MRI reconstruction method of subspace diffusion model based on orthogonal decomposition

Abstract

The invention provides an MRI (Magnetic Resonance Imaging) reconstruction method of a subspace diffusion model based on orthogonal decomposition. The MRI reconstruction method comprises the following steps: forming an open source brain data set; a subspace diffusion model based on orthogonal decomposition is constructed, and k-space data is decomposed into subspaces for diffusion, so that data distribution is better captured, and robustness is kept in a noise environment; designing an iterative solution algorithm for extracting prior information in the model; and applying an iterative solution algorithm to the model to test the test data set, and outputting a final restored image. According to the method, the learning of effective information in complex distribution is promoted, the inherent high-dimensional extrapolation challenge is solved, and the calculation cost related to a diffusion model is reduced. Comprehensive experiments on different data sets clearly show that the method is superior to other methods in the aspects of reconstruction speed and quality.

Description

Technical Field

[0001] The invention belongs to the technical field of image processing, and in particular 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 vital role in the diagnosis, treatment planning and preventive measures of diseases. However, due to its inherent data acquisition mode, the imaging time is too long, that is, the scanning of k-space data takes a long time, which has become a major bottleneck in clinical applications. Excessive imaging time can cause many problems, such as patient movement may cause artifacts in the reconstructed image. In addition, for the fields of cardiac dynamic imaging, interventional imaging, brain functional imaging and contrast-enhanced imaging, the existing MRI cannot meet the needs of fast imaging, which to a certain extent restricts its wide application in clinical practice. In summary, although MRI can provide detailed physiological structure information, if the imaging time can be significantly shortened and the image reconstruction quality can be ensured, the application prospects of MRI will be greatly improved. Therefore, fast magnetic resonance image reconstruction is not only a very challenging topic, but also has important scientific research value and social significance.

[0003] In order to improve scanning efficiency and accelerate the diagnostic process, existing technologies provide a variety of strategies to achieve undersampling of k-space data and combine prior knowledge for image reconstruction. From the initial compressed sensing-based technology to the deep learning-based models in recent years, these technologies have made great progress in clinical applications. However, how to shorten the imaging time while ensuring the accuracy of reconstruction remains an urgent problem. To this end, the diffusion model, as an emerging framework, has attracted much attention because it can more accurately characterize 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 the diffusion model has achieved certain results in the field of fast magnetic resonance image reconstruction, the reconstruction process still consumes a lot of computing resources due to the high dimensional complexity of k-space data itself. The diffusion model generation process is slow, the applicability to specific data types is limited, and the dimension cannot be effectively reduced. In order to meet this challenge, a series of related technologies have been developed, such as dual-domain end-to-end methods, self-consistent terms, and low-rank regularization of Hankel matrices. In addition, the segmentation of k-space data has also been proven to be an effective simplification strategy, such as high- and low-frequency separation. These methods not only help to overcome the current difficulties, but also have the value of further research.

[0005] At the same time, 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 stages, so the subspace modeling method shows higher robustness and accuracy than the full-space modeling. Studies have shown 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 Gaussian distribution faster than the components in the subspace. Therefore, 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 fraction 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 non-Gaussian components are modeled using smaller networks under high noise conditions, which can effectively reduce the amount of computation required.

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

[0007] The purpose of the present invention is to propose an MRI reconstruction method based on a subspace diffusion model of orthogonal decomposition, which is feasible, has excellent performance and strong environmental adaptability. 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 representation 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 a subspace diffusion model of orthogonal decomposition, comprising the following steps: 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: An iterative solution algorithm is applied to the subspace diffusion model based on orthogonal decomposition to test the test data set, and the peak signal-to-noise ratio value and structural similarity of the final repaired image and the test result image are output to evaluate the image quality.

[0009] Optionally, 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.

[0010] Optionally, the step B specifically includes the following sub-steps: (1) Design 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 jThey 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.

[0011] Optionally, 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.

[0012] Compared with the prior art, the present invention has the following beneficial effects: The present invention proposes a subspace diffusion model framework that uses joint orthogonal decomposition to handle complex distributions, aiming to improve reconstruction accuracy while increasing the sampling rate. Specifically, the inherent forward diffusion process of the diffusion model is migrated to the subspace to solve the high-dimensional extrapolation and computational cost problems existing in the diffusion model. At the same time, 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 signal can almost completely represent the original data. After a lot of theoretical analysis and rigorous experimental verification, it is confirmed that the present invention is not only superior to the existing full-space MRI reconstruction method, but also provides better results than the traditional score-based diffusion method. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a flow chart of an MRI reconstruction method based on a subspace diffusion model of orthogonal decomposition of the present invention; Figure 2 It is a schematic diagram of the training phase and iterative reconstruction phase of the subspace diffusion model based on orthogonal decomposition of the present invention; Figure 3 The figures are the reconstructed images, magnified images and error images of the present invention in the case of the radial sampling mode with an acceleration of 12 times, wherein (a) is the under-sampled image, (g) is the original image, and (b), (c), (d), (e) and (f) are the reconstruction result images of SAKE, ESPIRIT, EBMRec, HKGM and the present invention respectively; Figure 4 These are the reconstructed images, magnified images and error images of the present invention when the random sampling mode is accelerated by 12 times, where (a) is the under-sampled image, (g) is the original image, and (b)(c)(d)(e)(f) are the reconstruction result images of SAKE, ESPIRIT, EBMRec, HKGM and the present invention respectively. DETAILED DESCRIPTION

[0014] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. The specific embodiments described here are only used to explain the technical solution of the present invention and are not limited to the present invention.

[0015] In order to solve the problems of slow diffusion model generation process, limited applicability to specific data types, and inability to effectively reduce dimensionality in magnetic resonance image reconstruction tasks, the present invention proposes a new method of cascading orthogonal decomposition of k-space data and subspace diffusion generation for fast magnetic resonance image reconstruction: the dimensionality of complex k-space data is reduced through an orthogonal decomposition strategy, and mutually orthogonal high-frequency and low-frequency components are obtained. When generating samples, since the probability density is orthogonalized to reduce the dimensionality, the diffusion model can directly estimate the prior distribution in the low-dimensional data subspace.

[0016] (one) Figure 1 It is a flow chart of the present invention, now combined with the attached Figure 1 The specific steps of the method of the present invention are described. The present invention provides an MRI reconstruction method based on the subspace diffusion model of orthogonal decomposition, including steps A to D.

[0017] Step A: Form an open source brain dataset, which is divided into a training dataset and a test dataset.

[0018] 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.

[0019] In the specific implementation process of step A, for example, 500 original images provided by the Shenzhen Institute of Advanced Technology of the Chinese Academy of Sciences are prepared, and the prepared 500 original images are expanded to 4,000 images by flipping and rotating to form a training data set, thereby ensuring more comprehensive training to improve model performance. Some additional images are prepared to form a test data set. Among them, the training data set is used to train the model or determine the model parameters, and the test data set is to test the generalization ability of the trained model.

[0020] 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 the k-space data into subspaces to better capture the data distribution and maintain robustness in noisy environments.

[0021] Step B specifically includes the following sub-steps: (1) Design 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.

[0022] In the specific implementation of step B, for example: The intrinsic forward process of the diffusion model is transferred to the subspace Specifically, the forward diffusion starts in the entire space, but as time goes by, at a certain point in time, the k-space data is reduced to a 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: is the time point, and the diffusion time is divided into multiple sub-intervals, namely . Then, in In each interval of , the diffusion process in the subspace can be redefined as follows: , In the formula, is an orthogonal matrix, is the transposed matrix, satisfying , is the identity matrix. Mathematically, these definitions illustrate that the diffusion process is coupled or confined to the It occurs in a smaller subspace defined by For the drift coefficient It is expressed as: , In the formula, δ ( ) represents the Dirac function. The above formula shows that at time hour, Over time, the dimensionality of the subspace decreases, and learning a score function that matches the lower dimensionality leads to finer training coverage and further performance improvements.

[0023] In the subspace, we need to learn like the whole space Specifically, in the forward process, noise is gradually introduced into each wavelet component to transform the component data distribution into a known prior distribution. To match the score , the score matching strategy in the subspace is consistent with the whole space, except that the wavelet component is regarded as the original undiffused data. Through continuous iteration of this cycle, the subspace diffusion model of orthogonal decomposition is Learn the k-space data distribution, reach a convergence value through multiple iterations, and finally complete the model construction.

[0024] Step C: Design an iterative solution algorithm for extracting prior information within the subspace diffusion model based on orthogonal decomposition.

[0025] 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.

[0026] In the specific implementation process of step C, for example: To generate samples, use the corresponding interval Full-space fractional model in and subspace fractional model To solve the reverse 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 The estimated results in the updated full space are as follows: , In the formula, Current time step k-space data, is the next time step k-space data, and is the time step and The noise scale, is the trained full-space diffusion model. Follows a Gaussian distribution, representing random noise. For each updated , perform the following correction steps multiple times to refine it: , In the formula, is the k-space data obtained in the predictor step, It's time The step length, is the full-space diffusion model at the current time step right The score estimate of the variable follows a Gaussian distribution and represents random noise. Similar to the substitution sampling strategy, the data in the subspace is also reconstructed by alternately updating the predictor-corrector sampler. Since the reconstruction step is performed in the subspace, the original k-space data should first be orthogonally decomposed using wavelet transform to produce After that, the prediction steps using the subspace diffusion model trained in the previous section are as follows: , Afterwards, To perform the calibration procedure: , The predictor and corrector samplers are executed alternately between the full space and the subspace multiple times to achieve convergence. At the same time, in order 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 k-space, 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; By integrating the data consistency module into a unified diffusion framework, a mutual feedback loop can be formed with the regularization constraints. Traditionally, the reconstruction problem is conceptualized as a low-rank matrix completion problem. In order to achieve high-quality reconstruction results, the present invention adds a traditional low-rank optimization operator after the 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 to the Hankel matrix form, the hard threshold singular values ​​of the data matrix can be analyzed. Utilizing the inherent low-rank characteristics of the Hankel matrix, the problem of finding the best low-rank approximation is transformed into an optimization problem, thereby achieving effective analysis and reconstruction of the original data. 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.

[0027] 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 peak signal-to-noise ratio value and structural similarity of the final repaired image and the test result image are output to evaluate the image quality.

[0028] (two), Figure 2 This is a schematic diagram of the training phase and iterative reconstruction phase of the present invention. Figure 2 The specific steps of the method of the present invention are described as follows: A subspace diffusion model based on orthogonal decomposition of the present invention is intended to optimize the diffusion mechanism of k-space data during the noise evolution process. The subspace diffusion model based on orthogonal decomposition effectively limits the diffusion process by projecting the k-space data into a specific subspace, thereby avoiding the reasoning difficulties caused 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 the loss of information when mapping the original diffusion process to the subspace. In view of the approximately reversible 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, thereby improving the subspace diffusion model based on orthogonal decomposition.

[0029] In the specific implementation, the full space represents the original k-space data, which contains all possible frequency and phase information, while the subspace projects the full space data into a highly compact space through orthogonal decomposition, which simplifies data processing and retains key information. The sample full space is the k-space data collected from the actual data, mapped to the sample subspace through orthogonal decomposition, which reduces the data dimension and retains important features. The full space diffusion process involves complex noise evolution and data propagation mechanisms, while the subspace diffusion process makes the diffusion more efficient and controllable due to the compactness of the subspace.

[0030] In the reconstruction stage, the artificially undersampled multi-coil image is used as input. After being converted into k-space data through FFT (Fast Fourier Transform), the wavelet transform is first used for orthogonal decomposition to generate frequency components. Thereafter, the prediction step and the correction step are performed by the predictor-corrector sampler using the trained subspace diffusion model based on orthogonal decomposition. In order to maintain the accuracy of complex appearance features in the reconstruction results, the potential consistency module is integrated into a unified diffusion framework to enforce more accurate values ​​at the sampling positions in k-space. In order to achieve high-quality reconstruction results, the present invention adds a traditional low-rank optimization operator after the 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.

[0031] Through the above steps, the subspace diffusion model based on orthogonal decomposition can effectively process complex k-space data, generate accurate prior information, and ultimately achieve high-quality image reconstruction. Even when processing complex k-space data, the model is able to learn and provide accurate prior information to ensure high resolution and clarity of the reconstructed image.

[0032] (III) The experimental implementation configuration requirements of the subspace diffusion model based on orthogonal decomposition of the present invention are as follows: 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 CPU and a GeForce Titan XP. The training set is constructed from the open source brain dataset SIAT, from which 500 images are selected as the basic training set, and the dataset is expanded to 4000 images by flipping and rotating during the training phase.

[0033] Figure 3 and Figure 4The reconstruction images of different algorithms under the acceleration factor of 12 in Radial sampling mode and Random sampling mode are shown, where (a) is the under-sampled image, (g) is the original image, and (b)(c)(d)(e)(f) are the reconstruction results of SAKE, ESPIRIT, EBMRec, HKGM and the present invention, respectively. It can be seen from the figure that under the same acceleration factor, the visual effect of the present invention is consistent with the quantitative results compared with other methods. Specifically, SAKE and ESPIRiT reconstruction will have noise, aliasing and blur, resulting in image quality degradation and loss of fine structure. In contrast, EBMRec and HKGM, as deep learning technologies, have made significant improvements in restoring prominent structures and edges. However, a closer look will reveal that the structure reconstructed by EBMRec is not accurate, and fine details cannot be captured, and even severe noise and artifacts will appear at high acceleration factors. Although the HKGM method eliminates some artifacts, it leads to the loss of high-frequency details, and the noise suppression and structural detail retention effects at high acceleration coefficients are not ideal. It is worth noting that the present invention achieves a visual effect with the most texture details and the least noise, retains the most realistic high-frequency details, and effectively suppresses artifacts. Meanwhile, the reconstructed enlarged views and error maps further highlight the superiority of the proposed method.

[0034] The above only expresses the preferred embodiments of the present invention, and the description is relatively detailed and specific, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for ordinary technicians in this field, several modifications, improvements and substitutions can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be based on the attached 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: An iterative solution algorithm is applied to the subspace diffusion model based on orthogonal decomposition to test the test data set, and the peak signal-to-noise ratio value and structural similarity of the final repaired image and the test result image are output to evaluate the image quality.

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 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.

4. 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.

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