A multi-view function gradient density-based brain representative functional tissue exploration method

Abstract

The application discloses a brain representative functional tissue exploration method based on multi-view function gradient density, comprising the following steps: obtaining resting-state functional magnetic resonance imaging data and preprocessing to obtain standardized resting-state image data; processing the standardized resting-state image data based on resting-state functional connectivity to generate a function gradient density map; adopting a spherical wavelet transform method to perform multi-scale decomposition on the function gradient density map to obtain view data corresponding to multiple spatial frequency scales; calculating cross-individual differences of function gradient density features of different individuals under each view based on a Wasserstein distance, and constructing a similarity matrix corresponding to each view; adopting a multi-view spectral clustering method to perform fusion analysis on the similarity matrix to identify a brain representative functional tissue mode; and visually displaying the representative functional tissue mode; and fully considering the cerebral cortex geometric structure and multi-scale functional features, realizing stable identification and individual difference analysis of the brain functional tissue mode.

Description

Technical Field

[0001] This invention belongs to the field of medical image processing technology, specifically relating to a method for exploring representative functional tissues of the brain based on multi-view functional gradient density. Background Technology

[0002] Functional magnetic resonance imaging (fMRI) technology can indirectly reflect the functional activities and interconnections between different brain regions by detecting changes in blood oxygen level-dependent signals in brain tissue at rest. It has been widely used in brain functional network analysis, brain region functional differentiation research, and related brain disease research.

[0003] As research in brain science deepens, researchers have gradually recognized the significant complexity and individual variability in the functional organization of the brain. Traditional methods based on functional connectivity strength or fixed brain region divisions often fail to comprehensively characterize the functional changes of the cerebral cortex in continuous space, nor can they stably reflect the differences in functional organization between different individuals.

[0004] In recent years, functional gradient analysis (FGA) has revealed the continuous evolution of cortical functional organization from lower to higher levels by reducing the dimensionality of the functional connectivity matrix, providing a new analytical perspective for understanding the overall functional architecture of the brain. However, existing methods are typically based on a single scale or single feature perspective, making it difficult to simultaneously consider the structural characteristics of brain functional organization at different spatial scales. Furthermore, in cross-individual comparisons, commonly used metrics such as Euclidean distance fail to adequately consider the geometric structural characteristics of the cerebral cortex, making them susceptible to spatial registration errors and thus reducing the stability and reliability of the analytical results.

[0005] Therefore, there is an urgent need for a technical solution that can comprehensively characterize functional gradient density features under multi-scale and multi-perspective conditions, while also taking into account cortical geometric structure information, in order to achieve stable identification of representative functional organization patterns of the brain and analysis of individual differences. Summary of the Invention To address the shortcomings of existing technologies, the present invention aims to provide a method for exploring representative functional tissues of the brain based on multi-perspective functional gradient density. This method overcomes the limitations of single functional features, comprehensively characterizes the diversity and complexity of functional tissues in the cerebral cortex, accurately describes the interactions and functional boundaries of different brain regions, and clearly reveals the differences and commonalities in functional patterns among individuals. This provides reliable data support for personalized treatment, research on brain dysfunction, and precise diagnosis and treatment of diseases.

[0006] To achieve the above objectives, the present invention employs the following technical solution: A method for exploring representative functional organization of the brain based on multi-view functional gradient density includes the following steps: Step 1: Acquire functional magnetic resonance imaging (fMRI) data of healthy adults in a resting state, and preprocess the image data to obtain standardized resting state image data; Step 2: Process the standardized resting-state image data obtained in Step 1 based on resting-state functional connectivity to generate a functional gradient density map; Step 3: Perform multi-scale decomposition on the functional gradient density map using the spherical wavelet transform method to obtain viewpoint data corresponding to multiple spatial frequency scales; Step 4: Calculate cross-individual distances using Wasserstein distance for data from different individuals' perspectives, and construct similarity matrices for each perspective. Step 5: Use multi-view spectral clustering to perform fusion analysis on the similarity matrices corresponding to each perspective to identify representative functional organization patterns of the brain; Step 6: Visualize the representative functional organization pattern.

[0007] The present invention also has the following technical features: Preferably, the image data preprocessing in step one includes at least one or more of the following steps: motion correction, temporal denoising, spatial normalization, and standard spatial registration.

[0008] Preferably, the method for generating a functional gradient density map based on resting-state functional connectivity in step two includes: S1. Map the standardized resting-state image data obtained in step one from the voxel space to the cortical surface space to obtain the resting-state time series corresponding to each sampling position on the cortical surface. S2. Based on the resting-state time series, calculate the resting-state functional connectivity between each sampling location on the cortical surface, and construct a functional connectivity matrix, as follows: ; in, Represents the resting-state functional connectivity matrix. This represents the element value in the i-th row and j-th column of the RSFC matrix. (·) represents the correlation calculation function, used to quantify the degree of linear correlation between two time series. Represents the resting-state time series of the i-th cortical surface sampling location. The resting-state time series representing the sampling location of the j-th cortical surface; S3. Standardize the functional connection matrix to obtain a standardized functional connection matrix, as follows: in, The representative normalized matrix is ​​a... Standardized values ​​after Fisher-Z transform This represents the transformation from "correlation coefficient to normal distribution value" achieved through a nonlinear transformation of the natural logarithm. S4. Calculate the functional gradient representation based on the standardized functional connectivity matrix, and obtain the functional gradient representation of each sampling position on the cortical surface in a low-dimensional continuous space by performing similarity structure analysis on the matrix. S5. Perform boundary detection processing on the functional gradient representation to generate a binary boundary map. ,in: S6. For the binary boundary map Density statistical processing is performed to obtain the functional gradient density map. The functional gradient density map is used to characterize the spatial distribution intensity of the functional gradient boundaries on the cortical surface.

[0009] Preferably, the method for decomposing functional gradient density data using spherical wavelet transform in step three includes: S1. Define the functional gradient density map obtained in step two as a scalar function on a sphere, expressed as: in, I(θ, ) represents the cortical sphere or its subregion. () is the functional gradient density function on the surface of a sphere. Represents spherical coordinates; S2. Construct a set of spherical analysis filters with different spatial scales, assuming... for A set of spherical analysis filters, where each filter ( , This corresponds to a different spatial frequency scale. The integral region on the sphere represents the entire surface of the cerebral cortex. This represents the total number of scales, and n represents the frequency level. S3, by applying the functional gradient density function The spherical convolution operation is performed with the spherical analysis filter, and the calculation formula is as follows: n =I in, n At the frequency level Wavelet coefficients on Represents spherical convolution; Using the Laplace-Gaussian wavelet as the template wavelet Its definition is: ; In the formula, Indicates an extension operation; The representativeness of wavelet coefficients is evaluated by calculating their energy. The formula is as follows: .

[0010] Furthermore, the formula for calculating the Wasserstein distance mentioned in step four is as follows: in: and It is the perspective of subjects i and j Functional gradient density distribution on It is the set of all possible joint distributions. It is the optimal transmission plan. It is the Euclidean distance between different subjects for the functional gradient density; This represents the spatial domain in which the functional gradient density feature is defined. Represents the Cartesian product of the domain of the space; , They represent the subjects respectively. With the subjects Spatial sampling location; This represents the set of all feasible transmission plans that satisfy the edge constraints, where the edge constraints are such that the transmission plan is satisfied by the edge constraints on both sides. and The weight distribution is consistent.

[0011] Preferably, the conversion formula for the similarity matrix in step four is as follows: in, represents the similarity matrix, with values ​​in the matrix within the range of [0,1]. Wp represents the normalized distance matrix.

[0012] Preferably, the method for functional pattern clustering using multi-view spectral clustering on the similarity matrices corresponding to each viewpoint in step five includes: S1, for each perspective Similarity matrix First, construct the degree matrix. The calculation formula is as follows: S2, Based on the similarity matrix degree matrix Construct the symmetric normalized Laplacian matrix corresponding to each viewpoint and calculate the value for each viewpoint. The Laplace matrix is ​​calculated using the following formula: S3, for each perspective Laplace matrix Perform eigenvalue decomposition to obtain its antecedent The eigenvectors corresponding to the n eigenvalues ​​satisfy: in, Indicates the first 1 eigenvalue, This represents the corresponding feature vector; S3, the results obtained from each perspective. The feature vectors are concatenated to construct a joint feature matrix. in, Indicates the number of viewpoints; S4. For the joint feature matrix Cluster analysis was performed on the row vectors, with k-means clustering being the preferred method, to divide the subjects into groups. A representative functional organizational model.

[0013] Compared with the prior art, the present invention has the following technical effects: This invention models the continuous changes in the functional connectivity of the cerebral cortex by constructing multi-view functional gradient density features, avoiding reliance on a single scale or single functional feature for analysis, thereby improving the completeness and stability of the description of the brain's functional organizational structure. This invention employs overcomplete spherical wavelet transform to decompose functional gradient density into multiple spatial frequency scales, enabling the functional gradient density features to be expressed at different spatial scales. This approach takes into account both large-scale functional organization and local functional change features, which is beneficial for characterizing the diversity of functional organization in the cerebral cortex and its spatial hierarchical relationships. This invention introduces Wasserstein distance as a difference measure in the process of cross-individual functional feature comparison. By treating the functional gradient density feature as a distribution defined on the cortical space, it can explicitly consider the cortical geometric structure information in the distance calculation process, thereby reducing the impact of spatial registration error on the cross-individual comparison results. This invention constructs a similarity matrix from functional gradient density features obtained from different perspectives, and uses multi-perspective similarity fusion and spectral clustering methods for joint analysis, so that functional information from different spatial scales and perspectives can be comprehensively utilized, reducing the bias caused by single-perspective features and improving the consistency of functional organization pattern recognition results. This invention establishes a complete technical process from functional gradient density modeling, multi-scale decomposition, cross-individual difference measurement to multi-perspective clustering analysis, which can be used to systematically explore representative functional organizational patterns of the brain and provide an implementable technical solution for brain functional organizational structure analysis. Attached Figure Description

[0014] Figure 1 This is a flowchart illustrating the method for exploring representative functional tissues of the brain based on multi-view functional gradient density, as described in this invention. Figure 2 A visualization of the multi-view functional gradient density features is presented. Figure 3 This is a diagram showing four representative functions of the superior temporal lobe region. Detailed Implementation

[0015] The following detailed explanation of the specific content of the present invention is provided in conjunction with embodiments. These descriptions are intended to explain the present invention and not to limit it.

[0016] like Figure 1 As shown in the figure, this embodiment provides a method for exploring representative brain functional organizations based on multi-view functional gradient density, which includes the following steps.

[0017] Step 1: Acquisition and preprocessing of resting-state functional magnetic resonance imaging data: This study used data from 763 participants aged 22 to 35 years from the Human Connectome Project (HCP) S1200. T1-weighted imaging was acquired using a 3D PRAGE sequence. The acquisition parameters for T1-weighted imaging were as follows: 256 sagittal slices, 0.7 mm isotropic voxels, matrix size of 320, TR / TE = 2400 / 2.14 ms, flip angle of 8°, field of view (FOV) of 224 × 224 mm, and bandwidth (BW) of 210 Hz / pixel. T2-weighted imaging was acquired using a turbine spin echo (TSE) sequence with a variable flip angle. The acquisition parameters for T2-weighted imaging were the same as for T1-weighted imaging, with the same matrix size, field of view, and number of slices, but TR / TE was 3200 / 565 ms, and bandwidth was 744 Hz / pixel. The acquisition parameters for resting-state functional magnetic resonance imaging (rs-fMRI) data are as follows: 72 slices, 2.0 mm isotropic voxels, 90 × 104 matrix size, TR / TE of 720 / 33.1 ms, flip angle of 52°, field of view (FOV) of 208 × 180 mm, and bandwidth of 2290 Hz / pixel. Image data is preprocessed to obtain standardized resting-state image data. The image preprocessing process includes motion correction, denoising, normalization, and standard spatial registration, thereby reducing the impact of non-neural signals, motion artifacts, and spatial differences on subsequent analysis.

[0018] Step 2: Based on resting-state functional connectivity (RSFC), the standardized resting-state image data obtained in Step 1 is processed to generate a functional gradient density map, thereby quantifying and summarizing the functional connectivity strength between different regions of the cerebral cortex and clarifying functional boundaries. The functional gradient density map, as an important functional feature, can effectively reflect the functional organization pattern of the cerebral cortex and provide a reliable basis for subsequent analysis. The specific calculation process is as follows: S1. Using the HCPConnectomeWorkbench tool, the standardized resting-state image data obtained in step S1 is mapped from voxel space to cortical surface space, that is, converted from the original scan space to the local intermediate surface, with white matter and cortical surface as constraints. The time series of each voxel is extracted, the time series is downsampled, and Gaussian smoothing is performed on it using wavelet transform. S2. Based on the resting-state time series, calculate the resting-state functional connectivity between each sampling location on the cortical surface and construct a functional connectivity matrix. Specifically, by calculating the correlation between the time series of each hemisphere and the time series of the other hemisphere, construct a 32k×64k RSFC matrix, as shown below: in, Represents the resting-state functional connectivity matrix. This represents the element value in the i-th row and j-th column of the RSFC matrix. (·) represents the correlation calculation function, used to quantify the degree of linear correlation between two time series. Represents the resting-state time series of the i-th cortical surface sampling location. The resting-state time series representing the sampling location of the j-th cortical surface; S3. Standardize the functional connectivity matrix and calculate the RSFC-2nd matrix for each hemisphere. Through pairwise correlation analysis, obtain the 32k×32k standardized functional connectivity matrix. The calculation formula is as follows: in, The representative normalized matrix is ​​a... Standardized values ​​after Fisher-Z transform This represents the transformation from "correlation coefficient to normal distribution value" achieved through a nonlinear transformation of the natural logarithm. S4. Calculate the functional gradient representation based on the normalized functional connectivity matrix. By performing similarity structure analysis on the matrix, obtain the functional gradient representation of each sampling position on the cortical surface in a low-dimensional continuous space. Specifically, for each hemisphere, use the "cifti-gradient" function in HCPConnectomeWorkbench to calculate the gradient of the RSFC-2nd matrix and generate a 32k×32k gradient matrix. S5. Perform boundary detection processing on the functional gradient representation to generate a 32k binary boundary map. Mark the significant boundaries of functional connectivity in the cerebral cortex, where: S6. For the binary boundary map Density statistical processing was performed to obtain the 32k functional gradient density map. The functional gradient density map is used to characterize the spatial distribution intensity of functional gradient boundaries on the cortical surface. As input data for functional organization analysis, this map comprehensively reflects the strength and boundaries of functional connections between different regions of the cerebral cortex, thus providing a reliable foundation for subsequent multi-perspective functional pattern analysis.

[0019] Step 3: The functional gradient density data is decomposed into multiple scales using the spherical wavelet transform method to obtain perspective data at multiple spatial frequency scales. Through multi-scale analysis, the changes in functional gradient density at different spatial scales are further revealed, ensuring a comprehensive understanding of the functional organization of the cerebral cortex. The specific process includes the following steps: S1. Define the functional gradient density map obtained in step two as a scalar function on a sphere; assume I(θ, () is the functional gradient density function on the surface of a sphere. Represents spherical coordinates; in, Represents the cortical sphere or its subregions; S2. Construct a set of spherical analysis filters with different spatial scales, assuming... for A set of spherical analysis filters, where each filter ( , This corresponds to a different spatial frequency scale. Let be the integral region on the sphere, representing the entire surface of the cerebral cortex. This represents the total number of scales, and n represents the frequency level. S3, By analyzing the functional gradient density function The spherical convolution operation with the spherical analysis filter is calculated using the following formula: n =I in, n At the frequency level Wavelet coefficients on Represents spherical convolution; Using the Laplace-Gaussian wavelet as the template wavelet Its definition is: ; In the formula, This indicates an expansion operation, which extends the template wavelet. Adjusted to adapt to different spatial frequency scales; S4. Convert the wavelet coefficients corresponding to each scale. As perspective data at different spatial frequency scales, it is used to characterize the spatial distribution characteristics of functional gradient density under multi-scale conditions. The representativeness of wavelet coefficients is evaluated by calculating their energy. The formula is as follows: .

[0020] Step 4: Calculate cross-individual distances using Wasserstein distance for data from different individuals' perspectives, and construct similarity matrices for each perspective based on the calculation results. The formula for calculating Wasserstein distance is: in: and It is the perspective of subjects i and j Functional gradient density distribution on It is the set of all possible joint distributions. It is the optimal transmission plan. It is the Euclidean distance between different subjects for the functional gradient density; The spatial domain representing the functional gradient density feature is preferably the set of cortical spherical sampling locations or its corresponding coordinate space. The Cartesian product of the spatial domain is used to describe the transmission correspondence between different spatial locations; , They represent the subjects respectively. With the subjects Spatial sampling location; This represents the set of all feasible transmission plans that satisfy the edge constraints, where the edge constraints are defined as transmission plans that satisfy the edge constraints on both sides of the boundary. and The weight distribution is consistent; The calculation results are normalized using the following formula: Next, based on the normalized distance matrix, we convert it into a similarity matrix using the following formula: in, The matrix represents the similarity matrix, with values ​​ranging from [0,1]. Wp represents the normalized distance matrix. Larger values ​​in the similarity matrix indicate smaller distances, meaning higher similarity between samples.

[0021] Step 5: Use the Multi-view Spectral clustering method to cluster functional patterns in the similarity matrices corresponding to each viewpoint, identifying representative functional organizational features of the brain; this includes the following steps: S1, for each perspective Similarity matrix First, construct the degree matrix. Each element represents the degree of a node, which is the sum of the similarities between that node and all other nodes. S2, Based on the similarity matrix degree matrix Construct the symmetric normalized Laplacian matrix corresponding to each viewpoint and calculate the value for each viewpoint. The Laplace matrix of is calculated using the following formula: S3, for each perspective Laplace matrix Perform eigenvalue decomposition to obtain its antecedent The eigenvectors corresponding to the n eigenvalues ​​satisfy: in, Indicates the first 1 eigenvalue, This represents the corresponding feature vector; S3, the results obtained from each perspective. The feature vectors are concatenated to construct a joint feature matrix. in, Indicates the number of viewpoints; S4. For the joint feature matrix Cluster analysis is performed on the row vectors, with k-means clustering being the preferred method. The method divides the subjects into A representative functional organizational model.

[0022] Step Six: Visualize the identified representative functional organizational features of the brain to intuitively display the differences in functional organization of different brain regions and verify the spatial rationality of the multi-scale functional gradient density decomposition and functional pattern clustering results.

[0023] In all experiments, the parameters and number of clusters for spectral clustering were empirically set to 20 and 4, respectively. Considering the complex curled structure of the original mesocortical surface of the subjects, direct visualization of functional features may be affected by spatial distortion. Therefore, in order to better present the results and improve interpretability, this embodiment adopts a method of mapping all calculated functional features (i.e., functional gradient density, wavelet coefficients, and representative functional modes) onto an expanded 32kfs_LR surface, thereby achieving clearer and more accurate visualization.

[0024] Figure 1This is a schematic diagram of the functional organization exploration method based on functional gradient density and multi-view information of the present invention; Figure 2 A visualization illustrating the multi-view functional gradient density features is provided. Typically, an overcomplete wavelet transform is used to decompose the functional gradient density map into seven scale levels, thereby capturing functional information at different spatial frequencies. For example... Figure 2 As shown, the coarser wavelet coefficients can capture large-scale functional gradient density information, while the finer-scale coefficients embed smaller-scale functional gradient information. Through this multi-scale decomposition method, this embodiment can characterize the functional organization patterns of the cerebral cortex at different scales, thus effectively solving the problem of functional pattern omission or error that may arise from relying solely on a single scale for functional feature analysis. Specifically: The first-level wavelet coefficients (maximum-scale functional information) showed high similarity among subjects, thus exhibiting weak ability to distinguish functional patterns. The level 7 wavelet coefficients (high-frequency information) are greatly affected by noise, which may lead to errors and instability. Wavelet coefficients at levels 2 to 6, while preserving cross-subject consistency structure, can effectively characterize functional gradient changes at multiple scales, making them ideal scales for representing functional patterns.

[0025] In the superior temporal lobe, this area is associated with social cognitive processes and auditory processing. Figure 3 Four representative functional patterns were presented. In pattern (a), the functional gradient density exhibited a "Y" shape; in patterns (b) and (c), the functional gradient density was linear, but the linear pattern (c) was longer; in pattern (d), the functional gradient density exhibited a "U" shape. Among 647 participants, the percentages for the four patterns were 22.54%, 21.39%, 26.01%, and 30.06%, respectively.

[0026] Therefore, by mapping and demonstrating the effect of functional features on the inflated surface, this embodiment not only improves the accuracy of functional pattern recognition but also optimizes the multi-scale analysis of the functional gradient density of the cerebral cortex, significantly enhancing the stability and reliability of the proposed method in practical applications.

[0027] This invention enhances the multi-scale representation capability of functional gradient density features: by using overcomplete wavelet transform, it can effectively extract detailed information of brain functional gradient density across multiple spatial frequency scales. Compared to traditional wavelet transform, overcomplete wavelet transform achieves more comprehensive sampling and exhibits greater robustness and sensitivity in handling inter-group differences. Therefore, this technique can extract more representative features from complex functional patterns in the cerebral cortex, improving the accuracy of functional pattern recognition.

[0028] The similarity network fusion method employed in this invention effectively captures shared and complementary information of functional gradient density by nonlinearly fusing multi-view functional features. This makes the identification of functional patterns more comprehensive from different perspectives and reduces local errors caused by a single perspective.

[0029] By processing the fused similarity matrix using spectral clustering, functional gradient density patterns can be efficiently divided into different groups. This method not only improves the accuracy of clustering results but also has strong universality, making it suitable for functional gradient pattern analysis of different subjects.

Claims

1. A method for exploring representative functional organizations of the brain based on multi-view functional gradient density, characterized in that, Includes the following steps: Step 1: Acquire functional magnetic resonance imaging (fMRI) data of healthy adults in a resting state, and preprocess the image data to obtain standardized resting state image data; Step 2: Process the standardized resting-state image data obtained in Step 1 based on resting-state functional connectivity to generate a functional gradient density map; Step 3: Perform multi-scale decomposition on the functional gradient density map using the spherical wavelet transform method to obtain viewpoint data corresponding to multiple spatial frequency scales; Step 4: Calculate cross-individual distances using Wasserstein distance for data from different individuals' perspectives, and construct similarity matrices for each perspective. Step 5: Use multi-view spectral clustering to perform fusion analysis on the similarity matrices corresponding to each perspective to identify representative functional organization patterns of the brain; Step 6: Visualize the representative functional organization pattern.

2. The method for exploring representative brain functional organizations based on multi-view functional gradient density as described in claim 1, characterized in that, The image data preprocessing described in step one includes at least one or more of the following steps: motion correction, temporal denoising, spatial normalization, and standard spatial registration.

3. The method for exploring representative brain functional organizations based on multi-view functional gradient density as described in claim 1, characterized in that, The method for generating functional gradient density maps based on resting-state functional connectivity described in step two includes: S1. Map the standardized resting-state image data obtained in step one from the voxel space to the cortical surface space to obtain the resting-state time series corresponding to each sampling position on the cortical surface. S2. Based on the resting-state time series, calculate the resting-state functional connectivity between each sampling location on the cortical surface, and construct a functional connectivity matrix, as follows: ； in, Represents the resting-state functional connectivity matrix. This represents the element value in the i-th row and j-th column of the RSFC matrix. (·) represents the correlation calculation function, used to quantify the degree of linear correlation between two time series. Represents the resting-state time series of the i-th cortical surface sampling location. The resting-state time series representing the sampling location of the j-th cortical surface; S3. Standardize the functional connection matrix to obtain a standardized functional connection matrix, as follows: in, The representative normalized matrix is ​​a... Standardized values ​​after Fisher-Z transform This represents the transformation from "correlation coefficient to normal distribution value" through a nonlinear transformation of the natural logarithm. S4. Calculate the functional gradient representation based on the standardized functional connectivity matrix, and obtain the functional gradient representation of each sampling position on the cortical surface in a low-dimensional continuous space by performing similarity structure analysis on the matrix. S5. Perform boundary detection processing on the functional gradient representation to generate a binary boundary map. ,in: S6. For the binary boundary map Density statistical processing is performed to obtain the functional gradient density map. The functional gradient density map is used to characterize the spatial distribution intensity of the functional gradient boundaries on the cortical surface.

4. The method for exploring representative brain functional organizations based on multi-view functional gradient density as described in claim 1, characterized in that, The method for decomposing functional gradient density data using spherical wavelet transform as described in step three includes: S1. Define the functional gradient density map obtained in step two as a scalar function on a sphere, expressed as: in, I(θ, ) represents the cortical sphere or its subregion. () is the functional gradient density function on the surface of a sphere. Represents spherical coordinates; S2. Construct a set of spherical analysis filters with different spatial scales, assuming... for A set of spherical analysis filters, where each filter ( , This corresponds to a different spatial frequency scale. The integral region on the sphere represents the entire surface of the cerebral cortex. This represents the total number of scales, and n represents the frequency level. S3, by applying the functional gradient density function The spherical convolution operation is performed with the spherical analysis filter, and the calculation formula is as follows: n =I in, n At the frequency level Wavelet coefficients on Represents spherical convolution; Using the Laplace-Gaussian wavelet as the template wavelet Its definition is: ； In the formula, Indicates an extension operation; The representativeness of wavelet coefficients is evaluated by calculating their energy. The formula is as follows: 。 5. The method for exploring representative functional tissues of the brain based on multi-view functional gradient density as described in claim 1, characterized in that, The formula for calculating the Wasserstein distance mentioned in step four is as follows: in: and It is the perspective of subjects i and j Functional gradient density distribution on It is the set of all possible joint distributions. It is the optimal transmission plan. It is the Euclidean distance between different subjects for the functional gradient density; This represents the spatial domain in which the functional gradient density feature is defined. Represents the Cartesian product of the domain of the space; , They represent the subjects respectively. With the subjects Spatial sampling location; This represents the set of all feasible transmission plans that satisfy the edge constraints, where the edge constraints are such that the transmission plan is satisfied by the edge constraints on both sides. and The weight distribution is consistent.

6. The method for exploring representative functional tissues of the brain based on multi-view functional gradient density as described in claim 5, characterized in that, The conversion formula for the similarity matrix mentioned in step four is as follows: in, represents the similarity matrix, with values ​​in the matrix within the range of [0,1]. Wp represents the normalized distance matrix.

7. The method for exploring representative brain functional organizations based on multi-view functional gradient density as described in claim 1, characterized in that, The method for functional pattern clustering using multi-view spectral clustering on the similarity matrices corresponding to each viewpoint in step five includes: S1, for each perspective Similarity matrix First, construct the degree matrix. The calculation formula is as follows: S2, Based on the similarity matrix degree matrix Construct the symmetric normalized Laplacian matrix corresponding to each viewpoint and calculate the value for each viewpoint. The Laplace matrix is ​​calculated using the following formula: S3, for each perspective Laplace matrix Perform eigenvalue decomposition to obtain its antecedent The eigenvectors corresponding to the n eigenvalues ​​satisfy: in, Indicates the first 1 eigenvalue, This represents the corresponding feature vector; S3, the results obtained from each perspective. The feature vectors are concatenated to construct a joint feature matrix. in, Indicates the number of viewpoints; S4. For the joint feature matrix Cluster analysis was performed on the row vectors, with k-means clustering being the preferred method, to divide the subjects into groups. A representative functional organizational model.

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