[0087] b) Sub-block Q is used to update the network variable solved based on low-rank priori The structure is similar to sub-block P, which is composed of 4 layers of dense two-dimensional convolutional neural network, and the size of the convolution kernel is 3*3, which is used to learn the nonlinear mapping function The input variable of each layer is sequentially input into a two-dimensional convolution module and a linear rectifier function, and finally input into the next layer. The input of the first layer is Wherein the superscript H represents the complex conjugate operation, is the output variable of the sub-block P of the iterative block. represents the set of historical information of matrix Q. The output of the dense two-dimensional convolutional neural network is added to the updated variable Q kThe addition, i.e. the final output of the whole sub-block Q, is obtained. The complete sub-block Q is represented by the following non-linear mapping function:

[0088]

[0089] wherein, denotes the non-linear mapping function trained by the dense 2D convolutional neural network in the sub-block Q in the k-th iteration block, denotes the parameter set of the neural network.

[0090] c) The sub-block S is used to update the network variable solved by the data consistency operation The data consistency operation is used to maintain the intermediate variable and the consistency of the time-domain data y of the undersampled one-dimensional magnetic resonance spectrum on the sampling position Ω, wherein denotes the inverse Hankel operator, which converts the matrix into the time-domain data of the one-dimensional magnetic resonance spectrum, denotes the zero padding operation. denotes the trainable regularization parameter in the data consistency operation. Its mapping function denotes:

[0091]

[0092] wherein the specific form of the mapping function at the index value n is:

[0093]

[0094] d) The sub-block is used to update the network variable P solved by the low-rank optimization solver k+1 , Q k+1 , x k+1 . The input variables include the output variable of the sub-block Q in the current iteration block The output variable of the sub-block S and the time-domain data y of the undersampled one-dimensional magnetic resonance spectrum. The variables β k and λ k are trainable regularization parameters. Its mapping function denotes:

[0095]

[0096] The specific form represented by it is:

[0097]

[0098] wherein I denotes the unit matrix, (·) -1 denotes the inverse operation on the matrix.

[0099] In summary, by cascading the four sub-blocks P, Q, S, and O, a single iterative block can be represented by the following nonlinear mapping function:

[0100]

[0101] Where, θ k The parameter set of all sub-blocks of the k-th iteration block is represented by f; the input variable P of the iteration block is represented by f. k Q k ,x k ,y to output variable P k+1 Q k+1 ,x k+1 The nonlinear mapping function is a combination of function mappings for sub-blocks P, Q, S, and O. C(·) denotes the cascading operation of sub-blocks.

[0102] The initial input variables of the designed alternating iterative deep learning network model based on a low-rank model are obtained by Singular Value Decomposition (SVD):

[0103]

[0104] P 1 =U∑ 0.5

[0105] Q 1 =V H ∑ 0.5

[0106]

[0107] Finally, the reconstructed one-dimensional magnetic resonance spectrum time-domain data is output from the network model consisting of K=10 iteration blocks, based on the undersampled one-dimensional magnetic resonance spectrum time-domain data y. It can be represented as:

[0108]

[0109] Where F(·) represents the nonlinear mapping function of the network model composed of all cascaded iterative blocks, and θ represents the parameter set of the entire network model, the specific structure of which is as follows: Figure 1 As shown. In this embodiment, K = 10.

[0110] The loss function of the network consists of the loss functions of each of the 10 iteration blocks. and constitute:

[0111]

[0112] Specifically represented as:

[0113]

[0114]

[0115] where ∑ denotes summation operation, k denotes the kth iteration block, k = 1, 2, …, K, ||·||2denotes the two-norm term, and a is a regularization parameter. In this embodiment, K = 10 and a = 10 -2 .

[0116] The feedback function of the network is an important process for solving the parameter set of the network model. In the process of constructing the network model, according to the loss function of the network, the time domain data of the reconstructed one-dimensional magnetic resonance spectrum output by the network model are compared with the time domain data x of the fully sampled one-dimensional magnetic resonance spectrum, and the gradient is fed back to update all the parameters of the iteration block, so that the output value of the network model gradually approximates the time domain data of the fully sampled one-dimensional magnetic resonance spectrum.

[0117] Step 5: Using the training set obtained in step 3, solve the learnable parameter set of the alternating iterative deep learning network based on the low-rank model, and complete the neural network training.

[0118] The Adam optimizer (Diederik Kingma and Jimmy Ba, “Adam: A method for stochastic optimization,” arXiv:1412.6980, 2014.) well-performing in deep learning is adopted, and the training set obtained in step 3 is used for network training, so as to minimize the loss function in step 4 to obtain the optimal learnable parameter set , that is, the trained network model.

[0119] Step 6: Input the time domain data of the magnetic resonance spectrum to be reconstructed into the trained network to reconstruct the complete time domain data of the magnetic resonance spectrum.

[0120] For the to-be-reconstructed undersampled magnetic resonance spectrum time domain data with the length of direct dimension and indirect dimension being 1466 and 169 respectively Fourier transform is performed along the direct dimension to obtain magnetic resonance spectrum mixed space data, and the undersampled one-dimensional magnetic resonance spectrum time domain data is separated along the direct dimension

[0121] Then, each row of the to-be-reconstructed undersampled one-dimensional magnetic resonance spectrum time domain data is input into the network model F(·) constructed in step 4, and the learnable parameter set obtained in step 5 is used Output time-domain data of the reconstructed one-dimensional magnetic resonance spectrum. This process is represented as

[0122]

[0123] Finally, the time-domain data of each row of the reconstructed one-dimensional magnetic resonance spectrum are... By stitching together the complete reconstructed magnetic resonance spectrum mixed spatial data, and performing a Fourier transform along the indirect dimension, the complete reconstructed magnetic resonance spectrum frequency domain data can be obtained.

[0124] In this embodiment, the network input is a 50% sampling rate (undersampled template such as...). Figure 2 As shown in (b). In Figure 2 (b) In the undersampled template, white represents sampling points, indicating that the data corresponding to that position has been sampled; black represents points that were not sampled, and the data corresponding to that position is lost. This is the time-domain data of the undersampled magnetic resonance spectrum. The frequency domain data of the fully sampled magnetic resonance spectrum and the frequency domain data reconstructed by this invention at a 50% sampling rate are respectively as follows: Figure 2 (a) and Figure 2 (d)

[0125] It can be seen that the high-fidelity intelligent reconstruction method for magnetic resonance sampling signals using alternating iterative deep learning based on low-rank models can quickly reconstruct high-quality magnetic resonance spectra, and the reconstructed spectra are superior to those of state-of-the-art deep learning algorithms (Y. Huang, J. Zhao, Z. Wang, V. Orekhov, D. Guo, and X. Qu, "Exponential signal reconstruction with deep Hankel matrix factorization," IEEE Transactions on Neural Networks and Learning Systems, 2021, doi:10.1109 / TNNLS.2021.3134717.). Figure 2 (c)).

[0126] The reconstruction of k-space data from multi-coil magnetic resonance imaging includes the following steps:

[0127] Step 1: Obtain k-space data from actual one-dimensional multi-channel magnetic resonance imaging;

[0128] In this embodiment, an MRI scanner with a magnetic resonance imaging (MRI) field strength of 3 Tesla was used to image the knees of 13 volunteers. The MRI sequence parameters used in this embodiment were: echo time TE = 27 ms, repetition time TR = 2750 ms, and field of view size 160 × 126 mm. 2, and the layer thickness is 3mm. 273 k-space data of knee multi-coil from 13 volunteers after scanning by MRI instrument are used as the source of the training set of the network.

[0129] Each full-sampling multi-coil MRI k-space data obtained from the MRI scanner is represented as That is, the frequency encoding dimension length of the data is 320, the phase encoding dimension length is 314, and the number of channels is 15. Then, one-dimensional inverse Fourier transform is performed along the frequency encoding dimension to obtain multi-channel MRI mixed spatial data wherein represents the one-dimensional multi-channel MRI mixed spatial data of the mth row. Finally, each multi-channel MRI mixed spatial data E is split into 320 full-sampling one-dimensional multi-channel MRI k-space data along the frequency encoding dimension Finally, there are 87360 full-sampling one-dimensional multi-channel MRI k-space data.

[0130] Second step: zero-filling operation is performed on the uncollected data positions according to the actual undersampling template to generate zero-filled one-dimensional multi-channel MRI k-space data.

[0131] The multi-channel MRI k-space data is subjected to an undersampling operation with a sampling rate of 25% to obtain undersampled one-dimensional multi-channel MRI k-space data

[0132] Third step: the full-sampling one-dimensional multi-channel MRI k-space data of the first step is used as the output of the artificial intelligence network, and the undersampled one-dimensional multi-channel MRI k-space data and the undersampling template in the second step are used as the input of the network to form a training set:

[0133] The training set is composed of 87360 full-sampling one-dimensional multi-channel MRI k-space data K, corresponding undersampling operation and undersampled one-dimensional multi-channel MRI k-space data Y.

[0134] Fourth step: design an alternating iterative deep learning network model based on a low-rank model, a loss function, and a network feedback function.

[0135] The deep learning model is composed of iteration blocks, and a plurality of iteration blocks are stacked in series as the entire network structure, each iteration block is composed of a sub-block P, a sub-block Q, a sub-block S and a sub-block O, and the variables P k+1 , Q k+1 , K k+1. Wherein the sub-block P, sub-block Q and sub-block S constitute a deep learning module, and the sub-block O is referred to as an optimization module. Take the kth iteration block as an example:

[0136] a) The sub-block P is used for updating the network variable solved based on a low-rank priori , which is composed of 4 layers of dense two-dimensional convolutional neural networks, and the size of the convolution kernel is 3*3, which is used for learning a nonlinear mapping function The input variable of each layer is sequentially subjected to a two-dimensional convolution module and a linear rectifier function, and finally input to the next layer. The input of the first layer is , wherein represents a Hankel operator, which converts the k-space data of one-dimensional multi-channel magnetic resonance imaging into a Hankel matrix. K k , Q k are output variables of the previous iteration block. represents a set of historical information of the matrix P. The output of the dense two-dimensional convolutional neural network is added to the updated variable P k of the previous iteration block, so as to obtain the final output of the entire sub-block P. The complete sub-block P is expressed by the following nonlinear mapping function:

[0137]

[0138] , wherein represents a nonlinear mapping function trained by the dense two-dimensional convolutional neural network in the sub-block P in the kth iteration block, represents a parameter set of the neural network.

[0139] b) The sub-block Q is used for updating the network variable solved based on a low-rank priori The structure is similar to the sub-block P and is composed of 4 layers of dense two-dimensional convolutional neural networks, and the size of the convolution kernel is 3*3, which is used for learning a nonlinear mapping function The input variable of each layer is sequentially subjected to a two-dimensional convolution module and a linear rectifier function, and finally input to the next layer. The input of the first layer is , wherein the superscript H represents a complex conjugate operation, is an output variable of the sub-block P of the iteration block. represents a set of historical information of the matrix Q. The output of the dense two-dimensional convolutional neural network is added to the updated variable Q k of the previous iteration block, so as to obtain the final output of the entire sub-block Q. The complete sub-block Q is expressed by the following nonlinear mapping function:

[0140]

[0141] , wherein represents a nonlinear mapping function trained by the dense two-dimensional convolutional neural network in the sub-block Q in the kth iteration block, denotes the set of parameters of the neural network.

[0142] c) Sub-block S is used to update the network variable P solved by the data consistency operation Data consistency operation is used to keep the intermediate variable and the consistency of the k-space data Y of undersampled one-dimensional multi-channel magnetic resonance imaging on the sampling position Ω, where denotes the inverse Hankel operator, which converts the matrix into the k-space data of one-dimensional multi-channel magnetic resonance imaging, denotes the zero padding operation. denotes the trainable regularization parameter in the data consistency operation. Its mapping function is denoted as:

[0143]

[0144] where the mapping function at the index value n is specifically denoted as:

[0145] d) Sub-block is used to update the network variable P solved by the low-rank optimization solver k+1 , Q k+1 , K k+1 . The input variables include the output variables of the sub-block Q in the current iteration block The output variables of the sub-block S and the k-space data Y of undersampled one-dimensional multi-channel magnetic resonance imaging. The variables β k and λ k are trainable regularization parameters. Its mapping function is denoted as:

[0146]

[0147] is specifically denoted as:

[0148]

[0149] where I denotes the identity matrix, (·) -1 denotes the inverse operation of the matrix.

[0150] In summary, the above four sub-blocks P, Q, S and O are cascaded, and then a single iteration block can be represented by the following nonlinear mapping function:

[0151]

[0152] where θ kdenotes the parameter set of all sub-blocks of the k-th iteration block; f denotes the input variable P of the iteration block k k k k+1 k+1 k+1 The nonlinear mapping function F(·) is a combination of the function mapping of the sub-blocks P, Q, S and O. C(·) denotes the concatenation operation of the sub-blocks.

[0153] The initial input variable of the designed alternating iterative deep learning network model based on low-rank model is obtained by singular value decomposition (SVD):

[0154]

[0155] 1 0.5

[0156] 1 H 0.5

[0157]

[0158] Finally, the reconstructed k-space data Y of the undersampled one-dimensional multi-channel magnetic resonance imaging after the entire network model composed of K=5 iteration blocks is output which can be expressed as:

[0159]

[0160] wherein F(·) denotes the nonlinear mapping function of the network model composed of all iteration blocks, and θ denotes the parameter set of the entire network model. In this embodiment, K=5.

[0161] The loss function of the network is composed of the respective loss functions of the total of 5 iteration blocks and

[0162]

[0163] Specifically expressed as:

[0164]

[0165]

[0166] ​​​​​​​​​​​where ∑ denotes summation operation, k denotes the k-th iteration block, k = 1, 2, …, K, ||·||2denotes the 2-norm term, and a is the regularization parameter. In this embodiment, K = 5 and a = 10. -2 .

[0167] The feedback function of the network is an important process to solve the parameter set of the network model. In the process of constructing the network model, according to the loss function of the network, the k-space data of the reconstructed one-dimensional multi-channel magnetic resonance imaging output by the network model is compared with the k-space data of the fully sampled one-dimensional multi-channel magnetic resonance imaging K, and the gradient is fed back to update all the parameters of the iteration block, so that the output value of the network model gradually approaches the k-space data of the fully sampled one-dimensional multi-channel magnetic resonance imaging.

[0168] Step 5: Using the training set obtained in Step 3, solve the learnable parameter set of the alternating iterative deep learning network based on the low-rank model, and complete the neural network training.

[0169] The Adam optimizer (Diederik Kingma and Jimmy Ba, “Adam: A method for stochastic optimization,” arXiv: 1412.6980, 2014.) well-performing in deep learning is adopted, the training set obtained in Step 3 is used for network training, and the loss function in Step 4 is minimized to obtain the optimal learnable parameter set , so that the trained network model is obtained.

[0170] Step 6: Input the k-space data of the multi-channel magnetic resonance imaging to be reconstructed into the trained network, and reconstruct the complete k-space data of the multi-channel magnetic resonance imaging.

[0171] For the k-space data of the brain multi-channel magnetic resonance imaging to be reconstructed with the frequency encoding dimension length, the phase encoding dimension length and the channel number being 320, 314 and 15 respectively inverse Fourier transform along the frequency encoding dimension to obtain the multi-channel magnetic resonance imaging mixed spatial data, and separate into 320 rows of undersampled one-dimensional multi-channel magnetic resonance imaging k-space data along the frequency encoding dimension

[0172] Then, each row of the undersampled one-dimensional multi-channel magnetic resonance imaging k-space data to be reconstructed is input into the network model F(·) constructed in Step 4, and the learnable parameter set obtained in Step 5 is used to output the reconstructed one-dimensional multi-channel magnetic resonance imaging k-space data The process is represented as

[0173]

[0174] Finally, reconstructing k-space data of one-dimensional multi-channel magnetic resonance imaging of each row Splicing into complete reconstructed magnetic resonance spectrum mixed space data, and inverse Fourier transform along the phase encoding dimension can obtain a complete reconstructed magnetic resonance image.

[0175] In an embodiment, the input of the network is 25% sampling rate (undersampling template as Figure 3 (d). In Figure 3 (d), the white in the undersampling template is the sampling point, indicating that the data corresponding to the position is sampled; the black indicates the point that is not sampled, and the data corresponding to the position is lost). The fully sampled magnetic resonance imaging brain image and the reconstructed brain image of the present application under 25% sampling rate are respectively as shown in Figure 3 (a) and Figure 3 (c).

[0176] It can be seen that the high-fidelity magnetic resonance sampling signal intelligent reconstruction method based on alternating iterative deep learning of low-rank model can quickly reconstruct high-quality magnetic resonance images, and the reconstructed images are better than the reconstructed images of the leading deep learning algorithm (Zi Wang, Chen Qian, Di Guo, Hongwei Sun, Rushuai Li, Bo Zhao, and Xiaobo Qu, "One-dimensional deep low-rank and sparse network for accelerated MRI," IEEE Transactions on Medical Imaging, 2022, doi: 10.1109 / TMI.2022.3203312) ( Figure 3 (b) ).

[0177] The present application proposes a high-fidelity magnetic resonance sampling signal intelligent reconstruction method which simultaneously utilizes the low-rank characteristics of the magnetic resonance sampling signal and the fast calculation of deep learning. This method combines the advantages of deep learning and traditional optimization algorithm, not only retains the fast reconstruction time of the former, but also has the reliable theoretical support of the latter, and improves the generalization. The present application constrains the low-rank of the magnetic resonance sampling signal, designs an alternating iterative deep learning and optimization algorithm network model, and has the characteristics of fast reconstruction, high fidelity and strong generalization.

Claims

1. A method of intelligent reconstruction of high-fidelity magnetic resonance sampling signals, characterized by The method comprises the following steps: 1) obtaining a full-sampling one-dimensional magnetic resonance sampling signal, i.e. time-domain data of a simulated one-dimensional magnetic resonance spectrum or k-space data of a real one-dimensional magnetic resonance imaging; For acquiring time-domain data of a simulated one-dimensional magnetic resonance spectrum, time-domain data of a fully sampled one-dimensional magnetic resonance spectrum is simulated according to an exponential function model The expression is: wherein represents a complex vector of length N, J represents the number of exponential functions; j = 1,..., J represents an index of the number of exponential functions; n = 0,..., N-1 represents an index of the number of sampling points of the time-domain data x of one-dimensional magnetic resonance spectroscopy, Δt represents a time interval, A j , φ j , τ j , and f j represent the amplitude, phase, decay factor, and normalized frequency of the jthexponential function, respectively. For acquiring the k-space data of the one-dimensional multi-channel magnetic resonance imaging, first, obtaining the full-sampling multi-coil magnetic resonance imaging k-space data from a magnetic resonance imaging scanner wherein M, Z and C represent the frequency encoding dimension length, the phase encoding dimension length and the channel number respectively; then performing one-dimensional inverse Fourier transform along the frequency encoding dimension to obtain the multi-channel magnetic resonance imaging hybrid spatial data wherein represents the one-dimensional multi-channel magnetic resonance imaging hybrid spatial data of the mth row; finally, splitting the multi-channel magnetic resonance imaging hybrid spatial data E along the frequency encoding dimension into M full-sampling one-dimensional multi-channel magnetic resonance imaging k-space data The time-domain data x of a fully sampled one-dimensional magnetic resonance spectrum and the k-space data K of a fully sampled one-dimensional multi-channel magnetic resonance imaging are collectively referred to as a fully sampled one-dimensional magnetic resonance sampling signal 2) performing a zero-filling operation on the uncollected data positions according to an actual undersampling template to generate a zero-filled one-dimensional magnetic resonance sampling signal; 3) taking the full-sampling signal in step 1) as an artificial intelligence network output, taking the undersampling signal and the undersampling template in step 2) as network inputs to form a training set; 4) designing an alternating iterative deep learning network model based on a low-rank model, a loss function and a feedback function of the network; 5) solving a set of learnable parameters of the alternating iterative deep learning network based on the low-rank model by using the training set obtained in step 3) to complete neural network training; 6) inputting an undersampling signal of a magnetic resonance to be reconstructed into the trained network to reconstruct a complete magnetic resonance signal.

2. The method of intelligent reconstruction of high-fidelity magnetic resonance sampling signals as claimed in claim 1, wherein In step 2), the zero-filled one-dimensional magnetic resonance sampling signal is generated by performing a zero-filling operation on the uncollected data positions according to the actual undersampling template. Undersampling a magnetic resonance sampling signal Obtaining an undersampled one-dimensional magnetic resonance sampling signal Specifically time domain data of an undersampled one-dimensional magnetic resonance spectrum Or k-space data of an undersampled one-dimensional multi-channel magnetic resonance imaging 3. The method of intelligent reconstruction of high-fidelity magnetic resonance sampling signals as claimed in claim 1, wherein In step 3), the full-sampling signal in step 1) is taken as an artificial intelligence network output, and the undersampling signal and the undersampling template in step 2) are taken as network inputs to form a training set. from fully sampled one-dimensional magnetic resonance sampling signals under-sampling operation and under-sampled one-dimensional magnetic resonance sampling signals comprise a training set.

4. A method of intelligent reconstruction of high-fidelity magnetic resonance sampling signals as defined in claim 1, wherein In step 4), the alternating iterative deep learning network model based on the low-rank model is composed of iteration blocks, and a plurality of iteration blocks are stacked in series as the entire network structure, and each iteration block is composed of four sub-blocks.

5. A method of intelligent reconstruction of high-fidelity magnetic resonance sampling signals as defined in claim 4, characterized by The internal structure of a single iteration block is composed of sub-block P, sub-block Q, sub-block S and sub-block O, and variables are updated in turn P k +1 , Q k+1 , Wherein the sub-block P, the sub-block Q and the sub-block S constitute a deep learning module, and the sub-block O is called an optimization module, and an example of the kth iteration block is shown: a) sub-block P is used to update the network variable solved based on low-rank priori is composed of L layers of dense two-dimensional convolutional neural networks, and the size of the convolution kernel is SxL, which is used to learn a nonlinear mapping function The input variable of each layer is sequentially input into a two-dimensional convolution module and a linear rectifier function, and finally input into the next layer; the input of the first layer is Wherein represents a Hankel operator, which converts a one-dimensional magnetic resonance sampling signal into a Hankel matrix; Q k are output variables of the previous iteration block, represents a set of historical information of matrix P, and the output of the dense two-dimensional convolutional neural network is added to the updated variable P k of the previous iteration block, that is, the final output of the entire sub-block P is obtained, and the complete sub-block P is represented by the following nonlinear mapping function: wherein, represents a non-linear mapping function trained by the dense two-dimensional convolutional neural network in the sub-block P in the k-th iteration block, represents a set of parameters of the neural network; b) sub-block Q is used to update the network variable solved based on low-rank priori The structure and sub-block P are similar, which are composed of L layers of dense two-dimensional convolutional neural networks, and the size of the convolution kernel is SxS, which is used to learn the nonlinear mapping function The input variable of each layer is sequentially subjected to a two-dimensional convolution module and a linear rectifier function, and finally input to the next layer; the input of the first layer is Wherein the superscript H represents the complex conjugate operation, is the output variable of the sub-block P of the iteration block; Indicates a set of historical information of matrix Q; the output of the dense two-dimensional convolutional neural network is added to the updated variable Q k of the previous iteration block, that is, the final output of the entire sub-block Q is obtained; the complete sub-block Q is represented by the following nonlinear mapping function: wherein, represents a non-linear mapping function trained by the dense two-dimensional convolutional neural network in the sub-block Q in the k-th iteration block, represents a set of parameters of the neural network; c) sub-block S is used to update the network variables solved based on the data check operation The data check operation is used to maintain intermediate variables and the undersampled one-dimensional magnetic resonance sampling signals in consistency at the sampling locations Ω, where denotes the inverse Hankel operator, which converts the matrix into one-dimensional magnetic resonance sampling signals, denotes a zero padding operation, denotes a trainable regularization parameter in the data check operation, whose mapping function is denoted as: where the mapping function at index value n is of the form: d) sub-block O is used to update network variable P solved by low-rank optimization solver k+1 k+1 The input variables of which include the output variables of sub-block Q in the current iteration block The output variables of sub-block S And the undersampled one-dimensional magnetic resonance sampling signal Variable β k And λ k The mapping function of which is trainable regularization parameters It is expressed as:​​ The specific form is represented as: where I denotes the identity matrix, (·) -1 denotes an inverse operation on a matrix; In summary, the four sub-blocks P, Q, S and O are cascaded, and a single iteration block can be represented by the following nonlinear mapping function: where θ k denotes the parameter set of all sub-blocks of the kth iteration block; f denotes the input variable P k ,Q k , to the output variable P k+1 ,Q k+1 , is a nonlinear mapping function, which is a combination of the function mapping of the sub-blocks P, Q, S and O, and C(·) represents the cascading operation of the sub-blocks. The initial input variables of the designed alternating iterative deep learning network model based on the low-rank model are obtained by singular value decomposition: P 1 = U∑ 0.5 Q 1 = V H ∑ 0.5 Finally, from the under-sampled one-dimensional magnetic resonance sampling signal After the entire network model consisting of K iteration blocks outputs the reconstructed one-dimensional magnetic resonance sampling signal is expressed as: Wherein, F(·) represents a nonlinear mapping function of the network model composed of all iteration blocks, and θ represents a set of parameters of the entire network model.

6. The method of intelligent reconstruction of high-fidelity magnetic resonance sampling signals as claimed in claim 1, wherein In step 4), the loss function is composed of the respective loss functions of the total of K iteration blocks and ​ The specific representation is: Wherein, ∑ represents a summation operation, k represents the kth iteration block, k=1, 2, …, K, ||·||2 represents a two-norm term, and α is a regularization parameter.

7. The method of intelligent reconstruction of high-fidelity magnetic resonance sampling signals as claimed in claim 1, wherein In step 4), the feedback function of the network is an important process to solve the parameter set of the network model. In the process of constructing the network model, the reconstructed one-dimensional magnetic resonance sampling signal output by the network model is compared with the full-sampling one-dimensional magnetic resonance sampling signal according to the loss function , and the feedback gradient is used to update all parameters of the iterative block, so that the output value of the network model gradually approaches the full-sampling one-dimensional magnetic resonance sampling signal. , and the feedback gradient is used to update all parameters of the iterative block, so that the output value of the network model gradually approaches the full-sampling one-dimensional magnetic resonance sampling signal.

8. The method of intelligent reconstruction of high-fidelity magnetic resonance sampling signals as defined in claim 1, wherein In step 5), the well-performing Adam optimizer in deep learning is adopted to train the network with the training set obtained in step 3) by minimizing the loss function in step 4) for the learned parameter set of the low-rank model-based alternating iterative deep learning network to obtain the optimal learned parameter set that is, the trained network model is obtained.

9. The method of intelligent reconstruction of high-fidelity magnetic resonance sampling signals as defined in claim 1, wherein In step 6), the undersampling signal of the magnetic resonance to be reconstructed is input into the trained network to reconstruct a complete magnetic resonance signal, and the specific method is as follows: a) separating the undersampling magnetic resonance sampling signal to be reconstructed into a plurality of rows of undersampling one-dimensional magnetic resonance sampling signals to be reconstructed, and the specific method is as follows: The time domain data of the undersampled magnetic resonance spectrum to be reconstructed for the direct dimension and the indirect dimension are A and B respectively The Fourier transform is performed along the direct dimension to obtain the magnetic resonance spectrum mixed spatial data, and separated into A rows of time domain data of the undersampled one-dimensional magnetic resonance spectrum along the direct dimension For the k-space data of the undersampled multi-coil magnetic resonance imaging to be reconstructed with the length of the frequency encoding dimension, the phase encoding dimension and the number of channels being C, D and E respectively Inverse Fourier transform along the frequency encoding dimension to obtain multi-channel magnetic resonance imaging mixed spatial data, and separate into C rows of one-dimensional multi-channel magnetic resonance imaging k-space data along the frequency encoding dimension Time domain data of an undersampled one-dimensional magnetic resonance spectrum to be reconstructed K-space data of an undersampled one-dimensional multi-channel magnetic resonance imaging to be reconstructed Collectively referred to as undersampled one-dimensional magnetic resonance sampling signals to be reconstructed b) the undersampled one-dimensional magnetic resonance sampling signals of each row to be reconstructed input the network model F(·) constructed in step 2) and use the set of learnable parameters obtained in step 3) output the reconstructed one-dimensional magnetic resonance sampling signals The procedure is represented as c) concatenating the reconstructed one-dimensional magnetic resonance sampling signals of each row into a complete reconstructed magnetic resonance mixed space data and converting into a desired data form; in particular, Fourier transforming the complete reconstructed magnetic resonance mixed space data along the indirect dimension yields a complete reconstructed magnetic resonance spectral frequency domain data and inverse Fourier transforming the complete reconstructed multi-channel magnetic resonance imaging mixed space data along the phase encoding dimension yields a complete reconstructed multi-channel magnetic resonance imaging data. c) concatenating the reconstructed one-dimensional magnetic resonance sampling signals of each row into a complete reconstructed magnetic resonance mixed space data and converting into a desired data form; in particular, Fourier transforming the complete reconstructed magnetic resonance mixed space data along the indirect dimension yields a complete reconstructed magnetic resonance spectral frequency domain data and inverse Fourier transforming the complete reconstructed multi-channel magnetic resonance imaging mixed space data along the phase encoding dimension yields a complete reconstructed multi-channel magnetic resonance imaging data.

Images