Cardiac magnetic resonance reconstruction method for low parameter learning

Abstract

The invention discloses a heart magnetic resonance reconstruction method based on low parameter learning, and relates to heart magnetic resonance imaging. Comprising the following steps: 1) acquiring heart dynamic data of C (C > 0) cardiac cycles, merging multi-channel data of each frame into a single-channel image, performing data segmentation and dimension reduction, and constructing an image dimension-time dimension data set; 2) designing a deep learning network of the teacher model and the student model based on optimization iteration expansion; 3) constructing a loss function, and performing network training by using the data set generated in the step 1); and 4) reconstructing the undersampled data by using the trained student model. The core of the method is that model parameter quantity is highly compressed, a teacher model is utilized to guide student model training, the difficulty of model learning complex mapping is reduced, and the low-parameter-quantity student model can perform high-quality rapid reconstruction of cardiac magnetic resonance.

Description

Technical Field

[0001] The present invention relates to cardiac magnetic resonance imaging, and in particular to a cardiac magnetic resonance reconstruction method that uses deep learning based on knowledge distillation to achieve fast and generalized learning with low parameter count. Background Art

[0002] Magnetic resonance imaging, as a non-invasive, high-spatial-resolution imaging technique, plays an important role in cardiac examination.

[0003] There are two main factors that limit the speed of magnetic resonance imaging: the data acquisition mechanism and the speed of the image reconstruction algorithm. In terms of data acquisition, the examination of heart disease requires covering hundreds of heart cycles, and the total acquisition time is proportional to the number of phase encodings. Although the repetition time can be shortened to 3-5 milliseconds using a fast gradient echo sequence, a single cardiac magnetic resonance movie in a cardiac examination takes as long as 10-15 minutes. The probability of unconscious movement in patients is high, which can cause artifacts in the image and affect the accuracy of the diagnosis. In terms of reconstruction algorithms, traditional iterative optimization algorithms usually take a long time to iterate. Deep learning methods can be roughly divided into two categories: end-to-end deep learning and deep learning based on optimized iteration.

[0004] End-to-end deep learning training is fast, but requires a large amount of data, lacks the support of physical models, and has poor interpretability. Compared with the original ADMM iterative algorithm, the deep learning alternating direction multiplier algorithm based on optimized iterative expansion significantly improves the reconstruction quality and speeds up the reconstruction speed ADMM-Net (Yan Yang, Jian Sun, Li Huibin, Xu Zongben, “Deep ADMM-Net for compressive sensing MRI,” Advances in Neural Information Processing Systems, vol. 29, 2016, pp. 10–18.); the method of adding low-rank and sparse constraints to deep learning makes the neural network more interpretable (Ziwen Ke, Wenqi Huang, et al., “Learned low-rank priors in dynamic MR imaging,” IEEE Transactions on Medical Imaging, 40 (12), 2021, 3698–3710.); some studies have used deep separable spatiotemporal learning for fast dynamic cardiac magnetic resonance imaging, which has excellent reconstruction quality and greatly reduces the number of required training samples (Zi Wang, Min Xiao, et al., “Deepseparable spatiotemporal learning for fast dynamic cardiac MRI", 2024, arXiv:2402.15939.).

[0005] However, the above methods have problems such as poor interpretability, slow reconstruction speed, large number of model parameters, and high data dependence. Summary of the Invention

[0006] The present invention aims to address existing problems in cardiac magnetic resonance imaging, such as poor interpretability, slow reconstruction speed, large number of model parameters, and high data dependency. This approach provides a low-parameter learning method for cardiac magnetic resonance reconstruction that enables fast, high-quality cardiac magnetic resonance imaging. This method employs a teacher-student model architecture, incorporating low-rank sparse priors and physical constraints into the teacher model to ensure reconstruction accuracy. Knowledge distillation techniques are then used to transfer deep feature information from the teacher model to a significantly reduced number of parameters in the student model, enabling fast, generalized, and high-quality reconstruction of dynamic cardiac images.

[0007] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions.

[0008] A cardiac magnetic resonance reconstruction method using low-parameter learning includes the following steps:

[0009] 1) Acquire cardiac dynamic data for C (C>0) cardiac cycles, merge the multi-channel data of each frame into a single-channel image, perform data segmentation and dimensionality reduction, and construct an image-dimensional-time-dimensional dataset;

[0010] 2) Designing a deep learning network of teacher and student models based on the optimized iterative expansion of the reconstruction model;

[0011] 3) Construct a loss function and use the data set generated in step 1) to train the network;

[0012] 4) Use the trained student model to reconstruct the undersampled data.

[0013] In step 1), the image dimension-time dimension dataset is constructed, and the full sampling k-space and the fully sampled k-space is constructed using the undersampled template Respectively expressed as:

[0014]

[0015] in, is the undersampling operator, is the Fourier transform operator, channel sensitivity map Merged single-channel image M, N, J, and T represent the frequency encoding length, phase encoding length, number of channels, and number of time frames, respectively. Indicates that and The Hadamard product of is arranged into the corresponding tensor, the operator correspond Operation on X; Y Perform two-dimensional inverse Fourier transform on the first two dimensions of each frame to obtain a multi-channel image To X J The channel dimension is merged to obtain a single-channel image X;

[0016] Will Split into M true value labels of teacher models Compression X m The first dimension of gets the true value labels of M student models Undersampled k-space Y u The first two dimensions of each frame are obtained by two-dimensional inverse Fourier transform To X uJ Channel dimension merging to obtain aliased image Then X u Segmentation and dimensionality reduction to obtain M aliased images and As network inputs for the teacher model and student model respectively; and The difference in the calculation of the neural network is that the former requires a three-dimensional convolution operation, and the number of calculations for a single two-dimensional convolution is:

[0017] O 2D =H out ×W out ×C out ×H kernel ×W kernel ×C in (3) Among them, M out ×N out ×C out H is the size of the output feature map, including width, height, and number of channels. kernel ×W kernel is the convolution kernel size, C in is the number of channels of the input feature map; the number of calculations of a single 3D convolution is:

[0018] O 3D =O 2D ×D kernel ×D out (4)

[0019] Among them, D kernel and D out They represent the dimensions of the convolution kernel and the output feature map respectively.

[0020] In step 2), the reconstructed model is expressed as:

[0021]

[0022] in, Depend on Split along the first dimension, represents extracting the nth vector from the phase encoding dimension, Indicates the extraction of the t-th vector from the time dimension, Ψ represents the sparse transformation, is a vertically concatenated Toeplitz matrix, ||·||1 is the l1 norm, ||·||2 is the l2 norm, ||·|| F is the Frobenius norm, λ1 and λ2 are regularization parameters;

[0023] A deep separable spatiotemporal learning network is used, which consists of S cascaded iterative blocks. Each iterative block contains three modules: a low-rank neural module, a sparse neural module, and a data verification module.

[0024] The low-rank neural module is designed as follows:

[0025]

[0026] in, represents the reconstruction result of step s-1, represents the low-rank module in the s-th iteration step, which Projected to the null space, the teacher model has N low-rank modules T convolutional layers, each of which contains n T convolution kernels, the convolution kernel size is 1×h×h; the student model is reduced to N S (N S <N T ) convolutional layers, the number of convolution kernels in each convolutional layer is reduced to n for different distillation levels S (n S <n T ), the convolution kernel size is h×h; Represents the output of the s-th step of the low-rank neural network;

[0027] The sparse neural module is implemented using a learnable soft threshold module:

[0028]

[0029] in, and denote the sparse neural module outputs at the s-1th and sth iteration steps, respectively, is the sth soft threshold module, which changes the input value below the threshold γ to zero. is the sth threshold learning module, from The threshold γ of the soft threshold function is learned in S γ represents the soft threshold function and is defined as:

[0030]

[0031] Where sign(·) is the sign function, and max(·) represents the maximum value. The data check item module is as follows:

[0032]

[0033] in, is the k-space output of step s, Y0 represents the undersampled k-space Y u , is the k-space of the output image of the s-th step low-rank module and sparse module, is an undersampling template whose values only contain 0 and 1, is the corresponding complementary template, is a full 1 matrix, ρ1 and ρ2 are learnable regularization parameters, represents the Hadamard product; image Depend on Obtained through inverse Fourier transform and channel merging.

[0034] In step 3), the constructed loss function includes the loss function of the teacher model and the loss function of the student model, which are as follows:

[0035] The loss function of the teacher model is composed of the model parameter low-rank loss And the true value loss

[0036]

[0037] Where, the superscript s represents the sth iteration block, Indicates the parameters θ of the low-rank module, ||·||1 is the l1 norm, is the relative difference between the teacher model output and the true value, α1 and α2 are weight coefficients;

[0038] The loss function of the student model is composed of feature layer loss and truth loss It consists of two parts:

[0039]

[0040] Where, the superscript s represents the sth iteration block, and are the outputs of the teacher model and the student model respectively, ||·|| F is the Frobenius norm, is the relative difference between the output of the student model and the true value, β1 and β2 are weight coefficients; the shapes of the iterative block reconstruction results of the teacher model and the student model are and Calculating losses First, the reconstruction result of the student model Transformation and Same shape;

[0041] During the training process of the student model DS-λ of the present invention, a strategy combining feature knowledge distillation and truth value learning is adopted to transfer the deep feature information of the teacher model by minimizing the difference between the outputs of the corresponding iterative blocks of the teacher model and the student model. The larger the λ, the higher the degree of model knowledge distillation and the smaller the corresponding parameter amount. Secondly, the fully sampled image is introduced as a reference for the accurate reconstruction of the student model.

[0042] In step 4), the reconstruction is to convert the aliased image Input into the teacher or student model for reconstruction, and get

[0043] Compared with the prior art, the outstanding technical effects and advantages of the present invention are:

[0044] The core of the method of the present invention lies in the high compression of model parameters and the use of teacher models to guide student model training, which reduces the difficulty of model learning complex mappings, so that the low-parameter student model can perform high-quality and rapid reconstruction of cardiac magnetic resonance. The parameter amount of the present invention is significantly reduced, and it is adapted to lightweight deployment. The parameter amount of the student model is compressed from 3.55 million of the teacher model to 290,000, breaking through the bottleneck of traditional deep learning methods with large parameters and dependence on high-performance computing hardware. The student model can run in real time on edge devices, support the deployment requirements of mobile terminals or low-resource clinical equipment, effectively reduce patient motion artifacts, and controllable reconstruction errors. The present invention explicitly constrains spatiotemporal redundancy through low-rank neural modules (LRMs), and implements adaptive threshold learning through sparse neural modules (SNMs), overcoming the problem of lack of physical meaning in end-to-end black box models (such as U-Net). The present invention provides key technical support for portable magnetic resonance equipment through a deep separable spatiotemporal learning architecture and a multi-level knowledge distillation strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is the deep learning model structure adopted by the present invention.

[0046] Figure 2 This is the knowledge distillation implementation method of the present invention.

[0047] Figure 3 1 is the cardiac short-axis reconstruction result with an acceleration factor of 6 in an embodiment of the present invention, wherein (a) is a fully sampled image and (b) is an image reconstructed using the student model of the present invention. DETAILED DESCRIPTION

[0048] To make the objectives, technical solutions, and advantages of the present invention more clearly understood, the following embodiments will be further described with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention. The present invention encompasses any alternatives, modifications, equivalent methods, and solutions made within the spirit and scope of the present invention as defined by the claims.

[0049] In an embodiment of the present invention, a heart data set is used to train a teacher model and a student model, and undersampled data is input into the trained model for reconstruction, thereby obtaining reconstruction results of models with different parameter amounts and comparing them with time.

[0050] The specific implementation process is as follows:

[0051] 1) Dataset construction: Contains a total of 1218 valid samples, divided into a training set (997 cases), a validation set (100 cases), and a test set (121 cases, including 97 short-axis test data and 24 long-axis test data) in a ratio of approximately 8:1:1. and the fully sampled k-space is constructed using the undersampled template Respectively expressed as:

[0052]

[0053] in, is the undersampling operator, is the Fourier transform operator, channel sensitivity map Merged single-channel image 192, 192, 32, and 12 represent the frequency encoding length, phase encoding length, number of channels, and number of time frames, respectively. Indicates that and The Hadamard product of is arranged into the corresponding tensor, the operator correspond Operation on X. Y Perform two-dimensional inverse Fourier transform on the first two dimensions of each frame to obtain a multi-channel image To X J The channel dimension is merged to obtain a single-channel image X.

[0054] Will Split into 192 true value labels of the teacher model Compression X m The first dimension of the 192 student models is the true value label Undersampled k-space Y u The first two dimensions of each frame are obtained by two-dimensional inverse Fourier transform To X uJ Channel dimension merging to obtain aliased image Then X u Segmentation and dimensionality reduction resulted in 192 aliased images and as input to the teacher model and the student model respectively.

[0055] 2) Constructing teacher model and student model:

[0056]

[0057] in, Depend on Split along the first dimension, represents extracting the nth vector from the phase encoding dimension, Indicates the extraction of the t-th vector from the time dimension, Ψ represents the sparse transformation, is a vertically concatenated Toeplitz matrix, ||·||1 is the l1 norm, ||·||2 is the l2 norm, ||·|| F is the Frobenius norm, and the values of λ1 and λ2 are replaced by the neural network module.

[0058] Use Figure 1The deep separable spatiotemporal learning network shown in the figure consists of 10 cascaded iterative blocks, each of which contains three modules: a low-rank neural module, a sparse neural module, and a data verification module.

[0059] The low-rank neural module is designed as follows:

[0060]

[0061] in, represents the reconstruction result of step s-1, represents the low-rank module in the s-th iteration step, which Projected to the null space, there are 6 convolutional layers in the low-rank module of the teacher model, each convolutional layer contains 64 convolution kernels, and the convolution kernel size is 1×3×3; the student model is reduced to 4 convolutional layers, and the number of convolution kernels in each convolution layer is reduced to 16 according to the degree of distillation, and the convolution kernel size is 3×3. Represents the output of the s-th step of the low-rank neural network.

[0062] The sparse neural module is implemented using a learnable soft threshold module:

[0063]

[0064] in, and denote the sparse neural module outputs at the s-1th and sth iteration steps, respectively, is the sth soft threshold module, which changes the input value below the threshold γ to zero. is the sth threshold learning module, from The threshold γ of the soft threshold function is learned in S γ represents the soft threshold function and is defined as:

[0065]

[0066] Where sign(·) is the sign function, and max(·) means taking the maximum value. The data check item module is as follows:

[0067]

[0068] in, is the k-space output of step s, Y0 represents the undersampled k-space Y u , is the k-space of the output image of the s-th step low-rank module and sparse module, is a random undersampling template whose values only contain 0 and 1, is the corresponding complementary template, is a full 1 matrix, ρ1 and ρ2 are learnable regularization parameters, Represents the Hadamard product. Reconstructed image Depend on Obtained through inverse Fourier transform and channel merging.

[0069] 3) The loss function of the teacher model is composed of the model parameter low-rank loss And the true value loss

[0070]

[0071] Where, the superscript s represents the sth iteration block, Indicates the parameters θ of the low-rank module, ||·||1 is the l1 norm, is the relative difference between the teacher model output and the true value, and α1 and α2 are 0.1 and 0.9 respectively.

[0072] The loss function of the student model is composed of feature layer loss and truth loss It consists of two parts:

[0073]

[0074] Where, the superscript s represents the sth iteration block, and are the outputs of the teacher model and the student model respectively, ||·|| F is the Frobenius norm, is the relative difference between the output of the student model and the true value, β1 and β2 are 0.8 and 0.2 respectively. The shapes of the iterative block reconstruction results of the teacher model and the student model are and Calculating losses First, the reconstruction result of the student model Transformation and The same shape. The invention's knowledge distillation is realized as follows Figure 2 As shown, X0 represents the initial aliased image of the input, Represents the feature layer loss of the last iterative block.

[0075] In terms of training data, the teacher model uses The student model is trained with mixed images of After 50 epochs of training, both models have converged.

[0076] 4) Reconstruction of student model and teacher model: The acceleration factor is set to 6. The undersampled data is obtained by processing the fully sampled data k-space using a Cartesian random undersampled template. The undersampled data is input into the model to obtain the reconstructed image. The relative L2 norm error (RLNE) of the single-frame reconstructed image is defined as:

[0077]

[0078] in, represent the single-frame true image and reconstructed image respectively, ||·|| F is the Frobenius norm. The performance comparison between the teacher model and the student model is shown in Table 1.

[0079] Table 1 Performance indicators of teacher model and student model

[0080]

[0081] Note: The best indicators are in bold.

[0082] Table 1 shows that after knowledge distillation, the student model significantly reduces the number of parameters while maintaining similar reconstruction accuracy to the teacher model. The student model's parameters are reduced from 3.55 million in the teacher model to 290,000, a 92% reduction, significantly reducing the model's computational resource requirements. Single-frame reconstruction time is shortened from 2.12 seconds to 0.35 seconds, a sixfold acceleration, meeting clinical real-time requirements. The RLNE increases only from 0.070 to 0.073, a less than 4.3% increase, demonstrating that knowledge distillation effectively transfers key feature information from the teacher model.

[0083] Figure 3 The results of cardiac short axis reconstruction with an acceleration factor of 6 in the embodiment of the present invention are shown in Figure 1, where (a) is a full sampling image and (b) is a student model reconstruction image of the present invention. Figure 3 It can be seen that the image reconstructed by the student model of the present invention has a quality similar to that of the fully sampled image, indicating that the student model reconstruction accuracy is good and the present invention has practical value.

[0084] Experimental results show that the present invention achieves high-fidelity reconstruction with extremely low parameter counts through deep separable spatiotemporal learning and feature layer distillation strategies, solving the problems of large parameter counts and high deployment costs in traditional deep learning methods, and providing a feasible technical solution for rapid cardiac magnetic resonance imaging on mobile terminals or edge devices.

[0085] The above embodiments are only preferred embodiments of the present invention and should not be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent of the present invention.

Claims

1. A cardiac magnetic resonance reconstruction method using low-parameter learning, characterized by the following steps: 1) Acquire cardiac dynamic data for C cardiac cycles, merge the multi-channel data of each frame into a single-channel image, perform data segmentation and dimensionality reduction, and construct an image-dimensional-time-dimensional dataset; where C>0; 2) Designing a deep learning network of teacher and student models based on the optimized iterative expansion of the reconstruction model; 3) Construct a loss function and use the data set generated in step 1) to train the network; 4) Use the trained student model to reconstruct the undersampled data.

2. A cardiac magnetic resonance reconstruction method with low parameter learning as claimed in claim 1, characterized in that In step 1), the image dimension-time dimension dataset is constructed, and the full sampling k-space and the fully sampled k-space is constructed using the undersampled template Respectively expressed as: in, is the undersampling operator, is the Fourier transform operator, channel sensitivity map Merged single-channel image M, N, J, and T represent the frequency encoding length, phase encoding length, number of channels, and number of time frames, respectively. Indicates that and The Hadamard product of is arranged into the corresponding tensor, the operator correspond Operation on X; Y Perform two-dimensional inverse Fourier transform on the first two dimensions of each frame to obtain a multi-channel image To X J The channel dimension is merged to obtain a single-channel image X; Will Split into M true value labels of teacher models Compression X m The first dimension of gets the true value labels of M student models Undersampled k-space Y u The first two dimensions of each frame are obtained by two-dimensional inverse Fourier transform To X uJ Channel dimension merging to obtain aliased image Then X u Segmentation and dimensionality reduction to obtain M aliased images and As network inputs for the teacher model and student model respectively; and The difference in the calculation of the neural network is that the former requires a three-dimensional convolution, and the number of calculations for a single two-dimensional convolution is: O 2D =H out ×W out ×C out ×H kernel ×W kernel ×C in (3) Among them, M out ×N out ×C out H is the size of the output feature map, including width, height, and number of channels. kernel ×W kernel is the convolution kernel size, C in is the number of channels of the input feature map; the number of calculations of a single 3D convolution is: O 3D =O 2D ×D kernel ×D out (4) Among them, D kernel and D out They represent the dimensions of the convolution kernel and the output feature map respectively.

3. A cardiac magnetic resonance reconstruction method with low parameter learning as claimed in claim 1, characterized in that In step 2), the reconstructed model is expressed as: in, Depend on Split along the first dimension, represents extracting the nth vector from the phase encoding dimension, Indicates the extraction of the t-th vector from the time dimension, Ψ represents the sparse transformation, is a vertically concatenated Toeplitz matrix, ||·||1 is the l1 norm, ||·||2 is the l2 norm, ||·|| F is the Frobenius norm, λ1 and λ2 are regularization parameters; A deep separable spatiotemporal learning network is used, which consists of S cascaded iterative blocks. Each iterative block contains three modules: a low-rank neural module, a sparse neural module, and a data verification module. The low-rank neural module is designed as follows: in, represents the reconstruction result of step s-1, represents the low-rank module in the s-th iteration step, which Projected to the null space, the teacher model has N low-rank modules T convolutional layers, each of which contains n T convolution kernels, the convolution kernel size is 1×h×h; the student model is reduced to N S (N S <N T ) convolutional layers, the number of convolution kernels in each convolutional layer is reduced to n for different distillation levels S (n S <n T ), the convolution kernel size is h×h; Represents the output of the s-th step of the low-rank neural network; The sparse neural module is implemented using a learnable soft threshold module: in, and denote the sparse neural module outputs at the s-1th and sth iteration steps, respectively, is the sth soft threshold module, which changes the input value below the threshold γ to zero. is the sth threshold learning module, from The threshold γ of the soft threshold function is learned in S γ represents the soft threshold function and is defined as: Where sign(·) is the sign function, and max(·) means taking the maximum value. The data check item module is as follows: in, is the k-space output of step s, Y0 represents the undersampled k-space Y u , is the k-space of the output image of the s-th step low-rank module and sparse module, is an undersampling template whose values only contain 0 and 1, is the corresponding complementary template, is a full 1 matrix, ρ1 and ρ2 are learnable regularization parameters, represents the Hadamard product; image Depend on Obtained through inverse Fourier transform and channel merging.

4. A cardiac magnetic resonance reconstruction method with low parameter learning as claimed in claim 1, characterized in that In step 3), the constructed loss function includes the loss function of the teacher model and the loss function of the student model, which are as follows: The loss function of the teacher model is composed of the model parameter low-rank loss And the true value loss Where, the superscript s represents the sth iteration block, Indicates the parameters θ of the low-rank module, ||·||1 is the l1 norm, is the relative difference between the teacher model output and the true value, α1 and α2 are weight coefficients; The loss function of the student model is composed of feature layer loss and truth loss It consists of two parts: Where, the superscript s represents the sth iteration block, and are the outputs of the teacher model and the student model respectively, ||·|| F is the Frobenius norm, is the relative difference between the output of the student model and the true value, β1 and β2 are weight coefficients; the shapes of the iterative block reconstruction results of the teacher model and the student model are and Calculating losses First, the reconstruction result of the student model Transformation and Same shape; During the training process of the student model DS-λ, a strategy combining feature knowledge distillation and true value learning is adopted. The deep feature information of the teacher model is transferred by minimizing the difference between the outputs of the corresponding iterative blocks of the teacher model and the student model. The larger the λ, the higher the degree of model knowledge distillation and the smaller the corresponding parameter amount. Secondly, the fully sampled image is introduced as a reference for the accurate reconstruction of the student model.

5. The cardiac magnetic resonance reconstruction method with low parameter learning as claimed in claim 1, characterized in that: In step 4), the reconstruction is to convert the aliased image Input into the teacher or student model for reconstruction, and get

Images