Regularization-based parallel magnetic resonance imaging reconstruction method and system

Abstract

The invention relates to a regularization-based parallel magnetic resonance imaging reconstruction method and a regularization-based parallel magnetic resonance imaging reconstruction system, which are used for realizing parallel magnetic resonance imaging reconstruction with high generalization, high stability and high convergence. The method comprises the steps of obtaining a to-be-reconstructed MRI image and an undersampling observation image, and obtaining an objective function of a typical ill-conditioned inverse problem according to the to-be-reconstructed MRI image and the undersampling observation image; setting regularization parameters in the objective function of the typical ill-conditioned inverse problem by adopting a deep learning technology to obtain an objective function fused with deep learning enhancement; and solving the fusion deep learning enhanced target function to obtain a final reconstructed MRI image.

Description

Technical Field

[0001] This application relates to the field of magnetic resonance imaging, and in particular to a regularized parallel magnetic resonance imaging reconstruction method and system. Background Technology

[0002] Parallel magnetic resonance imaging (pMRI) systems utilize multiple receiver coils to perform parallel undersampling of MRI data to reduce MRI imaging scan time. However, undersampled MRI data will result in a large number of aliasing artifacts in the imaging, blurring tissue structural details. Therefore, reconstruction algorithms need to be designed to reconstruct the data and obtain a final reconstructed MRI image.

[0003] Inversely extrapolating from complete MRI data based on undersampled data is a typical ill-conditioned inverse problem, characterized by non-unique and unstable solutions. Its objective function can often be expressed as the sum of a data consistency term and a regularization term, where the data consistency term is used to approximate the observed data, and the regularization term is used to shrink the solution space and impose constraints on the solution process.

[0004] Traditional MRI reconstruction algorithms are constrained by data consistency terms and regularization terms, resulting in an upper limit to the model. At low sampling rates, the data consistency terms struggle to correctly constrain MRI data, leading to reconstruction errors. With the rise of deep learning, researchers have combined deep learning techniques with traditional mathematical optimization models to improve reconstruction performance. However, inappropriate combination strategies can cause generalization problems in the joint model, interfering with the interpretability and convergence of traditional reconstruction models.

[0005] A search of existing technical literature revealed a patent application (application number 202410581595.8) entitled "A Method for Reconstructing Three-Dimensional Magnetic Resonance Compressed Images." This patent addresses the problems of traditional PnP framework schemes, which easily lose the overall image structure and may contain a large number of false details, interfering with diagnosis. It creates an optimization model for the reconstruction problem, including a low-rank regularization term and two implicit regularization terms, and solves the model iteratively using an alternating direction multiplier algorithm. However, this patent suffers from limitations in generalization and its ability to extract feature information that reflects the general laws of signals. Summary of the Invention

[0006] Therefore, it is necessary to provide a regularized parallel magnetic resonance imaging reconstruction method and system to address the above-mentioned technical problems, so as to achieve parallel magnetic resonance imaging reconstruction with high generalization, high stability and high convergence.

[0007] To solve the above-mentioned technical problems, the present invention provides the following technical solution: On one hand, the present invention provides a regularized parallel magnetic resonance imaging reconstruction method, the method comprising: S1: Obtain the MRI image to be reconstructed and the undersampled observation image, and obtain the objective function of the typical ill-conditioned inverse problem based on the MRI image to be reconstructed and the undersampled observation image; S2: The regularization parameter in the objective function of the typical ill-conditioned inverse problem is set using deep learning technology to obtain an objective function enhanced by deep learning. S3: Solve the objective function of the fused deep learning enhancement to obtain the final reconstructed MRI image.

[0008] Preferably, the objective function of the typical ill-conditioned inverse problem is calculated as follows:

[0009] in, This represents the MRI image to be reconstructed. This represents an undersampled observation image. Indicates data consistency items. Represents the regularization parameter. Represents a regular term, Indicates based on Perform regularization parameter calculation.

[0010] Preferably, data consistency items Defined based on the SENSE model or SPIRiT model.

[0011] Preferably, the deep learning technology employs a denoised score matching deep learning technique.

[0012] Preferably, the objective function calculation expression for the fusion deep learning enhancement is as follows:

[0013] in, This represents a deep learning network. Represents the parameters of a deep learning network. This indicates that the constraints of the MRI images to be reconstructed are obtained using a deep learning network. ,based on Perform regularization parameter calculation.

[0014] Preferably, a mathematical optimization iterative algorithm is used to iteratively solve the objective function of the fused deep learning enhancement.

[0015] Preferably, the objective function fused with deep learning enhancements is solved iteratively using a mathematical optimization iterative algorithm, including: S301: Set the iteration count k to zero; S302: Use a pre-trained deep learning network to constrain the MRI image to be reconstructed in the kth generation to obtain the regularization parameters of the kth generation. S303: Reconstruct the MRI image to be reconstructed in the kth generation according to the regularization parameter of the kth generation; S304: Increment the iteration count k by one; S305: Repeat steps S302 to S304 until the preset number of iterations is reached to obtain the final reconstructed MRI image.

[0016] Preferably, the mathematical optimization solution iterative algorithm includes the PD3O algorithm.

[0017] On the other hand, the present invention provides a regularized parallel magnetic resonance imaging reconstruction system, the system comprising: a function construction module, a function optimization module, and a function solving module; The function construction module is used to acquire the MRI image to be reconstructed and the undersampled observation image, and to obtain the objective function of a typical ill-conditioned inverse problem based on the MRI image to be reconstructed and the undersampled observation image; The function optimization module is used to set the regularization parameter in the objective function of the typical ill-conditioned inverse problem using deep learning technology, so as to obtain an objective function enhanced by deep learning. The function solving module is used to solve the objective function of the fused deep learning enhancement to obtain the final reconstructed MRI image.

[0018] Preferably, the objective function calculation expression for the fusion deep learning enhancement is as follows:

[0019] in, This represents the MRI image to be reconstructed. This represents an undersampled observation image. Indicates data consistency items. Represents the regularization parameter. Represents a regular term, This represents a deep learning network. Represents the parameters of a deep learning network. This indicates that the constraints of the MRI images to be reconstructed are obtained using a deep learning network. ,based on Perform regularization parameter calculation.

[0020] Compared with the prior art, the beneficial effects of the present invention are: This invention provides a regularization-based parallel magnetic resonance imaging (MRI) reconstruction method and system. In the parallel MRI reconstruction process, the deep learning technology used only affects the setting of regularization parameters, without affecting the solution and convergence of the original mathematical optimization model. It simply changes the process from manually adjusting regularization parameters to relying on deep learning priors for auxiliary settings, ensuring the model's stability and convergence. Simultaneously, it retains the classic linear regularization system, thus possessing the ability to constrain general prior laws of MRI signals (such as smoothness, sparsity, and low rank), thereby ensuring the regularization term's ability to suppress undersampling artifacts and noise, and thus guaranteeing the generalization ability of the joint optimization model to a certain extent. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of a regularization-based parallel magnetic resonance imaging reconstruction method in one embodiment. Figure 2 This is a schematic diagram of the main process of the k-th iteration of the regularized parallel magnetic resonance imaging reconstruction method using mathematical optimization to solve the iterative algorithm in one embodiment; Figure 3 This is a schematic diagram of the k-th iteration image data of a regularized parallel magnetic resonance imaging reconstruction method using a mathematical optimization solution iterative algorithm in one embodiment. Figure 4 This is a schematic diagram of a regularized parallel magnetic resonance imaging reconstruction system framework in one embodiment. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0023] Example 1 like Figure 1 As shown, this embodiment proposes a regularization-based parallel magnetic resonance imaging reconstruction method, the method comprising: S1: Obtain the MRI image to be reconstructed and the undersampled observation image, and obtain the objective function of the typical ill-conditioned inverse problem based on the MRI image to be reconstructed and the undersampled observation image; The specific implementation method for this step is as follows: Parallel magnetic resonance imaging (MRI) systems utilize multiple receiver coils to perform parallel undersampling of MRI data to reduce MRI imaging scan time. However, undersampled images result in numerous aliasing artifacts and blurred tissue details, necessitating the design of reconstruction algorithms to obtain clear MRI images. Back-calculating complete MRI data from undersampled images is a typical ill-conditioned inverse problem, characterized by non-unique and unstable solutions. Its objective function can often be expressed as the sum of a data consistency term and a regularization term, where the data consistency term approximates the observed data, and the regularization term shrinks the solution space, imposing constraints on the solution process. The objective function calculation expression for a typical ill-conditioned inverse problem is as follows:

[0024] In this mathematical optimization model This represents the MRI image to be reconstructed. This represents an undersampled observation image. This represents a data consistency term used to approximate undersampled observation images. , This represents the regularization parameter, used to adjust the weights between data consistency terms and regularization terms. Regularization terms, such as total variational regularization, wavelet regularization, and tight frame regularization, are used to extract signal features, impose additional prior constraints to shrink the solution space, and improve signal processing accuracy. Indicates based on Perform regularization parameter calculation.

[0025] However, traditional MRI reconstruction algorithms are constrained by data consistency terms and regularization terms, resulting in a model upper limit. When the sampling rate is low, the data consistency term struggles to correctly constrain the MRI data, leading to reconstruction errors. With the rise of deep learning technology, combining deep learning with traditional mathematical optimization models can improve reconstruction performance. However, inappropriate combination strategies can cause generalization problems in the joint model, interfering with the interpretability and convergence of traditional reconstruction models. Therefore, it is necessary to optimize the objective function of typical ill-conditioned inverse problems, using regularization parameters as a bridge to construct an objective function enhanced by deep learning, thereby improving the generalization, interpretability, and model convergence issues caused by combining deep learning techniques.

[0026] S2: The regularization parameter in the objective function of the typical ill-conditioned inverse problem is set using deep learning technology to obtain an objective function enhanced by deep learning. The specific implementation method for this step is as follows: Based on traditional mathematical optimization models, this invention proposes a novel joint optimization model that combines deep learning techniques, namely, an objective function that integrates deep learning enhancements, and its calculation expression is as follows:

[0027] in, This represents the MRI image to be reconstructed. This represents an undersampled observation image. Indicates data consistency items. Represents the regularization parameter. Represents a regular term, This represents a deep learning network. Represents the parameters of a deep learning network. This indicates that the constraints of the MRI images to be reconstructed are obtained using a deep learning network. ,based on The calculation of regularization parameters, in fact, means that the joint optimization model is to use deep learning technology to provide guidance on setting regularization parameters for reconstruction algorithms based on mathematical optimization models, capture potential prior information based on data-driven approaches, and thus improve the ability of regularization terms to suppress undersampling artifacts and noise, thereby improving reconstruction accuracy.

[0028] This joint optimization model has the following advantages: Deep learning techniques only affect the setting of regularization parameters and do not influence the solution or convergence of the original mathematical optimization model. They merely change the process from manually adjusting regularization parameters to relying on deep learning priors for auxiliary settings. The original model still strictly relies on mathematical algorithms for solving the problem, unaffected by the unknown implicit mappings associated with deep learning techniques, thus ensuring the model's stability and convergence.

[0029] It retains the classic linear regularization system, thus having the ability to constrain the general prior laws of MRI signals (such as smoothness, sparsity, and low rank), thereby ensuring the ability of the regularization term to suppress undersampling artifacts and noise, and thus ensuring the generalization of the joint optimization model to a certain extent.

[0030] Replacing experimental priors with manually set regularization parameters with deep priors obtained from data-driven learning provides additional potential prior information and improves solution accuracy.

[0031] For mathematical optimization models, regularization parameters are a common and important hyperparameter. They are usually set through additional strategies and do not affect the algorithm's solution. The joint optimization model that integrates deep learning enhancements can theoretically be widely used and has versatility.

[0032] S3: Solve the objective function of the fused deep learning enhancement to obtain the final reconstructed MRI image.

[0033] The specific implementation method for this step is as follows: The objective function fused with deep learning enhancements is iteratively solved using a mathematical optimization iterative algorithm. The main process of the k-th iteration of the mathematical optimization iterative algorithm is described as follows: Figure 2 As shown, as a plug-and-play regularization parameter setting method, based on the original mathematical optimization model solution iteration, the regularization parameters can be set in a plug-and-play manner only through deep learning technology (such as DSM technology).

[0034] Specifically, such as Figure 3 As shown, the first row represents the reconstructed image and the real target image in the k-th iteration. To improve the effectiveness of the regularization parameter, it is often estimated based on the information of the current reconstructed image. The second row represents the regularization parameter estimated based on the MRI image information in the first row. The third row represents the final reconstructed image and a magnified local image (the magnified local area is marked by the white box in the first row) obtained by the reconstruction algorithm based on the regularization parameter set in the second row. Based on the final reconstruction effect, it can be seen that as the number of iterations increases, the accuracy of the reconstructed image corresponding to the estimated regularization parameter continuously improves; and the highest reconstruction accuracy is achieved when using the regularization parameter estimated from the real target image.

[0035] Based on this experimental prior—that regularization parameters estimated from high-quality MRI signals with clear structure and no artifacts have a higher constraint on undersampling artifacts and noise—this invention proposes to transform this experimental prior into a deep prior using a deep learning denoiser. Specifically, denoising score matching (DSM) deep learning technology is used as a denoiser to optimize the MRI image data during algorithm iteration. Regularization parameters are then set based on the optimized MRI signal and applied to the algorithm iteration. This process achieves the setting of regularization parameters based on high-quality MRI signals, thus conforming to the aforementioned experimental prior and contributing to improved reconstruction accuracy.

[0036] Example 2 This embodiment further illustrates the regularization-based parallel magnetic resonance imaging reconstruction method proposed in the above embodiments.

[0037] The objective function for the typical ill-conditioned inverse problem is expressed as follows:

[0038] in, This represents the MRI image to be reconstructed. This represents an undersampled observation image. Indicates data consistency items. Represents the regularization parameter. Represents a regular term, Indicates based on Perform regularization parameter calculation.

[0039] Data Consistency Items Defined based on the SENSE model or SPIRiT model.

[0040] The deep learning technology mentioned employs a denoised score matching deep learning technique.

[0041] The objective function for the fusion deep learning enhancement is calculated as follows:

[0042] in, This represents a deep learning network. Represents the parameters of a deep learning network. This indicates that the constraints of the MRI images to be reconstructed are obtained using a deep learning network. ,based on Perform regularization parameter calculation.

[0043] The objective function of the fusion deep learning enhancement is solved iteratively using a mathematical optimization solution iterative algorithm.

[0044] The objective function fused with deep learning enhancements is solved iteratively using a mathematical optimization algorithm, including: S301: Set the iteration count k to zero; S302: Use a pre-trained deep learning network to constrain the MRI image to be reconstructed in the kth generation to obtain the regularization parameters of the kth generation. S303: Reconstruct the MRI image to be reconstructed in the kth generation according to the regularization parameter of the kth generation; S304: Increment the iteration count k by one; S305: Repeat steps S302 to S304 until the preset number of iterations is reached to obtain the final reconstructed MRI image.

[0045] The mathematical optimization iterative algorithm includes the PD3O algorithm.

[0046] The specific implementation method for this step is as follows: In this invention, the solution to the optimization model is not limited to a single mathematical optimization iterative algorithm, which is one of the advantages of this invention. The PD3O optimization algorithm has a rigorous convergence proof and high solution efficiency. In particular, the objective function of a typical ill-conditioned inverse problem has the following mathematical form:

[0047] in, This indicates a linear sampling operation. This indicates that the regularization system applies to signals. The feature extraction operations (such as total variation decomposition, wavelet decomposition, tight frame decomposition, etc.) are performed, and the remaining variables are defined as described above. Then, under the PD3O algorithm, the above model has the following iterative form:

[0048] in, This indicates the conjugate transpose operation. This represents the soft thresholding function. Based on this iterative process, it is clear that in solving the PD3O optimization algorithm, it is explicitly necessary to define the operators related to the regularization function. However, technologies such as plug-and-play and end-to-end network architecture, which do not have a clear definition of regularization functions, obviously cannot be applied in the PD3O algorithm.

[0049] Example 3 like Figure 4 As shown, a regularization-based parallel magnetic resonance imaging reconstruction system includes: a function construction module, a function optimization module, and a function solving module; The function construction module is used to acquire the MRI image to be reconstructed and the undersampled observation image, and to obtain the objective function of a typical ill-conditioned inverse problem based on the MRI image to be reconstructed and the undersampled observation image; The function optimization module is used to set the regularization parameter in the objective function of the typical ill-conditioned inverse problem using deep learning technology, so as to obtain an objective function enhanced by deep learning. The function solving module is used to solve the objective function of the fused deep learning enhancement to obtain the final reconstructed MRI image.

[0050] The objective function for the fusion deep learning enhancement is calculated as follows:

[0051] in, This represents the MRI image to be reconstructed. This represents an undersampled observation image. Indicates data consistency items. Represents the regularization parameter. Represents a regular term, This represents a deep learning network. Represents the parameters of a deep learning network. This indicates that the constraints of the MRI images to be reconstructed are obtained using a deep learning network. ,based on Perform regularization parameter calculation.

Claims

1. A regularized parallel magnetic resonance imaging reconstruction method and system, characterized in that, include: S1: Obtain the MRI image to be reconstructed and the undersampled observation image, and obtain the objective function of the typical ill-conditioned inverse problem based on the MRI image to be reconstructed and the undersampled observation image; S2: The regularization parameter in the objective function of the typical ill-conditioned inverse problem is set using deep learning technology to obtain an objective function enhanced by deep learning. S3: Solve the objective function of the fused deep learning enhancement to obtain the final reconstructed MRI image.

2. The regularization-based parallel magnetic resonance imaging reconstruction method and system according to claim 1, characterized in that, The objective function for the typical ill-conditioned inverse problem is expressed as follows: in, This represents the MRI image to be reconstructed. This represents an undersampled observation image. Indicates data consistency items. Represents the regularization parameter. Represents a regular term, Indicates based on Perform regularization parameter calculation.

3. The regularization-based parallel magnetic resonance imaging reconstruction method and system according to claim 2, characterized in that, Data Consistency Items Defined based on the SENSE model or SPIRiT model.

4. The regularization-based parallel magnetic resonance imaging reconstruction method and system according to claim 1, characterized in that, The deep learning technology mentioned employs a denoised score matching deep learning technique.

5. The regularization-based parallel magnetic resonance imaging reconstruction method and system according to claim 2, characterized in that, The objective function for the fusion deep learning enhancement is calculated as follows: in, This represents a deep learning network. Represents the parameters of a deep learning network. This indicates that the constraints of the MRI images to be reconstructed are obtained using a deep learning network. ,based on Perform regularization parameter calculation.

6. The regularization-based parallel magnetic resonance imaging reconstruction method and system according to claim 1, characterized in that, The objective function of the fusion deep learning enhancement is solved iteratively using a mathematical optimization solution iterative algorithm.

7. The regularization-based parallel magnetic resonance imaging reconstruction method and system according to claim 6, characterized in that, The objective function fused with deep learning enhancements is solved iteratively using a mathematical optimization algorithm, including: S301: Set the iteration count k to zero; S302: Use a pre-trained deep learning network to constrain the MRI image to be reconstructed in the kth generation to obtain the regularization parameters of the kth generation. S303: Reconstruct the MRI image to be reconstructed in the kth generation according to the regularization parameter of the kth generation; S304: Increment the iteration count k by one; S305: Repeat steps S302 to S304 until the preset number of iterations is reached to obtain the final reconstructed MRI image.

8. The regularization-based parallel magnetic resonance imaging reconstruction method and system according to claim 6 or 7, characterized in that, The mathematical optimization iterative algorithm includes the PD3O algorithm.

9. A regularization-based parallel magnetic resonance imaging reconstruction system, comprising: Function construction module, function optimization module, and function solving module; The function construction module is used to acquire the MRI image to be reconstructed and the undersampled observation image, and to obtain the objective function of a typical ill-conditioned inverse problem based on the MRI image to be reconstructed and the undersampled observation image; The function optimization module is used to set the regularization parameter in the objective function of the typical ill-conditioned inverse problem using deep learning technology, so as to obtain an objective function enhanced by deep learning. The function solving module is used to solve the objective function of the fused deep learning enhancement to obtain the final reconstructed MRI image.

10. The regularized parallel magnetic resonance imaging reconstruction system according to claim 9, characterized in that, The objective function for the fusion deep learning enhancement is calculated as follows: in, This represents the MRI image to be reconstructed. This represents an undersampled observation image. Indicates data consistency items. Represents the regularization parameter. Represents a regular term, This represents a deep learning network. Represents the parameters of a deep learning network. This indicates that the constraints of the MRI images to be reconstructed are obtained using a deep learning network. ,based on Perform regularization parameter calculation.

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