Rapid magnetic resonance fingerprint reconstruction method and system based on K uniform hypergraph regularization

Abstract

The invention discloses a rapid magnetic resonance fingerprint reconstruction method and system based on K uniform hypergraph regularization, and relates to the technical field of magnetic resonance fingerprint imaging. The invention aims to solve the problems that the imaging quality is reduced due to data undersampling artifacts in magnetic resonance fingerprint imaging at present, and a non-local irregular anatomical structure is difficult to model and the calculation complexity is high in the existing method. The method comprises the following steps: (1) acquiring undersampled magnetic resonance fingerprint data; (2) constructing a K uniform hypergraph; (3) establishing a magnetic resonance fingerprint reconstruction model based on K uniform hypergraph regularization; (4) constructing an iterative solution algorithm based on an incremental sub-gradient approximation method; (5) setting an iterative solution algorithm termination condition; and (6) reconstructing the magnetic resonance fingerprint data and the quantitative parameter image by using an iterative solution algorithm. Experiments show that under the condition of high-power undersampling, a high-quality magnetic resonance fingerprint image can be reconstructed by using less sampling data, the reconstruction time is shortened, and a more reliable quantitative image basis is provided for clinical disease diagnosis and treatment monitoring.

Description

Technical Field

[0001] This invention relates to the field of magnetic resonance fingerprint imaging technology, specifically to a fast magnetic resonance fingerprint reconstruction method and system based on K-uniform hypergraph regularization. Background Technology

[0002] Magnetic resonance fingerprinting (MRF) [1] is a fast quantitative magnetic resonance imaging technique based on pattern matching proposed in 2013. It can realize the simultaneous quantitative imaging of multiple tissue parameters under a new pulse sequence. It has a certain robustness to different imaging conditions and noise interference. It can also obtain good imaging results under under-sampling data acquisition mode. Magnetic resonance fingerprinting technology can perform rapid quantitative imaging of multiple tissue parameters, so it has a wide range of application prospects. Magnetic resonance fingerprinting technology proposes a new data acquisition and parameter reconstruction method, which mainly includes three parts: data acquisition, data reconstruction and parameter reconstruction. First, magnetic resonance fingerprinting uses a pseudo-random pulse sequence to make different tissues generate unique response signals, namely tissue magnetic resonance fingerprint signals. At the same time, a fingerprint dictionary containing theoretical magnetic resonance signals of all possible human tissues is constructed according to the Bloch model excited by the magnetic resonance signal. Then, based on the pattern matching method, the acquired tissue magnetic resonance fingerprint signal is matched with the entries in the fingerprint dictionary to realize the simultaneous quantitative imaging of multiple tissue parameters.

[0003] To accelerate data acquisition, magnetic resonance fingerprinting uses a high-magnification undersampling technique that is far below the Nyquist sampling law, collecting only 5% to 8% of the data for quantitative imaging. Compared with traditional imaging, which requires collecting 25% to 50% of the data, reconstruction algorithms usually have higher computational complexity, slower reconstruction speed, and lower accuracy, making it difficult to meet the needs of clinical applications.

[0004] Therefore, it is necessary to design a magnetic resonance fingerprint reconstruction method with high reconstruction accuracy and fast processing speed. Summary of the Invention

[0005] The technical problem to be solved by this invention is:

[0006] The purpose of this invention is to address the limitations of existing magnetic resonance fingerprint image reconstruction algorithms and to provide a fast magnetic resonance fingerprint reconstruction method and system based on K-uniform hypergraph regularization. By constructing a K-uniform hypergraph model, the high-order structural correlations between multiple voxels are effectively captured. Combined with Laplacian eigenmap regularization, the quality of the reconstructed image is improved and the reconstruction time is shortened.

[0007] The technical solution adopted by the present invention to solve the above problems is as follows:

[0008] (1) Acquire undersampled magnetic resonance fingerprint data;

[0009] (2) Construct a K-uniform hypergraph;

[0010] (3) Construct a magnetic resonance fingerprint reconstruction model based on K-uniform hypergraph regularization;

[0011] (4) Construct an iterative solution algorithm based on the fast iterative shrinkage threshold algorithm;

[0012] (5) Set the termination condition for the iterative solution algorithm;

[0013] (6) Reconstruct magnetic resonance fingerprint data and quantitative parameter images using an iterative solution algorithm.

[0014] Furthermore, in step (1) above, magnetic resonance imaging equipment is used to acquire magnetic resonance fingerprint data. A high-magnification undersampling technique, far below the Nyquist sampling law, is applied to accelerate data acquisition. A small amount of data, ranging from 5% to 8%, is acquired for quantitative imaging. The acquisition process can be represented by the following formula:

[0015]

[0016] in, This represents the undersampled data collected in the k-space. This indicates the number of samples collected by a single coil. This indicates the number of coils used when collecting data. Indicates the frame length of the magnetic resonance fingerprint data. This represents the distortion-free magnetic resonance fingerprint data to be reconstructed. and Indicates the size of the magnetic resonance image. This represents Gaussian noise introduced during the data acquisition process; This represents the linear degradation operator corresponding to the undersampling process, where This represents the coil sensitivity matrix, which is composed of the sensitivities of each coil. The expression represents the undersampling Fourier transform, and the subscript u corresponds to the undersampling template used in the undersampling process. The method of this invention is applicable to any undersampling template.

[0017] Quantitative parametric images can be obtained from reconstructed magnetic resonance fingerprint data. With a pre-built fingerprint signal dictionary The matching process can be represented as follows:

[0018]

[0019] in, This represents a matching operator built based on a dictionary. This represents a quantitative parameter image, where l represents the number of quantitative parameters in the image.

[0020] Furthermore, the construction of the K-uniform hypergraph in step (2) above is performed as follows:

[0021] A uniform hypergraph is defined as a weighted undirected hypergraph. vertex set Derived from MRF data voxel organization fingerprints, for resolution Collection length MRF data Through mapping function Each voxel The signal evolution sequence is defined as the vertex, i.e. , voxels Organizational fingerprints, similar parametric graph nodes can be defined as Hyperedgeset Used for carving Higher-order associations between vertices, including intra-cluster hyperedges Inter-cluster hyperedge In a K-uniform hypergraph, each hyperedge is fixedly connected. Vertices; weight set Weights are assigned to each hyperedge to quantify the similarity strength of vertices within the hyperedge, and the similarity is calculated based on the organization parameter vectors corresponding to the vertices. A schematic diagram of the construction of a K-uniform hypergraph is shown below. Figure 3 The specific definition process is as follows:

[0022] 1) Anatomical Perception Vertex Clustering: Based on the similarity of the tissue parameter vectors corresponding to the vertices, a clustering algorithm is used to cluster them. Divided into Clusters, with the clustering objective being , For cluster set, For distance measurement, , The vertex representing the tissue parameter of the vertex at the position of the isovox;

[0023] 2) Intra-cluster hyperedge construction: Calculate the similarity between vertices within each cluster, and select the K most similar vertices for each vertex to form intra-cluster hyperedges. The c-th cluster hyperedge set can be represented as: , For cluster and The most similar j-th vertex;

[0024] 3) Construction of inter-cluster hyperedges: Select 3 representative vertices from each cluster to form a hyperedge. ,in This represents the representative vertex selected from the i-th cluster, which can be randomly and uniformly selected. Calculate... Internal vertex similarity is used to select the K most similar vertices to form inter-cluster hyperedges, and the hyperedge set is formed. , for Internal and The most similar r-th vertex;

[0025] 4) Construction of the normalized hypergraph Laplacian matrix: The normalized hypergraph Laplacian matrix can be expressed as... ,in It is the identity matrix. Representation of the correlation matrix Its definition , Represents the j-th hyperedge; vertex degree matrix It is a diagonal matrix, and the values ​​of its diagonal elements are calculated according to the following formula. , The total number of hyperedges; the hyperedge degree matrix. Similarly, in a K-uniform hypergraph, the diagonal elements of a diagonal matrix are K, i.e. ; This represents the weight matrix, whose elements are calculated according to the following formula. , This is a variable hyperparameter, which can take the value of the median of intra-cluster similarity;

[0026] Further, step (3) is performed as follows:

[0027] The magnetic resonance fingerprint reconstruction model based on K-uniform hypergraph regularization can be expressed as:

[0028]

[0029] in, Describing the Frobenius norm For regularization parameters, The cone representing the Bloch response manifold describes the spatial distribution of the fingerprint signal.

[0030] Further, step (4) is performed as follows:

[0031] The reconstruction model constructed in step (3) can be solved based on the fast iterative shrinkage threshold algorithm. In the nth iteration, the algorithm proceeds according to the following iterative steps:

[0032]

[0033] in, and As an auxiliary variable, Indicates the iteration step size. The acceleration factor is represented by the following update method: .

[0034] Further, step (5) is performed as follows:

[0035] When solving the iterative algorithm constructed in step (4), a termination condition needs to be set. The convergence condition of the algorithm is defined as follows:

[0036]

[0037] in, This represents the reconstruction error calculated after the algorithm completes the nth iteration. The reconstruction error is calculated according to the following formula:

[0038]

[0039] When the algorithm iterations meet the convergence condition, the algorithm terminates and returns the reconstruction result.

[0040] Furthermore, step (6) above is performed as follows:

[0041] The collected undersampled data is used as the input to the algorithm, and the proposed algorithm is used for iterative solution. After each iteration, the reconstruction loss is calculated. When the termination condition set in step (5) is met, the iteration is terminated and the final reconstructed magnetic resonance fingerprint data is returned. And obtain the final quantitative parameter image. .

[0042] A fast magnetic resonance fingerprint reconstruction system based on K-uniform hypergraph regularization is provided. The system has program modules corresponding to the steps of the above-described technical solution, and executes the steps in the fast magnetic resonance fingerprint reconstruction method based on K-uniform hypergraph regularization during runtime.

[0043] A computer-readable storage medium storing a computer program configured to implement the steps of the fast magnetic resonance fingerprint reconstruction method based on K-uniform hypergraph regularization when invoked by a processor.

[0044] The present invention has the following beneficial technical effects:

[0045] This invention solves the problem of undersampling artifacts reducing image quality in current magnetic resonance fingerprint imaging, and improves the accuracy of reconstructed images while shortening reconstruction time. The invention includes the following steps: (1) acquiring undersampling magnetic resonance fingerprint data; (2) constructing a K-uniform hypergraph; (3) constructing a magnetic resonance fingerprint reconstruction model based on K-uniform hypergraph regularization; (4) constructing an iterative solution algorithm based on a fast iterative threshold shrinkage algorithm; (5) setting the termination condition for the iterative solution algorithm; and (6) reconstructing the magnetic resonance fingerprint data and quantitative parameter image using the iterative solution algorithm. This invention can reconstruct high-quality magnetic resonance fingerprint images with less sampled data under high-magnification undersampling conditions, and shortens the reconstruction time.

[0046] The fast magnetic resonance fingerprint reconstruction method based on K-uniform hypergraph regularization provided in this invention can quickly obtain high-quality magnetic resonance fingerprint reconstructed images from high-magnification undersampled data. The algorithm proposed in this invention has high computational efficiency and can be easily accelerated using GPUs, making it a highly efficient algorithm. Experiments show that, compared with existing methods, this invention can significantly improve the quality of the reconstructed parametric map and greatly shorten the algorithm reconstruction time, thus achieving the goal of accelerating magnetic resonance fingerprint image reconstruction. Attached Figure Description

[0047] Figure 1 This is a flowchart of the method of the present invention.

[0048] Figure 2 The diagram shows several common sampling templates; from left to right, they are: rectilinear Cartesian, pseudo-radial Cartesian, variable-density spiral trajectory, and the spiral trajectory undersampling template.

[0049] Figure 3 A schematic diagram of constructing a K-uniform hypergraph.

[0050] Figure 4 This is a comparison chart of the reconstruction results of the method of this invention with other currently advanced methods.

[0051] Figure 5 To and Figure 4 The corresponding Normalized Mean Square Error (NMSE) plot. Detailed Implementation

[0052] The present invention will now be described in detail with reference to the accompanying drawings and examples.

[0053] See the flowchart of the method of this invention. Figure 1 The specific implementation steps are as follows:

[0054] (1) Acquire undersampled magnetic resonance fingerprint data;

[0055] (2) Construct a K-uniform hypergraph;

[0056] (3) Construct a magnetic resonance fingerprint reconstruction model based on K-uniform hypergraph regularization;

[0057] (4) Construct an iterative solution algorithm based on the fast iterative shrinkage threshold algorithm;

[0058] (5) Set the termination condition for the iterative solution algorithm;

[0059] (6) Reconstruct magnetic resonance fingerprint data and quantitative parameter images using an iterative solution algorithm.

[0060] The above step (1) is performed as follows:

[0061] Magnetic resonance imaging (MRI) is used to acquire magnetic resonance fingerprint data. A high-magnification undersampling technique, far below the Nyquist sampling law, is applied to accelerate data acquisition. A small amount of data (5%–8%) is collected for quantitative imaging. The acquisition process can be represented by the following formula:

[0062]

[0063] in, This represents the undersampled data collected in the k-space. This indicates the number of samples collected by a single coil. This indicates the number of coils used when collecting data. Indicates the frame length of the magnetic resonance fingerprint data. This represents the distortion-free magnetic resonance fingerprint data to be reconstructed. and Indicates the size of the magnetic resonance image. This represents Gaussian noise introduced during the data acquisition process; This represents the linear degradation operator corresponding to the undersampling process, where This represents the coil sensitivity matrix, which is composed of the sensitivities of each coil. The expression represents the undersampling Fourier transform, and the subscript u corresponds to the undersampling template used in the undersampling process. The method of this invention is applicable to any undersampling template.

[0064] Quantitative parametric images can be obtained from reconstructed magnetic resonance fingerprint data. With a pre-built fingerprint signal dictionary The matching process can be represented as follows:

[0065]

[0066] in, This represents a matching operator built based on a dictionary. This represents a quantitative parameter image, where l represents the number of quantitative parameters in the image.

[0067] Step (2) above shall be performed as follows:

[0068] A uniform hypergraph is defined as a weighted undirected hypergraph. vertex set Derived from MRF data voxel organization fingerprints, for resolution Collection length MRF data Through mapping function Each voxel The signal evolution sequence is defined as the vertex, i.e. , voxels Organizational fingerprints, similar parametric graph nodes can be defined as Hyperedgeset Used for carving Higher-order associations between vertices, including intra-cluster hyperedges Inter-cluster hyperedge In a K-uniform hypergraph, each hyperedge is fixedly connected. Vertices; weight set Weights are assigned to each hyperedge to quantify the similarity strength of vertices within the hyperedge, and the similarity is calculated based on the organization parameter vectors corresponding to the vertices. A schematic diagram of the construction of a K-uniform hypergraph is shown below. Figure 3 The specific definition process is as follows:

[0069] 1) Anatomical Perception Vertex Clustering: Based on the similarity of the tissue parameter vectors corresponding to the vertices, a clustering algorithm is used to cluster them. Divided into Clusters, with the clustering objective being , For cluster set, For distance measurement, , The vertex representing the tissue parameter of the vertex at the position of the isovox;

[0070] 2) Intra-cluster hyperedge construction: Calculate the similarity between vertices within each cluster, and select the K most similar vertices for each vertex to form intra-cluster hyperedges. The c-th cluster hyperedge set can be represented as: , For cluster and The most similar j-th vertex;

[0071] 3) Construction of inter-cluster hyperedges: Select 3 representative vertices from each cluster to form a hyperedge. ,in This represents the representative vertex selected from the i-th cluster, which can be randomly and uniformly selected. Calculate... Internal vertex similarity is used to select the K most similar vertices to form inter-cluster hyperedges, and the hyperedge set is formed. , for Internal and The most similar r-th vertex;

[0072] 4) Construction of the normalized hypergraph Laplacian matrix: The normalized hypergraph Laplacian matrix can be expressed as... ,in It is the identity matrix. Representation of the correlation matrix Its definition , Represents the j-th hyperedge; vertex degree matrix It is a diagonal matrix, and the values ​​of its diagonal elements are calculated according to the following formula. , The total number of hyperedges; the hyperedge degree matrix. Similarly, in a K-uniform hypergraph, the diagonal elements of a diagonal matrix are K, i.e. ; This represents the weight matrix, whose elements are calculated according to the following formula. , This is a variable hyperparameter, which can take the value of the median of intra-cluster similarity;

[0073] Step (3) above shall be performed as follows:

[0074] The magnetic resonance fingerprint reconstruction model based on K-uniform hypergraph regularization can be expressed as:

[0075]

[0076] in, Describing the Frobenius norm For regularization parameters, The cone representing the Bloch response manifold describes the spatial distribution of the fingerprint signal.

[0077] The above step (4) shall be performed as follows:

[0078] The reconstruction model constructed in step (3) can be solved based on the fast iterative shrinkage threshold algorithm. In the nth iteration, the algorithm proceeds according to the following iterative steps:

[0079]

[0080] in, and As an auxiliary variable, Indicates the iteration step size. The acceleration factor is represented by the following update method: .

[0081] Step (5) above shall be performed as follows:

[0082] When solving the iterative algorithm constructed in step (4), a termination condition needs to be set. The convergence condition of the algorithm is defined as follows:

[0083]

[0084] in, This represents the reconstruction error calculated after the algorithm completes the nth iteration. The reconstruction error is calculated according to the following formula:

[0085]

[0086] When the algorithm iterations meet the convergence condition, the algorithm terminates and returns the reconstruction result.

[0087] The above step (6) shall be performed as follows:

[0088] The collected undersampled data is used as the input to the algorithm, and the proposed algorithm is used for iterative solution. After each iteration, the reconstruction loss is calculated. When the termination condition set in step (5) is met, the iteration is terminated and the final reconstructed magnetic resonance fingerprint data is returned. And obtain the final quantitative parameter image. .

[0089] To quantitatively evaluate the performance of the method proposed in this invention, two quantitative evaluation metrics, signal-to-noise ratio (SNR) and normalized mean square error (NMSE), were used in the experiment. SNR is defined as follows:

[0090]

[0091] in, and These represent the true and reconstructed magnetic resonance fingerprint data, respectively. The NMSE is defined as follows:

[0092]

[0093] in, and This represents the actual parameter value and the reconstructed parameter value at a specific index i.

[0094] Figure 4 A comparison chart of the reconstruction quantitative parameter plots of the method of this invention and other current advanced methods is shown. Each column from left to right corresponds to the truth plot and the parameter plots reconstructed by FLOR[2], SL-SP[3] and the method proposed in this invention (HG-MRF). The first, second and third rows show the longitudinal relaxation time (T1), lateral relaxation time (T2) parameter plots and proton density (PD) reconstructed by each method, respectively. Figure 5 The corresponding error graphs are shown, with specific NMSE error values ​​marked. As can be seen from the graphs, the method proposed in this invention for magnetic resonance fingerprint reconstruction can obtain the most accurate tissue parameter maps, significantly improving the quality of the reconstructed parameter maps.

[0095] Table 1. Quantitative comparison results of different methods on the test dataset

[0096]

[0097] Table 1 lists the quantitative comparison results of the reconstruction of the method of this invention with other current state-of-the-art methods, including the signal-to-noise ratio of the reconstructed magnetic resonance fingerprint data and the reconstruction time. The quantitative comparison results show that, compared with existing methods, the present invention can significantly improve the reconstruction quality and greatly shorten the algorithm reconstruction time.

[0098] The existing references cited in this invention are detailed below:

[0099] [1]D. Ma, V. Gulani, N. Seiberlich, and et al., “Magnetic resonancefingerprinting,” Nature, vol. 495, no. 7440, pp. 187–192.

[0100] [2]G. Mazor, L. Weizman, and et al., “Low-rank magnetic resonancefingerprinting,” Medical physics, vol. 45, no. 9, pp. 4066–4084, 2018.

[0101] [3]Y. Hu, P. Li, and et al., “High-Quality MR FingerprintingReconstruction Using Structured Low-Rank Matrix Completion and SubspaceProjection,” IEEE Transactions on Medical Imaging, vol. 41, no. 5, pp. 1150–1164, 2021.

Claims

1. A fast magnetic resonance fingerprint reconstruction method based on K-uniform hypergraph regularization, characterized in that, The method includes the following steps: (1) Acquire undersampled magnetic resonance fingerprint data; (2) Construct a K-uniform hypergraph; (3) Construct a magnetic resonance fingerprint reconstruction model based on K-uniform hypergraph regularization; (4) Construct an iterative solution algorithm based on the fast iterative shrinkage threshold algorithm; (5) Set the termination condition for the iterative solution algorithm; (6) Reconstruct magnetic resonance fingerprint data and quantitative parameter images using an iterative solution algorithm.

2. The method as described in claim 1, characterized in that, In step (1), magnetic resonance fingerprint data is acquired using a magnetic resonance imaging device. A high-magnification undersampling technique, far below the Nyquist sampling law, is applied to accelerate data acquisition. A small amount of data, ranging from 5% to 8%, is acquired for quantitative imaging. The acquisition process can be represented by the following formula: in, This represents the undersampled data collected in the k-space. This indicates the number of samples collected by a single coil. This indicates the number of coils used when collecting data. Indicates the frame length of the magnetic resonance fingerprint data. This represents the distortion-free magnetic resonance fingerprint data to be reconstructed. and Indicates the size of the magnetic resonance image. This represents Gaussian noise introduced during the data acquisition process; This represents the linear degradation operator corresponding to the undersampling process, where This represents the coil sensitivity matrix, which is composed of the sensitivities of each coil. The expression represents the undersampling Fourier transform, and the subscript u corresponds to the undersampling template used in the undersampling process. The method of this invention is applicable to any undersampling template. Quantitative parametric images can be obtained from reconstructed magnetic resonance fingerprint data. With a pre-built fingerprint signal dictionary The matching process can be represented as follows: in, This represents a matching operator built based on a dictionary. This represents a quantitative parameter image, where l represents the number of quantitative parameters in the image.

3. The method as described in claim 1, characterized in that, The above step (2) K-uniform hypergraph construction is performed according to the following steps: A uniform hypergraph is defined as a weighted undirected hypergraph. vertex set Derived from MRF data voxel organization fingerprints, for resolution Collection length MRF data Through mapping function Each voxel The signal evolution sequence is defined as the vertex, i.e. , voxels Organizational fingerprints, similar parametric graph nodes can be defined as Hyperedgeset Used for carving Higher-order associations between vertices, including intra-cluster hyperedges Inter-cluster hyperedge In a K-uniform hypergraph, each hyperedge is fixedly connected. Vertices; weight set Weights are assigned to each hyperedge, the similarity strength of vertices within the hyperedge is quantified, and the similarity is calculated based on the organization parameter vectors corresponding to the vertices. The construction process of the K-uniform hypergraph is as follows: 1) Anatomical Perception Vertex Clustering: Based on the similarity of the tissue parameter vectors corresponding to the vertices, a clustering algorithm is used to cluster them. Divided into Clusters, with the clustering objective being , For cluster set, For distance measurement, , The vertex representing the tissue parameter of the vertex at the position of the isovox; 2) Intra-cluster hyperedge construction: Calculate the similarity between vertices within each cluster, and select the K most similar vertices for each vertex to form intra-cluster hyperedges. The c-th cluster hyperedge set can be represented as: , For cluster and The most similar j-th vertex; 3) Construction of inter-cluster hyperedges: Select 3 representative vertices from each cluster to form a hyperedge. ,in This represents the representative vertex selected within the i-th cluster, which can be randomly and uniformly selected; calculate... Internal vertex similarity is used to select the K most similar vertices to form inter-cluster hyperedges, and the hyperedge set is formed. , for Internal and The most similar r-th vertex; 4) Construction of the normalized hypergraph Laplacian matrix: The normalized hypergraph Laplacian matrix can be expressed as... ,in It is the identity matrix. Representation of the correlation matrix Its definition , Represents the j-th hyperedge; vertex degree matrix It is a diagonal matrix, and the values ​​of its diagonal elements are calculated according to the following formula. , The total number of hyperedges; the hyperedge degree matrix. Similarly, in a K-uniform hypergraph, the diagonal elements of a diagonal matrix are K, i.e. ; This represents the weight matrix, whose elements are calculated according to the following formula. , This is a variable hyperparameter, which can take the value of the median of intra-cluster similarity.

4. The method as described in claim 1, characterized in that, Step (3) above shall be performed as follows: The magnetic resonance fingerprint reconstruction model based on K-uniform hypergraph regularization can be expressed as: in, Denotes the Frobenius norm. For regularization parameters, The cone representing the Bloch response manifold describes the spatial distribution of the fingerprint signal.

5. The method as described in claim 1, characterized in that, The above step (4) shall be performed as follows: The reconstruction model constructed in step (3) can be solved based on the fast iterative shrinkage threshold algorithm. In the nth iteration, the algorithm proceeds according to the following iterative steps: in, and As an auxiliary variable, Indicates the iteration step size. The acceleration factor is represented by the following update method: .

6. The method as described in claim 1, characterized in that, Step (5) above shall be performed as follows: When solving the iterative algorithm constructed in step (4), a termination condition needs to be set. The convergence condition of the algorithm is defined as follows: in, This represents the reconstruction error calculated after the algorithm completes the nth iteration. The reconstruction error is calculated according to the following formula: When the algorithm iterations meet the convergence condition, the algorithm terminates and returns the reconstruction result.

7. The method as described in claim 1, characterized in that, The above step (6) shall be performed as follows: The collected undersampled data is used as the input to the algorithm, and the proposed algorithm is used for iterative solution. After each iteration, the reconstruction loss is calculated. When the termination condition set in step (5) is met, the iteration is terminated and the final reconstructed magnetic resonance fingerprint data is returned. And obtain the final quantitative parameter image. .

8. A fast magnetic resonance fingerprint reconstruction system based on K-uniform hypergraph regularization, characterized in that: The system has a program module corresponding to the steps of any one of the claims 1-7 above, and executes the steps in the fast magnetic resonance fingerprint reconstruction method based on K-uniform hypergraph regularization when it runs.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program configured to, when invoked by a processor, implement the steps of the fast magnetic resonance fingerprint reconstruction method based on K-uniform hypergraph regularization as described in any one of claims 1-7.

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