An MRI reconstruction method based on an orthogonal decomposition-based subspace diffusion model

Abstract

The present invention provides an MRI reconstruction method based on an orthogonal decomposition-based subspace diffusion model, including: forming an open-source brain dataset; constructing an orthogonal decomposition-based subspace diffusion model, which diffuses by decomposing k-space data into subspaces to better capture the data distribution and maintain robustness in a noisy environment; designing an iterative solution algorithm for extracting prior information within the model; applying the iterative solution algorithm to the model to test a test dataset and output a final repaired image. The present invention promotes the learning of effective information in complex distributions, solves the inherent high-dimensional extrapolation challenge, and reduces the computational cost associated with diffusion models. Comprehensive experiments on different datasets clearly show that the present invention is superior to other methods in terms of reconstruction speed and quality.

Description

Technical Field

[0001] The present invention belongs to the technical field of image processing, and particularly relates to an MRI reconstruction method based on a subspace diffusion model of orthogonal decomposition. Background Art

[0002] MRI (Magnetic Resonance Imaging) has become an indispensable part of the modern medical system and plays a crucial role in disease diagnosis, treatment planning, and preventive measures. However, due to its inherent data acquisition mode, the imaging time is too long, that is, the scanning of k-space data requires a long time, which has become a major bottleneck in clinical applications. The overly long imaging time can cause many problems. For example, patient movement may lead to artifacts in the reconstructed image. In addition, for fields such as cardiac dynamic imaging, interventional imaging, brain functional imaging, and contrast-enhanced imaging, the existing MRI still cannot meet the requirements of fast imaging, which to a certain extent restricts its wide application in clinical practice. To sum up, although MRI can provide detailed physiological structure information, if the imaging time can be significantly shortened while ensuring the image reconstruction quality, the application prospect of MRI will be greatly improved. Therefore, fast magnetic resonance image reconstruction is not only a highly challenging topic but also has important scientific research value and social significance.

[0003] To improve the scanning efficiency and accelerate the diagnosis process, the prior art provides various strategies to achieve undersampling of k-space data and combines prior knowledge for image reconstruction. From the initial technology based on compressed sensing to the models based on deep learning in recent years, these technologies have made great progress in clinical applications. However, how to shorten the imaging time while ensuring the reconstruction accuracy remains an urgent problem to be solved. For this reason, the diffusion model, as an emerging framework, has attracted much attention because it can more accurately represent the data distribution and shows great potential in reconstructing MRI images. The diffusion model defines a forward diffusion process, gradually adds Gaussian noise to the input data in several steps, and learns a reverse diffusion process to recover a clear image from the noisy data.

[0004] Although certain achievements have been made in the research of the diffusion model in the field of fast magnetic resonance image reconstruction, due to the high-dimensional complexity of k-space data itself, the reconstruction process still consumes a large amount of computing resources, the diffusion model generation process is slow, the applicability to specific data types is limited, and the dimension cannot be effectively reduced. To address this challenge, a series of related technologies have been developed, such as the dual-domain end-to-end method, the self-consistent term, and the low-rank regularization of the Hankel matrix. In addition, the segmentation of k-space data has also been proven to be an effective simplification strategy, such as high-low frequency separation. These methods not only help to overcome the current problems but also have the value of further research.

[0005] Meanwhile, based on the spatial redundancy in the image signal, there is no need to maintain full-dimensional information during the generation process, especially in the early stage. Therefore, the subspace modeling method exhibits higher robustness and accuracy compared to the full-space modeling. Research shows that in many practical cases, the target data is close to a linear subspace. Under the action of linear diffusion, the data components orthogonal to the subspace tend to the Gaussian distribution faster than the components within the subspace. Thus, the high-dimensional data processed by the orthogonal decomposition strategy can gradually diffuse into the subspace, while being compatible with the underlying continuous diffusion framework, retaining all the advantages of the continuous fractional model, such as likelihood evaluation, probability flow sampling, and controllable generation. Based on the above theory, full-dimensional network modeling is performed under low-noise conditions, and a smaller network is used to model the non-Gaussian components under high-noise conditions, which can effectively reduce the required computational amount.

[0006] In summary, applying the subspace orthogonal method to MRI image reconstruction has considerable potential and broad prospects. However, since its adaptation to magnetic resonance images is still in the early stage, there is still room for improvement. Summary of the Invention

[0007] The object of the present invention is to propose a feasible, excellent-performance, and strong-environment-adaptability MRI reconstruction method based on the subspace diffusion model of orthogonal decomposition. For magnetic resonance image reconstruction, this method can not only efficiently reconstruct magnetic resonance images but also effectively retain the structural details of magnetic resonance images, thereby obtaining clear texture performance and significantly improving the overall quality of magnetic resonance images.

[0008] To achieve the above object, the technical solution provided by the present invention is as follows: An MRI reconstruction method based on the subspace diffusion model of orthogonal decomposition, comprising the following steps:

[0009] Step A: Form an open-source brain dataset, which is divided into a training dataset and a test dataset;

[0010] Step B: Based on the training dataset, construct a subspace diffusion model based on orthogonal decomposition. The subspace diffusion model based on orthogonal decomposition diffuses by decomposing the k-space data into the subspace, so as to better capture the data distribution and maintain robustness in a noisy environment;

[0011] Step C: Design an iterative solution algorithm for extracting the prior information within the subspace diffusion model based on orthogonal decomposition;

[0012] Step D: Apply the iterative solution algorithm to the subspace diffusion model based on orthogonal decomposition to test the test dataset, and output the final repaired image, the peak signal-to-noise ratio and the structural similarity of the test result image, so as to evaluate the image quality.

[0013] Optionally, the formation process of the training dataset in step A specifically includes:

[0014] Prepare a first quantity of original images;

[0015] Expand the first quantity of original images into a second quantity of images through flipping and rotation to form a training dataset.

[0016] Optionally, step B specifically includes the following sub-steps:

[0017] (1) Design the network structure

[0018] Diffusion model: The diffusion process is described by an SDE, and the mathematical formula is as follows:

[0019] ,

[0020] In the formula, is the drift coefficient of the SDE, is the diffusion coefficient, is the standard Brownian motion, t is the continuous time variable, x is the data sample;

[0021] The reverse diffusion process is described by a reverse SDE, and the mathematical formula is as follows:

[0022] ,

[0023] In the formula, is an infinitesimal reverse time step, is the reverse Brownian motion, is the fractional function;

[0024] Taking m as the time point, divide the diffusion time into multiple sub-intervals , and the mathematical formula for the sub-space diffusion process is as follows:

[0025] ,

[0026] In the formula, is an orthogonal matrix, and T is the transpose of the matrix;

[0027] Drift coefficient The mathematical formula is as follows:

[0028] ,

[0029] In the formula, δ ( ) represents the Dirac function, is the identity matrix;

[0030] The high-dimensional probability distribution from k-space data is decomposed into low-frequency components and high-frequency components in the diffusion process through DWT, and the mathematical formula is as follows:

[0031] ,

[0032] ,

[0033] In the formula, W represents DWT, represents the LL low-frequency component, represent the LH high-frequency component, HL high-frequency component, and HH high-frequency component respectively, represents the inner product, i and j represent one of the LL low-frequency component, LH high-frequency component, HL high-frequency component, and HH high-frequency component respectively;

[0034] All these frequency components K in the wavelet domain, the mathematical formula is as follows:

[0035] ;

[0036] (2) Train the subspace diffusion model based on orthogonal decomposition

[0037] The diffusion process in the subspace is described by SDE, and the mathematical formula is as follows:

[0038] ;

[0039] The subspace diffusion model based on orthogonal decomposition is trained through the following mathematical formula:

[0040] ,

[0041] In the formula, represents the expectation with respect to time , λt is a positive weight function, represents the expectation with respect to the initial data distribution , represents the conditional distribution of given and the expectation of sampling, is the estimated log probability function, is the gradient of the exact log probability function;

[0042] The subspace diffusion model based on orthogonal decomposition is made to learn the k-space data distribution through continuous cyclic iteration until a convergence value is reached through multiple iterations, and finally the model construction is completed.

[0043] Optionally, step C specifically includes the following sub-steps:

[0044] Predictions are made through a subspace diffusion model based on orthogonal decomposition, followed by correction. The predictor-corrector sampler alternates multiple times between the full space and the subspace to achieve convergence;

[0045] Enforce data consistency within the subspace to guide the sampling process, with the mathematical formula as follows:

[0046] ,

[0047] In the formula, is the imaging operator, is the k-space data to be reconstructed, is the measured data, is the data term generated by the subspace diffusion model based on orthogonal decomposition in the k-space, is the regularization parameter;

[0048] After network iteration, a traditional low-rank optimization operator is added to convert the k-space data matrix into the form of a Hankel matrix and recover the low-rank matrix, with the mathematical formula as follows:

[0049] ,

[0050] In the formula, is the Hankel pseudo-inverse operator, is the low-rank matrix with low-rank properties after performing hard-threshold singular value operation, is the low-rank matrix is the rank of, is the k-space data optimized through low-rank matrix completion.

[0051] Compared with the prior art, the beneficial effects of the present invention are:

[0052] The present invention proposes a subspace diffusion model framework that uses joint orthogonal decomposition to handle complex distributions, aiming to improve the reconstruction accuracy while increasing the sampling rate. Specifically, the inherent forward diffusion process of the diffusion model is migrated into the subspace to address the high-dimensional extrapolation and computational cost problems existing in the diffusion model. Meanwhile, the orthogonal transformation further decomposes the complex high-dimensional k-space into multiple low-dimensional frequency sub-components, making it easier to distinguish and learn the true distribution of noise in the high-frequency space. Therefore, the low-dimensional signals can almost completely represent the original data. Through a large number of theoretical analyses and strict experimental verifications, it is confirmed that the present invention not only outperforms the existing full-space MRI reconstruction methods, but also provides better results compared with the traditional score-based diffusion methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1It is a flowchart of an MRI reconstruction method based on an orthogonal decomposition subspace diffusion model of the present invention;

[0054] Figure 2 It is a schematic diagram of the training stage and iterative reconstruction stage of the subspace diffusion model based on orthogonal decomposition of the present invention;

[0055] Figure 3 They are the reconstruction diagram, enlarged diagram and error diagram of the present invention under the Radial sampling mode with an acceleration multiple of 12, where (a) is the under-sampled diagram, (g) is the original diagram, and (b), (c), (d), (e), (f) are the reconstruction result diagrams of SAKE, ESPIRIT, EBMRec, HKGM and the present invention respectively;

[0056] Figure 4 They are the reconstruction diagram, enlarged diagram and error diagram of the present invention under the Random sampling mode with an acceleration multiple of 12, where (a) is the under-sampled diagram, (g) is the original diagram, and (b), (c), (d), (e), (f) are the reconstruction result diagrams of SAKE, ESPIRIT, EBMRec, HKGM and the present invention respectively. Detailed implementation manners

[0057] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are only used to explain the technical solutions of the present invention and are not limited to the present invention.

[0058] In order to solve the problems that in the magnetic resonance image reconstruction task, the diffusion model has a slow generation process, limited applicability to specific data types, and inability to effectively reduce dimensions, etc., the present invention intends to propose a new method that cascades the orthogonal decomposition of k-space data and subspace diffusion generation for fast magnetic resonance image reconstruction: by using an orthogonal decomposition strategy to reduce the dimension of complex k-space data and obtain mutually orthogonal high-frequency components and low-frequency components. When generating samples, since the probability density is orthogonalized to reduce the dimension, the diffusion model can directly estimate the prior distribution in the low-dimensional data subspace.

[0059] (1) Figure 1 It is a flowchart of the present invention. Now, with reference to the attached Figure 1 The specific steps of the method of the present invention will be described. An MRI reconstruction method based on an orthogonal decomposition subspace diffusion model provided by the present invention includes steps A to D.

[0060] Step A: Form an open-source brain dataset, which is divided into a training dataset and a test dataset.

[0061] The formation process of the training dataset in step A specifically includes:

[0062] Prepare a first quantity of original images;

[0063] Expand the first quantity of original images into a second quantity of images through flipping and rotation to form a training dataset.

[0064] In the specific implementation of step A, for example: Prepare 500 original images provided by the Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences. Expand the prepared 500 original images to 4000 images through flipping and rotation to form a training dataset, thereby ensuring more comprehensive training to improve the model performance. Additionally, prepare some extra images to form a test dataset. Among them, the training dataset is used to train the model or determine the model parameters, while the test dataset is used to test the generalization ability of the already trained model.

[0065] Step B: Based on the training dataset, construct a subspace diffusion model based on orthogonal decomposition. The subspace diffusion model based on orthogonal decomposition performs diffusion by decomposing k-space data into subspaces, thereby better capturing the data distribution and maintaining robustness in a noisy environment.

[0066] Step B specifically includes the following sub-steps:

[0067] (1) Design the network structure

[0068] Diffusion model: Use SDE to describe the diffusion process. The mathematical formula is as follows:

[0069] ,

[0070] In the formula, is the drift coefficient of SDE, is the diffusion coefficient, is the standard Brownian motion, t is the continuous time variable, x is the data sample;

[0071] Use the reverse SDE to describe the reverse diffusion process. The mathematical formula is as follows:

[0072] ,

[0073] In the formula, is an infinitesimal reverse time step, is the reverse Brownian motion, is the fractional function;

[0074] Taking m as the time point, divide the diffusion time into multiple sub-intervals , and the mathematical formula of the subspace diffusion process is as follows:

[0075] ,

[0076] wherein is an orthogonal matrix, and T is the transpose of the matrix;

[0077] drift coefficient has the following mathematical formula:

[0078] ,

[0079] wherein δ ( ) represents the Dirac function, is the identity matrix;

[0080] The high-dimensional probability distribution of the data from the k-space is decomposed into low-frequency components and high-frequency components in the diffusion process through DWT, and the mathematical formula is as follows:

[0081] ,

[0082] ,

[0083] wherein, W represents DWT, represents the LL low-frequency component, respectively represent the LH high-frequency component, the HL high-frequency component, and the HH high-frequency component, represents the inner product, i and j respectively represent one of the LL low-frequency component, the LH high-frequency component, the HL high-frequency component, and the HH high-frequency component;

[0084] All these frequency components K in the wavelet domain have the following mathematical formula:

[0085] ;

[0086] (2) Training the subspace diffusion model based on orthogonal decomposition

[0087] The diffusion process in the subspace is described by SDE, and the mathematical formula is as follows:

[0088] ;

[0089] The subspace diffusion model based on orthogonal decomposition is trained by the following mathematical formula:

[0090] ,

[0091] wherein represents the expectation with respect to time , λt is a positive weight function, represents the expectation with respect to the initial data distribution , represents that given condition, for Conditional distribution The expectation of sampling, is the estimated log probability function, which is the gradient of the exact log probability function;

[0092] The subspace diffusion model based on orthogonal decomposition learns the k-space data distribution through continuous iterative loops until a convergence value is reached through multiple iterations, and finally the model construction is completed.

[0093] In the specific implementation of step B, for example:

[0094] The inherent forward process of the diffusion model is migrated to the subspace Specifically, the forward diffusion starts in the entire space, but over time, at a certain point in time, the k-space data is reduced to the subspace using DWT (Discrete Wavelet Transform), and the forward diffusion is projected and restricted to a smaller subspace. For any form of diffusion process, the present invention defines the corresponding subspace diffusion as follows: taking as the time point, the diffusion time is divided into multiple sub-intervals, that is . Subsequently, in each interval of, the diffusion process in the subspace can be redefined as follows:

[0095] ,

[0096] wherein, is an orthogonal matrix, is the transpose matrix, satisfying , is the identity matrix. Mathematically, these definitions clarify that the diffusion process occurs in a smaller subspace defined by with a time interval of . For the drift coefficient it is expressed as:

[0097] ,

[0098] wherein, δ ( ) represents the Dirac function. The above equation shows that at time , is projected onto the subspace. As time goes by, the dimension of the subspace decreases, and learning to match the score function of the lower dimension brings a finer training coverage and further improves the performance.

[0099] In the subspace, it is necessary to learn . Specifically, in the forward process, noise is gradually introduced into each wavelet component to transform the component data distribution into a known prior distribution. A subspace diffusion model based on orthogonal decomposition can be trained to match the fraction . In the subspace, the fraction matching strategy is consistent with that in the full space, except that the wavelet components are regarded as the original undiffused data. By continuously iterating in this way, the subspace diffusion model based on orthogonal decomposition learns the k-space data distribution and reaches a convergence value through multiple iterations, finally completing the construction of the model.

[0100] Step C: Design an iterative solution algorithm for extracting the prior information within the subspace diffusion model based on orthogonal decomposition.

[0101] Step C specifically includes the following sub-steps:

[0102] Make predictions through the subspace diffusion model based on orthogonal decomposition, and then perform correction. The predictor-corrector sampler alternates between the full space and the subspace multiple times to achieve convergence;

[0103] Enforce data consistency within the subspace to guide the sampling process. The mathematical formula is as follows:

[0104] ,

[0105] In the formula, is the imaging operator, is the k-space data to be reconstructed, is the measurement data, is the data term generated by the subspace diffusion model based on orthogonal decomposition in the k-space, is the regularization parameter;

[0106] After network iteration, a traditional low-rank optimization operator is added to convert the k-space data matrix into the form of a Hankel matrix and recover the low-rank matrix. The mathematical formula is as follows:

[0107] ,

[0108] In the formula, is the Hankel pseudo-inverse operator, is the low-rank matrix with low-rank attributes after performing the hard-threshold singular value operation, is the rank of the low-rank matrix , is the k-space data optimized through low-rank matrix completion.

[0109] In the specific implementation process of Step C, for example:

[0110] To generate samples, use the corresponding interval Full-space fractional model and subspace fractional model to solve inverse diffusion. In the implementation of the present invention, the reverse diffusion process is equipped with a predictor-corrector sampler. The predictor uses the full-space diffusion model trained above to update the estimation result in the full space as follows:

[0111] ,

[0112] wherein k-space data at the current time step , is the k-space data at the next time step , and are the noise scales at time steps and , is the trained full-space diffusion model. The variable follows a Gaussian distribution and represents random noise. For each updated , the following correction steps are performed multiple times to refine it:

[0113] ,

[0114] wherein is the k-space data obtained from the predictor step, is the step size at time , is the fractional estimate of the full-space diffusion model at the current time step for , and the variable follows a Gaussian distribution and represents random noise. Similar to the alternative sampling strategy, the data in the subspace is also reconstructed by alternately updating the predictor-corrector sampler. Since the reconstruction step is performed within the subspace, the original k-space data should first be orthogonally decomposed using wavelet transform to generate . Thereafter, the prediction step is performed using the subspace diffusion model trained in the previous section as follows:

[0115] ,

[0116] Subsequently, the correction step is performed on :

[0117] ,

[0118] The predictor and corrector samplers alternate multiple times between the full space and the subspace to achieve convergence. At the same time, to maintain the accuracy of complex appearance features in the reconstruction results, a data consistency module is introduced. By integrating the data consistency module into a unified diffusion framework, more accurate values are enforced at the sampling positions in the k-space, and the mathematical formula is as follows:

[0119] ,

[0120] In the formula, is the imaging operator, is the k-space data to be reconstructed, is the measurement data, is the data term generated in the k-space by the subspace diffusion model based on orthogonal decomposition, is the regularization parameter;

[0121] By integrating the data consistency module into a unified diffusion framework, a mutual feedback loop can be formed with the regularization constraint. Traditionally, the reconstruction problem has been conceptualized as a low-rank matrix completion problem. To achieve high-quality reconstruction results, the present invention adds a traditional low-rank optimization operator after network iteration, which helps to further recover the low-rank matrix. The object of the traditional low-rank optimization operator is the data matrix generated by the network. As the k-space data matrix is converted into the Hankel matrix form, the hard-threshold singular values of the data matrix can be analyzed. Utilizing the inherent low-rank property of the Hankel matrix, the problem of finding the best low-rank approximation is transformed into an optimization problem, thereby realizing the effective analysis and reconstruction of the original data, and the mathematical formula is as follows:

[0122] ,

[0123] In the formula, is the Hankel pseudo-inverse operator, is the low-rank matrix with low-rank property after performing the hard-threshold singular value operation, is the low-rank matrix 's rank, is the k-space data optimized by low-rank matrix completion.

[0124] Step D: An iterative solution algorithm is applied to the subspace diffusion model based on orthogonal decomposition to test the test data set, and the final repaired image, the peak signal-to-noise ratio and the structural similarity of the test result image are output, so as to evaluate the image quality.

[0125] (2), Figure 2 is a schematic diagram of the training stage and the iterative reconstruction stage of the present invention. Now, in combination with the attached Figure 2 the specific steps of the method of the present invention are described as follows:

[0126] A subspace diffusion model based on orthogonal decomposition according to the present invention aims to optimize the diffusion mechanism of k-space data during the noise evolution process. The subspace diffusion model based on orthogonal decomposition projects the k-space data into a specific subspace, effectively restricting the diffusion process, thereby avoiding the inference problems brought about by the complexity and high-dimensional characteristics of the k-space data. By constructing a highly compact subspace, the subspace diffusion model based on orthogonal decomposition can ensure that accurate prior information can be generated with only a few simple iterations. In addition, the present invention also adopts an orthogonal decomposition strategy based on wavelet transform, which can effectively avoid information loss when mapping the original diffusion process to the subspace. Given the approximately invertible nature of the orthogonal decomposition strategy, the entire diffusion process is reversible, which provides a mechanism for mutual feedback for the diffusion processes in different spaces, thus improving the subspace diffusion model based on orthogonal decomposition.

[0127] In specific implementation, the full space represents the original k-space data, which contains all possible frequency and phase information, while the subspace is obtained by projecting the full space data into a highly compact space through orthogonal decomposition, simplifying data processing and retaining key information. The sample full space is mapped from the actually acquired k-space data to the sample subspace through orthogonal decomposition, reducing the data dimension and retaining important features. The full space diffusion process involves complex noise evolution and data propagation mechanisms, while the subspace diffusion process is more efficient and controllable due to the compactness of the subspace.

[0128] In the reconstruction stage, the artificially undersampled multi-coil image is taken as the input. After being transformed into k-space data through FFT (Fast Fourier Transform), orthogonal decomposition is first performed using wavelet transform to generate frequency components. Thereafter, the trained subspace diffusion model based on orthogonal decomposition performs prediction steps and correction steps through a predictor-corrector sampler. In order to maintain the accuracy of complex appearance features in the reconstruction result, a latent consistency module is integrated into the unified diffusion framework to enforce more accurate values at the sampling positions in the k-space. In order to achieve high-quality reconstruction results, the present invention adds a traditional low-rank optimization operator after network iteration to impose constraints on the results of each iteration. Finally, the reconstructed k-space data is subjected to IFFT (Inverse Fast Fourier Transform) to obtain the reconstructed image.

[0129] Through the above steps, the subspace diffusion model based on orthogonal decomposition can effectively process complex k-space data, generate accurate prior information, and finally achieve high-quality image reconstruction. Even when dealing with complex k-space data, the model can learn and provide accurate prior information to ensure the high resolution and clarity of the reconstructed image.

[0130] (3) The experimental implementation configuration requirements of a subspace diffusion model based on orthogonal decomposition of the present invention are as follows:

[0131] The proposed architecture has been implemented in Pytorch, and all experiments have been run on a desktop computer equipped with an Intel Core i7-7700 central processing unit and a GeForce Titan XP. The training set was constructed from the open-source brain dataset SIAT, and 500 images were selected as the basic training set, which was expanded to 4000 images by flipping and rotating during the training phase.

[0132] Figure 3 and Figure 4 Figs. show the reconstructed images of different algorithms in the Radial sampling mode and the Random sampling mode with an acceleration ratio of 12, where (a) is the under-sampled image, (g) is the original image, and (b), (c), (d), (e), and (f) are the reconstructed results of SAKE, ESPIRIT, EBMRec, HKGM, and the present invention, respectively. It can be seen from the figures that at the same acceleration ratio, compared with other methods, the visual effect of the present invention is consistent with the quantitative results. Specifically, noise, aliasing, and blurring occur in the SAKE and ESPIRiT reconstructions, resulting in a decrease in image quality and the loss of fine structures. In contrast, as deep learning techniques, EBMRec and HKGM have shown significant improvements in restoring prominent structures and edges. However, upon closer inspection, it can be found that the structures reconstructed by EBMRec are not accurate, unable to capture fine details, and even severe noise and artifacts appear at high acceleration ratios. Although the HKGM method eliminates some artifacts, it results in the loss of high-frequency details, and the noise suppression and structure detail retention effects at high acceleration coefficients are not ideal. It is worth noting that the present invention achieves the visual effect with the most texture details and the least noise, retains the most realistic high-frequency details, and effectively suppresses artifacts. At the same time, the enlarged view and error map after reconstruction further highlight the superiority of the proposed method.

[0133] The above only expresses the preferred embodiments of the present invention, and the description thereof is relatively detailed and specific, but it should not be construed as a limitation on the scope of the patent of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present invention, several deformations, improvements, and substitutions can be made, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be subject to the appended claims.

Claims

1. An MRI reconstruction method based on a subspace diffusion model of orthogonal decomposition, characterized in that: The following steps are involved: Step A: Form an open source brain dataset, which is divided into a training dataset and a test dataset; Step B: Based on the training data set, a subspace diffusion model based on orthogonal decomposition is constructed. The subspace diffusion model based on orthogonal decomposition diffuses by decomposing the k-space data into subspaces, thereby better capturing the data distribution and maintaining robustness in a noisy environment. Step C: Designing an iterative solution algorithm for extracting prior information in the subspace diffusion model based on orthogonal decomposition; Step D: Using an iterative solution algorithm to apply the subspace diffusion model based on orthogonal decomposition to test the test data set, output the peak signal-to-noise ratio value and structural similarity of the final repaired image and the test result image, so as to evaluate the image quality; The step B specifically includes the following sub-steps: (1) Designing the network structure Diffusion model: SDE is used to describe the diffusion process. The mathematical formula is as follows: ， In the formula, is the drift coefficient of SDE, is the diffusion coefficient, is the standard Brownian motion, t is the continuous time variable, x is a data sample; The reverse SDE is used to describe the reverse diffusion process. The mathematical formula is as follows: ， In the formula, is an infinitesimal reverse time step, It is the reverse Brownian motion. is a fractional function; Taking m as the time point, the diffusion time Divide into multiple sub-intervals , the mathematical formula of the subspace diffusion process is as follows: ， In the formula, is an orthogonal matrix, T is the transpose of the matrix; Drift coefficient The mathematical formula is as follows: ， In the formula, δ ( ) represents the Dirac function, is the identity matrix; The high-dimensional probability distribution from k-space data is decomposed into low-frequency components and high-frequency components in the diffusion process by DWT. The mathematical formula is as follows: ， ， Where W represents DWT, represents the LL low-frequency component, They represent the LH high frequency component, the HL high frequency component, and the HH high frequency component respectively. represents the inner product, i and j They represent one of the LL low-frequency component, the LH high-frequency component, the HL high-frequency component, and the HH high-frequency component respectively; The mathematical formula for all these frequency components K in the wavelet domain is as follows: ； (2) Training the subspace diffusion model based on orthogonal decomposition SDE is used to describe the diffusion process in the subspace, and the mathematical formula is as follows: ； The subspace diffusion model based on orthogonal decomposition is trained using the following mathematical formula: ， In the formula, Indicates time expectations, λt is a positive weight function, Represents the initial data distribution expectations, Indicates that in a given Under the conditions, The conditional distribution of The expectation of sampling, is the estimated log probability function, is the gradient of the exact log-probability function; Through continuous cyclic iterations, the subspace diffusion model based on orthogonal decomposition learns the k-space data distribution until a convergence value is reached through multiple iterations, and finally the model construction is completed.

2. The method according to claim 1, characterized in that The process of forming the training data set in step A specifically includes: preparing a first number of original images; The first number of original images is expanded into a second number of images by flipping and rotating to form a training data set.

3. The method according to claim 1, characterized in that The step C specifically includes the following sub-steps: Prediction is performed through a subspace diffusion model based on orthogonal decomposition, followed by correction, and the predictor-corrector sampler is executed multiple times alternating between the full space and the subspace to reach convergence; Data consistency is enforced within the subspace to guide the sampling process, as shown in the following mathematical formula: ， In the formula, is the imaging operator, is the k-space data to be reconstructed, is the measurement data, is the data item generated in k-space by the subspace diffusion model based on orthogonal decomposition, is the regularization parameter; After the network iteration, the traditional low-rank optimization operator is added to convert the k-space data matrix into the Hankel matrix form and restore the low-rank matrix. The mathematical formula is as follows: ， In the formula, is the Hankel pseudo-inverse operator, is a low-rank matrix with low-rank properties after hard threshold singular value operation, is a low-rank matrix rank, It is the k-space data optimized by low-rank matrix completion.

Images