A Physical Intelligence High-Definition Magnetic Resonance Diffusion Imaging Method

Abstract

A physical intelligent high-definition magnetic resonance diffusion imaging method includes the following steps: 1) Obtain multi-channel single-shot or multi-shot magnetic resonance images with a phase and a b-value of 0 mm / s², and estimate the channel sensitivity; 2) Obtain the simulated motion phase according to the polynomial phase model of rigid body motion; 3) Use the magnetic resonance images with a phase, the channel sensitivity, and the simulated motion phase to generate a large number of multi-shot diffusion-weighted image data as the training data of the intelligent reconstruction network; 4) Construct an intelligent reconstruction network including multiple iterative blocks, where each iterative block includes a low-rank module, a sparse module, and a data verification module. The last iterative block further includes a denoising module. And use the simulated data to train the intelligent reconstruction network; 5) Obtain the multi-shot diffusion-weighted data to be reconstructed; 6) Use the trained intelligent reconstruction network to reconstruct the multi-shot diffusion-weighted data to obtain the reconstructed image.

Description

Technical Field

[0001] The present invention relates to a physical intelligent high-definition magnetic resonance diffusion imaging method, in particular to a method that uses polynomial simulation to generate multi-excitation diffusion-weighted imaging training data and an intelligent reconstruction network based on sparsity and low rank. Background Art

[0002] Diffusion weighted imaging is a method for evaluating the molecular function and microstructure of the human body, and can non-invasively detect the diffusion movement of water molecules in tissues (V. Baliyan et al., “Diffusionweighted imaging: technique and applications,” World Journal of Radiology, 8, 785, 2016). The multi-excitation echo planar imaging technique has the ability to improve resolution and reduce low distortion in diffusion weighted applications (H. An, X. Ma, Z. Pan, H. Guo, E. Y. P. Lee, “Qualitative and quantitative comparisonof image quality between single-shot echo-planar and interleaved multi-shotecho-planar diffusion-weighted imaging in female pelvis,” European radiology, 30, 1876-1884, 2020). However, there are serious phase errors between different excitations, resulting in serious motion artifacts (A. W. Anderson, J. C. Gore, “Analysis and correction of motion artifacts indiffusion weighted imaging,” Magnetic Resonance in Medicine, 32, 379-387, 1994).

[0003] In recent years, many reconstruction methods based on low-rank iterative models have been used to correct the motion phases between different excitations and achieve artifact-free reconstruction. MUSSELS constructs a structured Hankel matrix by establishing the phase annihilation relationship between images of different excitations and constrains the low rank of the matrix to achieve reconstruction (M. Mani, M. Jacob, D. Kelley, V. Magnotta, "Multi-shot sensitivity-encoded diffusion data recovery using structured low-rank matrix completion (MUSSELS)," Magnetic Resonance in Medicine, 78, 494-507, 2017). PLRHM utilizes the smooth phase prior of magnetic resonance images to construct a structured low-rank matrix and realizes reconstruction by constraining the sum of some larger singular values of the low-rank matrix (Y. Huang et al., "Phase-constrained reconstruction for high-resolution multi-shot diffusion weighted image," Journal of Magnetic Resonance, 312:106690, 2020). PAIR reconstructs the amplitude and phase alternately to utilize the structural detailed information in the image domain and the low-rank information in the Fourier space to achieve the reconstruction of multi-excitation diffusion-weighted data (C. Qian et al., "A paired phase and magnitude reconstruction for advanced diffusion-weighted imaging," arXiv preprint, arXiv:2203.14559, 2022).

[0004] Recently, deep learning methods have shown great potential in multi-excitation diffusion-weighted imaging (Aggarwal. H. K., M. Mani, M. Jacob, "MoDL-MUSSELS: Model-based deep learning for multi-shot sensitivity-encoded diffusion MRI", IEEE Transactions on Medical Imaging, 39, 1268-1277, 2019). However, high-quality training labels are lacking in multi-excitation diffusion-weighted images, and the training labels generated by traditional iterative reconstruction methods greatly limit the potential of these intelligent reconstruction methods.

[0005] In summary, the current intelligent reconstruction methods for multi-shot diffusion-weighted imaging are limited by the difficulty of obtaining high-quality training data and cannot effectively unleash the potential of intelligent reconstruction methods. The present invention proposes a polynomial simulation model based on rigid body motion to generate multi-shot diffusion-weighted imaging training data and an intelligent reconstruction network based on sparsity and low rank (Q. Yang, Z. Wang, K. Guo, C. Cai, and X. Qu, “Physics-driven synthetic data learning for biomedical magnetic resonance: The imaging physics-based data synthesis paradigm for artificial intelligence,” IEEE Signal Processing Magazine., DOI: 10.1109 / MSP.2022.3183809, 2022). Summary of the Invention

[0006] The object of the present invention is to provide a physics-intelligent high-definition magnetic resonance diffusion imaging method.

[0007] The present invention includes the following steps:

[0008] 1) Obtain multi-channel single-shot or multi-shot diffusion-weighted magnetic resonance images with a b-value of 0 mm / s 2 with phase, and estimate the channel sensitivity;

[0009] 2) Simulate multiple sets of motion phases according to the polynomial phase model;

[0010] 3) Use the diffusion-weighted magnetic resonance images with phase, channel sensitivity, and motion phases to simulate multi-shot diffusion-weighted image data as the training data for the intelligent reconstruction network;

[0011] 4) Construct an intelligent reconstruction network including multiple iterative blocks, where each iterative block includes a low-rank module, a sparse module, and a data verification module. The last iterative block also includes a denoising module; and train the intelligent reconstruction network using the simulated training data;

[0012] 5) Obtain the multi-shot diffusion-weighted data to be reconstructed;

[0013] 6) Use the trained intelligent reconstruction network to reconstruct the multi-shot diffusion-weighted data to obtain a reconstructed image.

[0014] In step 1), the obtained diffusion-weighted magnetic resonance images with phase can be obtained from a single-shot sequence or from a multi-shot sequence with a b-value of 0 mm / s 2The data, where N and M are the lengths of the frequency and phase encoding dimensions of the image respectively, and the acquired data is used to estimate the channel sensitivity where the total number of channels is H.

[0015] In step 2), the specific method for simulating multiple sets of motion phases using the polynomial phase model is as follows:

[0016] The polynomial motion phase model is:

[0017]

[0018] where x and y are the coordinates of the two-dimensional image, and i is the imaginary symbol; is the phase obtained by simulation, and N and M are the lengths of the frequency and phase encoding dimensions of the image respectively; L is the polynomial order, and m and l - m are the x and y powers of each phase included in the current l-th order polynomial; A lm is the x m y l-m coefficient of the term, is the noise of the two-dimensional Gaussian distribution, where μ and σ are the mean and variance respectively; J motion phases can be obtained using the polynomial motion phase model, forming a set of simulated phase data for the multi-excitation diffusion weighted data J is equal to the number of excitations of the multi-excitation diffusion weighted data to be reconstructed for the target.

[0019] In step 3), the simulation process formula for the diffusion weighted data of multiple excitations is:

[0020]

[0021] where, is the simulated diffusion weighted Fourier space data, is the simulated complete diffusion weighted image, C is the channel sensitivity, P is the simulated motion phase; m is the diffusion weighted magnetic resonance image with phase, is the undersampling operator corresponding to the Fourier space sampling template of the multi-excitation diffusion weighted data, is the Fourier transform. Using formula (1), a large number of simulated multi-excitation diffusion weighted can be obtained as the training data for the intelligent reconstruction network. The complete diffusion weighted image I is directly Fourier transformed to obtain X GT . Finally, Y, X GT , C together form a pair of training data.

[0022] In step 4), the intelligent reconstruction network contains K iterative blocks, each iterative block contains a low-rank module, a sparse module, a data verification module, and the last iterative block also contains a denoising module;

[0023] The network design of the low-rank module LR is as follows:

[0024]

[0025] Among them, is an intermediate variable of the network, where k represents the k-th iteration block, and X k-1 is the output of the previous iteration block, and X 0 = Y is the initial input of the network, is the low-rank module, which consists of L LR layers of convolutional neural networks. Each layer of convolution contains multiple two-dimensional convolutional kernels. The layers of convolution are connected by a rectified linear unit function, and the input of each layer is the output of the previous layer.

[0026] The network design of the sparse module SP is as follows:

[0027]

[0028] Among them, is an intermediate variable of the network, is the output of the previous low-rank module, and are the Fourier transform and the inverse Fourier transform respectively. soft(·; θ k ) is a soft thresholding operation, defined as soft(x; θ k ) = max{|x| - θ k} · x / |x|, where θ k is a trainable threshold; consists of L SP layers of convolutional neural networks. Each layer of convolution contains multiple two-dimensional convolutional kernels. The layers of convolution are connected by a rectified linear unit function, and the input of each layer is the output of the previous layer; After the output of passes through the soft thresholding operation, it enters the and networks, and

[0029] The network design of the data verification module is as follows:

[0030]

[0031] Among them, and are the Fourier transform and the inverse Fourier transform respectively, is the undersampling operator corresponding to the Fourier space sampling template of the multi-excitation diffusion weighted data, is its conjugate operator; D is the identity matrix, and λ1 is a learnable regularization parameter. is the output of the sparse module; Y is the simulated diffusion-weighted Fourier space data. C is the channel sensitivity, and C * is the conjugate matrix of the channel sensitivity. X k is an intermediate variable of the network; if the current iteration block is not the last iteration block, X k will be input into the low-rank module of the next iteration block; if the current iteration block is the last iteration block, i.e., the Kth iteration block, X K will be input into the denoising module.

[0032] The specific design of the denoising module is as follows:

[0033]

[0034] Among them, and respectively represent the operator and the conjugate operator for constructing the structured Hankel matrix; SVT r is the singular value decomposition and threshold operation operator. After performing singular value decomposition on the first r singular values are retained. is the final output.

[0035] The loss function for training the intelligent network is:

[0036]

[0037] Among them, T is the total number of training samples, K is the number of network iteration blocks, and X k,t is the output of the kth iteration block after the tth sample is input into the network, is the training label of the tth sample, which is generated by the aforementioned simulation method; ||·|| F is the Frobenius norm; the learnable convolution kernels and parameters in the network are trained and updated through the commonly used Adam optimizer in deep learning, and finally a trained network model is obtained.

[0038] In step 5), the data to be reconstructed is the multi-shot echo-planar diffusion-weighted data read out in segments in the phase encoding dimension.

[0039] In step 6), the obtained multi-shot echo-planar diffusion-weighted data is input into the trained intelligent reconstruction network to reconstruct an image without motion artifacts.

[0040] Compared with the existing deep learning multi-shot diffusion-weighted image reconstruction, the proposed physical intelligent reconstruction scheme of the present invention has the following outstanding advantages:

[0041] 1. The present invention generates simulation data approximating measured data through a rigid body motion model, without the need for measured training data to train the network, thus solving the problem of lack of high-quality training data for multi-excitation diffusion weighted images.

[0042] 2. The physics-informed neural network designed in the present invention comprehensively utilizes two complementary prior information: sparsity in the image domain and low-rankness in the Fourier space.

[0043] 3. The present invention can effectively remove motion artifacts existing in multi-excitation diffusion weighted images and achieve fast and high-quality reconstruction. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 The phase-encoded magnetic resonance image for simulation and the estimated channel sensitivities.

[0045] Figure 2 A set of simulated motion phases for four excitations.

[0046] Figure 3 The input to the intelligent reconstruction method, i.e., the four-excitation diffusion weighted image with b-value of 1000 mm / s to be reconstructed. 2

[0047] Figure 4 The output of the intelligent reconstruction method, i.e., the reconstructed four-excitation diffusion weighted image with b-value of 1000 mm / s. 2 DETAILED DESCRIPTION OF THE INVENTION

[0048] The embodiments of the present invention are specific processes for high-resolution diffusion weighted reconstruction of multi-excitation Fourier space signals. In conjunction with the accompanying drawings, a physics-informed high-definition magnetic resonance diffusion imaging method proposed by the present invention will be described in detail.

[0049] The specific implementation process is as follows:

[0050] First step, use a magnetic resonance scanner with a magnetic field strength of 3.0 Tesla to scan 6 volunteers to obtain the phase-encoded diffusion weighted magnetic resonance images m with b-value of 0 mm / s 2 for four excitations, and obtain the parameters: field of view 220*220 mm 2 , slice thickness 5 mm, 32-channel coil, and the matrix size is 180*180 after cropping. A total of 144 phase-encoded magnetic resonance images and corresponding 144 channel sensitivities C are obtained from the 6 volunteers. The phase-encoded magnetic resonance images and channel sensitivities are as Figure 1 shown.

[0051] Second step, simulate the motion phases. The polynomial phase model is as follows:

[0052]

[0053] Among them, x and y are the coordinates of the two-dimensional image, and i is the imaginary symbol. is the phase obtained by simulation. The frequencies of the image and the length of the phase encoding dimension are both 180. The polynomial order L is 7, and m and l - m are the x and y powers of each phase included in the current l-th order polynomial. x m y l-m The coefficient A of the term lm is randomly obtained from a uniform distribution of [0, 0.1 l . is the noise of the two-dimensional Gaussian distribution, where the mean μ and the variance σ are 0 and 0.01 respectively. Using the polynomial motion phase model, 4 motion phases can be obtained, forming a set of simulated phase data of the multi-excitation diffusion weighted data A total of 1440 groups of motion phases are simulated.

[0054] Step 3: Simulate the multi-excitation diffusion weighted data. The simulation process formula is:

[0055]

[0056] Among them, is the diffusion weighted Fourier space data obtained by simulation, is the complete diffusion weighted image obtained by simulation. C is the channel sensitivity, and P is the motion phase obtained by simulation. m is the diffusion weighted magnetic resonance image with phase, is the undersampling operator corresponding to the Fourier space sampling template of the multi-excitation diffusion weighted data, is the Fourier transform. Using formula (1), a large number of simulated multi-excitation diffusion weighted can be obtained as the training data of the intelligent reconstruction network. The complete diffusion weighted image I is directly Fourier transformed to obtain X GT . Finally, Y, X GT , and C together form a pair of training data. Each amplitude data m with phase and the channel sensitivity C can be combined with 10 groups of simulated motion phases. In this way, a total of 1440 groups of training data are obtained. Figure 2 shows one group of simulated motion phases.

[0057] Step 4: In building the intelligent reconstruction network, there are a total of 5 iterative blocks. Each iterative block includes a low-rank module, a sparse module, and a data verification module. The last iterative block also includes a denoising module.

[0058] a) The network design of the low-rank module LR is specifically as follows:

[0059]

[0060] Among them, is an intermediate network variable, where k represents the k-th iteration block. X k-1 is the output of the previous iteration block, X 0 = Y is the network initialization input, Figure 3 shows the image domain of the network input, that is, the un-reconstructed multi-excitation diffusion-weighted magnetic resonance data. is a low-rank module, composed of a 6-layer convolutional neural network. Each convolutional layer contains 48 two-dimensional convolutional kernels. The convolutional layers are connected by a rectified linear unit function, and the input of each layer is the output of the previous layer.

[0061] b) The network design of the sparse module SP is as follows:

[0062]

[0063] Among them, is an intermediate network variable, is the output of the previous low-rank module, and are the Fourier transform and the inverse Fourier transform respectively, soft(·; θ k ) is a soft-thresholding operation, defined as soft(x; θ k ) = max{|x| - θ k}·x / |x|, where θ k is a trainable threshold, initialized to 0.01. is composed of a 3-layer convolutional neural network. Each convolutional layer contains 48 two-dimensional convolutional kernels. The convolutional layers are connected by a rectified linear unit function, and the input of each layer is the output of the previous layer. The output of enters the and networks after the soft-thresholding operation,

[0064] c) The network design of the data verification module is as follows:

[0065]

[0066] Among them, and are the Fourier transform and the inverse Fourier transform respectively, is the undersampling operator corresponding to the Fourier space sampling template of the multi-excitation diffusion-weighted data, is its conjugate operator. D is the identity matrix, and λ1 is a learnable regularization parameter. is the output of the sparse module. Y is the simulated diffusion-weighted Fourier space data. C is the channel sensitivity, C * is the conjugate matrix of the channel sensitivity. X kis an intermediate network variable. If the current iteration block is not the last iteration block, X k will be input into the low-rank module of the next iteration block. If the current iteration block is the last iteration block, i.e., the K-th iteration block, X K will be input into the denoising module.

[0067] d) The specific design of the denoising module is as follows:

[0068]

[0069] Among them, and respectively represent the operator and conjugate operator for constructing the structured Hankel matrix, and the size of the sliding window is [5,5]. SVT r is the singular value decomposition and threshold operation operator. After performing singular value decomposition on the first 30 singular values are retained. is the final output.

[0070] The loss function for intelligent network training is:

[0071]

[0072] Among them, the total number of training samples is 1200, the number of validation samples is 240, the number of network iteration blocks is 5, X k,t is the output of the k-th iteration block after the t-th sample is input into the network, is the training label of the t-th sample, which is generated by the aforementioned simulation method. ||·|| F is the Frobenius norm. The learnable convolution kernels and parameters in the network are trained and updated through the commonly used Adam optimizer in deep learning, and finally a trained network model is obtained.

[0073] In the fourth step, a diffusion-weighted magnetic resonance image with four excitations is acquired by scanning a volunteer using a magnetic resonance scanner with a magnetic field strength of 3.0 Tesla. The obtained parameters are: TR / TE = 3000 / 60 ms, b value 1000 mm / s 2 , 3 diffusion directions, field of view 220*220 mm 2 , slice thickness 5 mm, number of slices 12, 32-channel coil, and the matrix size is 180*180 after cropping. And the channel sensitivity is calculated.

[0074] In the fifth step, the four-excitation diffusion-weighted data collected is input into the trained intelligent reconstruction network to reconstruct an image without motion artifacts. Figure 4 Shows the reconstructed four-excitation diffusion-weighted image with a b value of 1000 mm / s 2 of the four excitations.

Claims

1. A physical intelligent high-definition magnetic resonance diffusion imaging method, characterized in that Including the following steps: 1) Obtain single-shot or multi-shot diffusion-weighted magnetic resonance images with a b-value of 0 mm / s for multiple channels, and estimate the channel sensitivities; 2 with phase information 2) Simulate multiple sets of motion phases according to the polynomial phase model of rigid body motion; The specific process of simulating multiple sets of motion phases using the polynomial phase model is as follows: The polynomial motion phase model based on rigid body motion is: where x and y are the coordinates of the two-dimensional image, and i is the imaginary symbol; is the phase obtained by simulation, N and M are the frequency and the length of the phase encoding dimension of the image respectively; L is the polynomial order, and m and l - m are the x and y powers of each phase included in the current l-th order polynomial; A lm is the x m y l-m coefficient of the term, is the noise of the two-dimensional Gaussian distribution, where μ and σ are the mean and variance respectively; J motion phases can be obtained using the polynomial motion phase model, forming a set of simulated phase data of the multi-excitation diffusion-weighted data J is equal to the number of excitations of the multi-excitation diffusion-weighted data to be reconstructed for the target; 3) Use the magnetic resonance images with phases, channel sensitivities, and motion phases to simulate the diffusion-weighted image data of multiple excitations as the training data for the intelligent reconstruction network; 4) Construct an intelligent reconstruction network containing multiple iterative blocks, where each iterative block includes a low-rank module, a sparse module, a data verification module, and the last iterative block also includes a denoising module; and train the intelligent reconstruction network using the simulation training data; 5) Obtain the multi-excitation diffusion-weighted data to be reconstructed; 6) Use the trained intelligent reconstruction network to reconstruct the multi-excitation diffusion-weighted data to obtain a reconstructed image.

2. The physical intelligent high-definition magnetic resonance diffusion imaging method according to claim 1, wherein In step 1), the obtained diffusion-weighted magnetic resonance image with phase is obtained from a single-shot sequence or has a b-value of 0 mm / s for a multi-shot sequence. N and M are the lengths of the frequency and phase-encoding dimensions of the image respectively, and the obtained data is used to estimate the channel sensitivity 2 where the total number of channels is H ​ 3. The physical intelligent high-definition magnetic resonance diffusion imaging method according to claim 1, wherein In step 3), the simulation process formula for the multi-excitation diffusion-weighted data is: Among them, are the diffusion-weighted Fourier space data of each channel for each excitation obtained by simulation, is the complete diffusion-weighted image obtained by simulation, C is the channel sensitivity, P is the motion phase obtained by simulation, and m is the diffusion-weighted magnetic resonance image with phase, is the undersampling operator corresponding to the Fourier space sampling template of the multi-excitation diffusion-weighted data, is the Fourier transform. Using formula (1), a large number of simulated multi-excitation diffusion-weighted data are obtained as the training data of the intelligent reconstruction network. The complete diffusion-weighted image I is directly Fourier-transformed to obtain X GT , and finally Y, X GT , and C together form a pair of training data.

4. The physical intelligent high-definition magnetic resonance diffusion imaging method according to claim 1, characterized in that In step 4), the intelligent reconstruction network contains K iterative blocks, each iterative block includes a low-rank module, a sparse module, a data verification module, and the last iterative block also includes a denoising module; The network design of the low-rank module LR is specifically as follows: Among them, is an intermediate network variable, where k represents the k-th iteration block, and X k-1 is the output of the previous iteration block, and X 0 = Y is the network initialization input, is a low-rank module, consisting of L LR layers of convolutional neural networks. Each layer of convolution contains multiple two-dimensional convolutional kernels. The convolutional layers are connected by rectified linear units, and the input of each layer is the output of the previous layer; The network design of the sparse module SP is specifically as follows: Among them, is an intermediate network variable, is the output of the previous low-rank module, and are the Fourier transform and the inverse Fourier transform respectively, and soft(·; θ k ) is a soft threshold operation, defined as soft(x; θ k ) = max{|x| - θ k}·x / |x|, where θ k is a trainable threshold; is composed of an L SP -layer convolutional neural network. Each layer of convolution contains multiple two-dimensional convolutional kernels. The convolutional layers are connected by a rectified linear unit, and the input of each layer is the output of the previous layer. After the output of passes through the soft threshold operation, it enters the and networks, which have an anti-symmetric network structure; The network design of the data verification module is specifically as follows: Among them, and are the Fourier transform and the inverse Fourier transform respectively, is the undersampling operator corresponding to the Fourier space sampling template of the multi-excitation diffusion weighted data, is its conjugate operator; D is the identity matrix, and λ1 is a learnable regularization parameter; is the output of the sparse module, Y is the diffusion weighted Fourier space data obtained by simulation, C is the channel sensitivity, and C * is the conjugate matrix of the channel sensitivity, and X k is the intermediate variable of the network; if the current iteration block is not the last iteration block, X k will be input into the low-rank module of the next iteration block. If the current iteration block is the last iteration block, that is, the Kth iteration block, X K will be input into the denoising module; The specific design of the denoising module is as follows: Among them, and respectively represent the operator and the conjugate operator for constructing the structured Hankel matrix. SVT r is the singular value decomposition and threshold operation operator. After performing the singular value decomposition on , the first r singular values are retained; is the final output; The loss function for the intelligent network training is: where T is the total number of training samples, K is the number of network iteration blocks, and X k,t is the output of the k-th iteration block after the t-th sample is input into the network, is the training label of the t-th sample, generated by the aforementioned simulation method, and ||·|| F is the Frobenius norm; the learnable convolution kernels and parameters in the network are trained and updated by the commonly used Adam optimizer in deep learning, and finally a trained network model is obtained.

5. The physical intelligent high-definition magnetic resonance diffusion imaging method according to claim 1, wherein In step 5), the data to be reconstructed obtained is the multi-excitation echo-planar diffusion-weighted data read out in segments in the phase-encoding dimension.

6. The physical intelligent high-definition magnetic resonance diffusion imaging method according to claim 1, characterized in that In step 6), input the obtained multi-excitation echo-planar diffusion-weighted data into the trained intelligent reconstruction network to reconstruct an image without motion artifacts.

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