Variation sparse source imaging method based on time basis matrix algorithm

Abstract

The invention discloses a variational sparse source imaging method based on a time basis matrix algorithm, and belongs to the technical field of brain magnetic source imaging. The method comprises the steps that a sensor is used for collecting and preprocessing original data of cranial nerve activity; projecting the preprocessed cranial nerve activity original data to a low-rank feature space of a time basis matrix, converting the data into a time domain, and representing the data as a time sequence formed by combining a plurality of time basis functions; converting the time sequence into a plurality of groups of base weight estimation problems by using guide field constraint and norm constraint on the time sequence; building a complete model constraint, optimizing a target function through a multiplier alternating direction method, solving a multi-group base weight estimation problem, and reconstructing a brain activity signal of a source space. According to the method, the robust performance can be achieved in low-signal-to-noise-ratio, large-source and multi-source environments, high robustness is shown in spatial range reconstruction, and the imaging performance of an OPM-MEG system is effectively improved through fusion of prior information.

Description

Technical Field

[0001] The present invention belongs to the technical field of brain magnetic source imaging, and in particular relates to a variational sparse source imaging method based on a time basis matrix (VSSI-TBM) algorithm. Background Art

[0002] Magnetoencephalography (MEG) combined with source imaging technology has been widely used in clinical practice, particularly in the areas of epileptic focus localization and detection of abnormal brain function. By capturing brain activity signals non-invasively, MEG technology provides neurologists with an important tool for surgical planning and treatment effectiveness assessment.

[0003] In addition, MEG has also played an important role in studying complex cognitive tasks and brain network functions. In order to reconstruct brain source signals from MEG data, the distributed current density model (DCD) is used to divide the cortical area into a large number of triangular meshes, each mesh representing a brain source. However, this model faces many challenges in practical applications. First, the source reconstruction process is susceptible to factors such as noise interference and unstable data acquisition system, resulting in inaccurate reconstruction results. Second, the pathological nature of the model makes it impossible for the algorithm to accurately locate brain sources, especially under low signal-to-noise ratio conditions or when brain area activity is more complex, the reconstruction results are often too vague.

[0004] While existing methods such as minimum norm estimation (MNE) and low-resolution electroencephalography (LORETA) have improved imaging, they remain insufficient for complex clinical environments, particularly in the presence of high noise and distributed brain activity. To improve the accuracy of source reconstruction, some studies have attempted to fuse multimodal data, such as functional magnetic resonance imaging (fMRI) or epileptic focus data recorded using invasive electrodes. However, existing algorithms still struggle to achieve globally sparse and locally smooth source reconstructions when incorporating this prior information. Therefore, it is crucial to develop a source reconstruction algorithm that can flexibly handle noisy and multimodal data in complex practical scenarios. Such an algorithm should maintain high accuracy under low signal-to-noise ratio conditions and be able to incorporate different types of prior information, providing a more robust solution for epileptic focus localization, brain dysfunction detection, and other clinical and research applications. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a variational sparse source imaging method based on a time basis matrix (VSSI-TBM) algorithm, which projects the source signal into the low-rank feature space of the time basis matrix. The low-rank decomposition makes the source space signal consist of several time basis functions to extract useful signals; the norm constraints of the variational space and the source space are introduced to obtain a locally smooth and globally sparse solution; in the compressed space, the mixed norm constraints and the cortical source variation operator are used to ensure spatial sparsity and smoothness; the objective function is optimized using the alternating direction method of multipliers (ADMM); and the use of guiding field constraints when spatial prior information is available can further enhance the reconstruction results.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A variational sparse source imaging method based on a time basis matrix algorithm, the method comprising:

[0008] Step S1: Use sensors to collect raw brain nerve activity data and perform preprocessing;

[0009] Step S2: Projecting the preprocessed raw brain neural activity data into the low-rank feature space of the time basis matrix, converting the preprocessed raw brain neural activity data into the time domain through low-rank decomposition, and combining it with the variational sparsity constraint to express it as a time series composed of several time basis functions;

[0010] Step S3: confirm that spatial prior information is available, use the guided field constraint on the time series and impose the norm constraint in the compressed space to convert the time series into a multi-group basis weight estimation problem, filter out redundant information and reduce the computational cost in the time domain;

[0011] Step S4: Establish complete model constraints to achieve the variational sparse prior mapping target of time domain decomposition, optimize the objective function through the alternating direction method of multipliers, solve the multi-group basis weight estimation problem and reconstruct the brain activity signal in the source space.

[0012] On the other hand, the present invention provides a variational sparse source imaging device based on a time basis matrix algorithm, wherein the modules included in the device can implement the various steps of the aforementioned method, specifically including:

[0013] An acquisition unit, used to collect raw data of brain nerve activity using sensors and perform preprocessing;

[0014] A conversion unit is used to project the preprocessed raw brain neural activity data into the low-rank feature space of the time basis matrix, convert the preprocessed raw brain neural activity data into the time domain through low-rank decomposition, and combine the variational sparsity constraint to express it as a time series composed of several time basis functions;

[0015] The constraint unit is used to confirm that spatial prior information is available, use the guided field constraint on the time series, and impose the norm constraint in the compressed space to convert the time series into a multi-group basis weight estimation problem, thereby filtering out redundant information and reducing the computational cost in the time domain;

[0016] The reconstruction unit is used to establish complete model constraints to achieve the variational sparse prior mapping target of time domain decomposition, optimize the objective function through the alternating direction method of multipliers, solve the multi-group basis weight estimation problem and reconstruct the brain activity signal in the source space.

[0017] In a third aspect, the present invention provides an electronic device comprising: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned variational sparse source imaging method based on a time basis matrix algorithm.

[0018] In a fourth aspect, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enables the processor to implement the aforementioned variational sparse source imaging method based on a time basis matrix algorithm.

[0019] The beneficial effects of the present invention are:

[0020] The VSSI-TBM proposed in this paper introduces sparse priors, enabling more accurate source localization during reconstruction. Furthermore, prior fusion based on the sparse Bayesian framework (SBF) helps reduce computational costs and improves adaptability to small-scale source reconstruction. By optimizing the objective function using the ADMM (Alternating Direction Method of Multipliers) and incorporating sparse priors, the algorithm achieves rapid convergence, reducing computational cost and time complexity. This makes the method more efficient for processing large datasets. Furthermore, the VSSI-TBM can effectively incorporate spatial priors (such as fMRI data), further improving imaging performance under low signal-to-noise ratio conditions. Compared to traditional methods (such as SISSY and SBF), the VSSI-TBM's integration of spatial prior information is more flexible and can be adjusted to suit different experimental conditions, thereby improving the accuracy and robustness of source reconstruction. Furthermore, the present invention demonstrates stable performance under varying experimental conditions and parameter settings. In particular, the method can be flexibly adjusted while maintaining high reconstruction accuracy when the number of sources is large or small. This makes the VSSI-TBM suitable for diverse experimental scenarios, including clinical and complex research environments.

[0021] In summary, the present invention can have robust performance in low signal-to-noise ratio, large source and multi-source environments, and has been evaluated in an open source dataset and a magnetoencephalography system based on an optically pumped magnetometer. It shows strong robustness in spatial range reconstruction, and the fusion of prior information effectively improves the imaging performance of the OPM-MEG system, which can play an important role in more clinical and scientific research fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 This is a flow chart of a variational sparse source imaging method based on a time basis matrix algorithm according to the present invention;

[0023] Figure 2 The performance index distribution diagram for different number of sources;

[0024] Figure 3 The performance index distribution diagram for different adjacency orders;

[0025] Figure 4 The distribution diagram of performance indicators under different signal-to-noise ratios. DETAILED DESCRIPTION

[0026] The technical solutions in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application.

[0027] In the following description, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Obviously, the embodiments described herein represent only a portion of the present invention, not all of it. All other embodiments derived by persons of ordinary skill in the art based on the embodiments herein without inventive effort are intended to fall within the scope of protection of the present invention.

[0028] In order to solve the pathological nature of distributed source reconstruction, researchers have proposed various prior constraint strategies. Most imaging algorithms are not ideal in source reconstruction and are easily affected by various environmental conditions (such as noise interference, distributed brain activity, acquisition system, etc.). In addition, some prior information can sometimes be obtained (such as epileptic foci detected by invasive detection electrodes). This prior fusion will help improve the accuracy of source reconstruction. Some studies have shown that brain activity reconstruction with high spatiotemporal resolution benefits from combining multimodal prior information, such as Figure 1 As shown, the present invention provides a variational sparse source imaging method based on a time basis matrix algorithm, which specifically includes the following steps:

[0029] Step S1: Use sensors to collect raw brain nerve activity data and perform preprocessing;

[0030] In particular, preprocessing includes filtering, artifact removal, and time locking. The raw data can be regarded as the representation of brain activity signals in the sensor space. The brain activity signal S in the source space is linearly converted to the data B in the sensor space through the guidance field matrix L, which is expressed as ,in It is environmental noise;

[0031] Step S2: Project the brain activity signal in the source space into the low-rank feature space of the time basis matrix. Convert the brain activity signal in the source space into the time domain through low-rank decomposition. Combined with the variational sparsity constraint, express it as a time series composed of several time basis functions.

[0032] In particular, we assume that the source space S is a linear combination of multiple time basis functions, which can be expressed as , and transform the data in the sensor space into .in is the coefficient distribution from the source space to the time basis space, represents a TBM composed of time basis functions, Represents the coefficient distribution of the transformation from sensor space to time basis space;

[0033] Assuming that the brain activity signal in the source space is low-rank, the robust principal component analysis technique is used to impose low-rank constraints on the brain activity signal in the source space by mixing matrices. Then, the data-driven singular value decomposition method is used to determine the time basis function and matrix according to the Kaiser rule. At the same time, the variational sparsity constraint is introduced to ensure the spatial smoothness of the source signal reconstruction by creating the first-order difference matrix to capture the difference between adjacent dipoles. The formula is as follows:

[0034] ,

[0035] ,

[0036] Where p is the number of sides of the triangular element. captures the first-order differences between adjacent dipoles, where each row corresponds to a shared edge Source and The values ​​1 and -1 indicate the direction of the difference, ensuring spatial smoothness in the source reconstruction. Therefore, there will be large variation values ​​at the boundaries of the source space. This variational constraint ensures that the boundaries of the source can be accurately located.

[0037] Step S3: Confirm that spatial prior information is available, apply guided field constraints to the time series, and further enhance the reconstruction results using guided field constraints; compress the time domain signal, impose norm constraints in the compressed space to convert the time series into a multi-group basis weight estimation problem, filter out redundant information and reduce the computational cost in the original space.

[0038] Prior constraints are usually implemented by imposing norm constraints on the source space or the transformed domain. This type of model can be described by the following formula:

[0039] ,

[0040] in represents the Frobenius norm, h(S) is the constraint imposed on the source space, and L is the guide field matrix. corresponds to the negative log-likelihood which can be viewed as Gaussian white noise under the Bayesian model, corresponds to the negative logarithm of the prior on the source space.

[0041] Considering the multimodal information that can usually be provided in clinical or research, when spatial prior information is available, the spatial prior provided by fMRI is applied to the algorithm, and the source space signal that guides the field matrix reconstruction is expressed as , represents the corresponding forward coupling matrix constant, Represented as the i-th column corresponding to the lead matrix, is the corresponding pseudo-inverse matrix, which realizes the low-dimensional projection of multiple dipole points in the source space;

[0042] Considering the sparsity of all time basis corresponding coefficients in the source space, by using L 2,1 The norm instead of L1 norm is used to realize the case of spatial structure sparsity, and its formula is defined as follows:

[0043] ,

[0044] L 2,1 The norm promotes a sparse structure, where a small number of non-zero rows correspond to active dipoles and almost all zero rows correspond to inactive dipoles. The sparsity of the coefficients is guaranteed in the compressed domain.

[0045] Step S4: Establish complete model constraints to achieve the variational sparse prior mapping goal of time-domain decomposition, and optimize the objective function through the alternating direction method of multipliers to solve the multi-group basis weight estimation problem and reconstruct the brain activity signal in the source space. Analyze the sparsity and smoothness of the brain activity signal in the source space to verify the effectiveness of the model.

[0046] In particular, in order to construct a complete model constraint, the time basis matrix is ​​used to project the source signal into the low-rank subspace of the time basis function, the L2 norm is introduced to promote the row sparse structure, and the finite difference matrix is ​​used. To ensure smooth signal differences between adjacent dipoles while maintaining global sparsity, we introduce the lead matrix provided by fMRI , this method can enhance the reconstruction effect under low signal-to-noise ratio conditions; This type of heuristic regularization term ensures that the system maintains local smoothness while being globally sparse. The values ​​of the regularization parameters λ and α are determined by cross-validation or empirical methods in the range of 0.001≤λ≤10.

[0047] The complete model constraint form is as follows:

[0048] ,

[0049] The regularization parameter Balancing reconstruction error and constraints, parameters Control the sparsity of the source and prevent the estimated signal vector from being too biased.

[0050] Use ADMM algorithm to optimize the objective function. Introduce auxiliary variables and , the original problem can be equivalently constructed as an augmented Lagrangian function:

[0051]

[0052] In the formula, and is the Lagrange multiplier, and is the penalty parameter, both of which are set to constants greater than 0.

[0053] By alternately updating these variables and minimizing the augmented Lagrangian function, when updating the parameters, the basis with too small total energy in each iteration result is eliminated, which accelerates convergence and ensures the low rank of the source space signal.

[0054] At this point, the algorithm has converged and stops updating. The source space reconstruction result is .

[0055] In summary, the present invention discloses a variational sparse source imaging method based on the time basis matrix (VSSI-TBM) algorithm, which can have robust performance in low signal-to-noise ratio, large source and multi-source environments, such as Figure 2-Figure 4As shown in the figure. The method achieves local smoothing and global sparse reconstruction of the source space signal by low-rank decomposition of the temporal basis matrix and combining multiple constraints and variational space constraints. The flexibility of VSSI-TBM allows the algorithm to combine different types of prior constraints to improve the accurate estimation of the source, which is suitable for source reconstruction in different scenarios. Simulation and real data experiments show that VSSI-TBM performs well on sources with low signal-to-noise ratio, distributed brain regions, and large areas. In particular, its energy is more concentrated in complex signal environments and has good robustness. VSSI-TBM is suitable for improving MEG imaging applications in complex clinical and research environments.

[0056] On the other hand, the present invention provides a variational sparse source imaging device based on a time basis matrix algorithm, wherein the modules included in the device can implement the various steps of the aforementioned method, specifically including:

[0057] An acquisition unit, used to collect raw data of brain nerve activity using sensors and perform preprocessing;

[0058] A conversion unit is used to project the preprocessed raw brain neural activity data into the low-rank feature space of the time basis matrix, convert the preprocessed raw brain neural activity data into the time domain through low-rank decomposition, and combine the variational sparsity constraint to express it as a time series composed of several time basis functions;

[0059] The constraint unit is used to confirm that spatial prior information is available, use the guided field constraint on the time series, and impose the norm constraint in the compressed space to convert the time series into a multi-group basis weight estimation problem, thereby filtering out redundant information and reducing the computational cost in the time domain;

[0060] The reconstruction unit is used to establish complete model constraints to achieve the variational sparse prior mapping target of time domain decomposition, optimize the objective function through the alternating direction method of multipliers, solve the multi-group basis weight estimation problem and reconstruct the brain activity signal in the source space.

[0061] In a third aspect, the present invention provides an electronic device comprising: one or more processors; a memory for storing one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the aforementioned variational sparse source imaging method based on a time basis matrix algorithm.

[0062] In a fourth aspect, the present invention provides a computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, enables the processor to implement the aforementioned variational sparse source imaging method based on a time basis matrix algorithm.

[0063] The specific embodiments described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A variational sparse source imaging method based on a time basis matrix algorithm, characterized in that: The method comprises: Step S1: Use sensors to collect raw brain nerve activity data and perform preprocessing; Step S2: Projecting the preprocessed raw brain neural activity data into the low-rank feature space of the time basis matrix, converting the preprocessed raw brain neural activity data into the time domain through low-rank decomposition, and combining it with the variational sparsity constraint to express it as a time series composed of several time basis functions; Step S3: confirm that spatial prior information is available, use the guided field constraint on the time series and impose the norm constraint in the compressed space to convert the time series into a multi-group basis weight estimation problem, filter out redundant information and reduce the computational cost in the time domain; Step S4: Establish complete model constraints to achieve the variational sparse prior mapping target of time domain decomposition, optimize the objective function through the alternating direction method of multipliers, solve the multi-group basis weight estimation problem and reconstruct the brain activity signal in the source space.

2. The variational sparse source imaging method based on the time basis matrix algorithm according to claim 1, characterized in that: The pre-processing in step S1 includes filtering, artifact removal and time locking.

3. The variational sparse source imaging method based on the time basis matrix algorithm according to claim 1, characterized in that: The original data in step S1 is the brain activity signal of the source space Represented in sensor space, by the guidance field matrix , the brain activity signal in the source space Data linearly transformed into sensor space ,in It's environmental noise.

4. The variational sparse source imaging method based on the time basis matrix algorithm according to claim 3, characterized in that: In step S2, a low-rank constraint is imposed on the brain activity signal in the source space by using a mixed matrix method using a robust principal component analysis technique, and then a data-driven singular value decomposition method is used to determine the time basis function and matrix according to the Kaiser rule. ; The variational sparsity constraint is achieved by creating a first-order difference matrix Capture the difference between adjacent dipoles: ， ， in is the number of edges of the triangular element, the first-order difference matrix Each row corresponds to a shared edge Source and , values ​​1 and -1 indicate the direction of the difference, when the brain activity signal in the source space is a linear combination of multiple time basis functions, which can be expressed as , and transform the data in the sensor space into ,in is the coefficient distribution from the source space to the time basis space, represents the time basis matrix composed of time basis functions, Represents the coefficient distribution of the transformation from sensor space to time basis space.

5. The variational sparse source imaging method based on the time basis matrix algorithm according to claim 4, characterized in that: In step S3, the prior constraint is achieved by imposing a norm constraint on the source space or the transformation domain: ， in represents the Frobenius norm, is the constraint imposed on the source space, L is the guide field matrix, and the formula corresponds to the negative log-likelihood of Gaussian white noise under the Bayesian model, corresponds to the negative logarithm of the prior on the source space.

6. The variational sparse source imaging method based on the time basis matrix algorithm according to claim 5, characterized in that: When spatial prior information is available, the spatial prior provided by fMRI is applied to the reconstructed brain activity signal in the source space. Expressed as , represents the corresponding forward coupling matrix constant, It is represented by the i-th column corresponding to the forward guide matrix, is the pseudo-inverse matrix; By using L 2,1 The norm realizes the case of spatial structure sparsity, and its formula is defined as follows: 。 7. The variational sparse source imaging method based on the time basis matrix algorithm according to claim 6, characterized in that: In step S4, the complete model constraint form is as follows: ， The regularization parameter Balancing reconstruction error and constraints, parameters Control the sparsity of the source and prevent the estimated signal vector from being too biased; Use the multiplier alternating direction method to optimize the objective function and introduce auxiliary variables and , solving the multi-group basis weight estimation problem is equivalently constructed as an augmented Lagrangian function: ， Where, and is the Lagrange multiplier, and is the penalty parameter; by alternately updating the variables of the augmented Lagrangian function, minimizing the augmented Lagrangian function until convergence, the source space reconstruction result is obtained .

8. A variational sparse source imaging device based on a time basis matrix algorithm, characterized in that: include: An acquisition unit, used to collect raw data of brain nerve activity using sensors and perform preprocessing; A conversion unit is used to project the preprocessed raw brain neural activity data into the low-rank feature space of the time basis matrix, convert the preprocessed raw brain neural activity data into the time domain through low-rank decomposition, and combine the variational sparsity constraint to express it as a time series composed of several time basis functions; The constraint unit is used to confirm that spatial prior information is available, use the guided field constraint on the time series, and impose the norm constraint in the compressed space to convert the time series into a multi-group basis weight estimation problem, thereby filtering out redundant information and reducing the computational cost in the time domain; The reconstruction unit is used to establish complete model constraints to achieve the variational sparse prior mapping target of time domain decomposition, optimize the objective function through the alternating direction method of multipliers, solve the multi-group basis weight estimation problem and reconstruct the brain activity signal in the source space.

9. An electronic device, characterized in that: include: one or more processors; a memory for storing one or more programs; Wherein, when one or more programs are executed by the one or more processors, the one or more processors implement the variational sparse source imaging method based on the time basis matrix algorithm as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that Executable instructions are stored thereon, and when the instructions are executed by a processor, the processor can implement the variational sparse source imaging method based on the time basis matrix algorithm as described in any one of claims 1 to 7.

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