CN110335682B - A Sparse Representation Method for Complex fMRI Data Based on the Combination of Real and Imaginary Parts - Google Patents

Abstract

The invention discloses a complex fMRI data sparse representation method combining real and imaginary parts, which belongs to the field of biomedical signal processing. Divide fMRI complex data into two parts, real part and imaginary part, to generate joint data of real part and imaginary part; use sparse representation algorithm to separate joint data, and obtain a series of SM components; according to the spatial reference network of the components of interest, the absolute value of the correlation coefficient is the largest The index of the component of interest is selected according to the principle of optimization, and polarity correction is performed; finally, the SM component of the component of interest is output. Compared with the widely used sparse representation method of amplitude fMRI data, the present invention can extract more meaningful activation voxels. For example, for complex fMRI data of 16 subjects' task states, the task-related components estimated by the present invention extracted 87% more activated voxels. The invention can effectively analyze complete fMRI data, obtain more comprehensive brain function information, and has good application prospects in brain function research and brain disease diagnosis.

Description

A Sparse Representation Method for Complex fMRI Data Based on the Combination of Real and Imaginary Parts

technical field

The invention relates to the field of biomedical signal processing, and relates to a complex functional magnetic resonance imaging (functional magnetic resonance imaging, fMRI) data sparse representation method with a combination of real and imaginary parts.

Background technique

fMRI is a non-invasive medical imaging technique that is very valuable in both scientific research and clinical fields. Because people's understanding of the brain is still limited, using data-driven methods such as sparse representation, a series of spatial map (spatial map, SM) components and their components can be extracted from fMRI data without any prior knowledge. time series components. These components belong to the source signal, which has important value in the research of brain cognition and brain diseases, such as for the localization of brain function activation area, as a node of functional network connection to investigate the brain function connection mode related to disease, and as a Biomarkers (biomarkers) distinguish healthy people from sick people.

Sparse representations have achieved compelling results in the analysis of magnitude fMRI data, especially in the extraction of brain networks and the study of brain functional connectivity. The sparse representation method can extract more brain activation areas and components of interest than the independent component analysis (ICA) method, and is superior to the ICA method and the non-negative matrix factorization method in terms of classification accuracy and stability. However, complete fMRI data are complex, including both magnitude and phase. Although the phase data is larger than the amplitude in noise, it contains unique and physiologically meaningful brain function information that the amplitude data does not have, and it also has fingerprint characteristics. Existing studies have shown that more complete brain activation regions can be extracted from complete fMRI complex data. Therefore, it is of great significance to mine brain function information from complex fMRI data using sparse representation methods.

Contents of the invention

The purpose of the present invention is to realize a sparse representation method of complete complex fMRI data by jointly analyzing the real part and imaginary part data of complex fMRI data, and extract more activation voxels than amplitude fMRI data.

The technical scheme of the present invention is, firstly, divide fMRI complex number data into real part and imaginary part two parts, generate the joint data of real part and imaginary part; Then, utilize sparse representation algorithm to separate joint data, estimate and obtain a series of SM components; Then, according to The spatial reference network of the component of interest, based on the principle of maximizing the absolute value of the correlation coefficient with the SM component, selects the index of the component of interest from all the components estimated by the sparse representation, and performs polarity correction; finally, the SM component of the component of interest is output . The specific implementation steps are as follows:

其中T表示时间点数，V表示一维化的脑内体素数。Step 1: Input single-subject complex fMRI data

Where T represents the number of time points, and V represents the number of one-dimensional voxels in the brain.

虚部数据为

生成实部虚部联合数据如下：Step 2: Generate joint data of real part and imaginary part. Divide X into two parts, the real part and the imaginary part, and record the data of the real part as

The imaginary part data is

Generate the joint data of real part and imaginary part as follows:

The third step: sparse decomposition. Assuming that the real part data X _re and the imaginary part data X _{im of X} share the coefficient matrix α, the model for sparse decomposition of Y is as follows:

和

分别对应实部字典和虚部字典，

为过完备字典矩阵，即2T＜M＜＜V，系数矩阵

的列矢量α_i是稀疏的，i＝1,…,V。in,

and

Corresponding to the real part dictionary and the imaginary part dictionary respectively,

It is an over-complete dictionary matrix, that is, 2T<M<<V, and the coefficient matrix

The column vector α _i of is sparse, i=1,...,V.

According to the sparse decomposition model (2), use the K-SVD algorithm (Aharon M, Elad M, Bruckstein A, K-SVD: an algorithm for designing overcomplete dictionaries for sparse representation. IEEE Transactions on Signal Processing, 4311-4322, 2006) to solve alternately D and α until the maximum number of iterations is reached. Among them, the objective functions of alternately solving D and α are as follows:

(1) Knowing D, solve the sparse coefficient α, the objective function is as follows:

Wherein, δ is a normal number, representing the degree of sparsity of α _i , i=1,...,V. y _i is the column vector of Y. In the K-SVD algorithm, the sparse coefficient α is solved using the OMP algorithm (Pati YC, Rezaiifar R, Krishnaprasad PS, Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition. Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, 40- 44, 1993).

(2) The sparse coefficient α is known, and the dictionary D is learned. The objective function is as follows:

即为SM成分，j＝1,…,M，即共有M个SM成分。After the sparse representation algorithm converges, the row vector of α

That is, they are SM components, j=1,...,M, that is, there are M SM components in total.

(j＝1,…,M)中选取感兴趣成分的索引如下：Step 4: Selection of components of interest. Using the spatial reference network α _ref of the component of interest, based on the principle of maximizing the absolute value of the correlation coefficient, from M SM components

The index of selecting the components of interest in (j=1,...,M) is as follows:

where "corr" represents the correlation coefficient.

进行极性校正如下：Step 5: Polarity correction. SM component to the component of interest

Perform polarity correction as follows:

Among them, "sign" means to take the sign.

Step 6: Output the SM component of the component of interest

The effect and benefit achieved by the present invention are that, compared with the widely used sparse representation method of amplitude fMRI data, more meaningful activation voxels can be extracted by utilizing the complete fMRI data by combining the real part and imaginary part data . For example, for the complex fMRI data collected under the finger tapping task of 16 subjects, the number of activation voxels of the acquired SM components is sparsely decomposed, and the spatial reference of the components of interest (as shown in (1) in Figure 2) The correlation coefficient is a performance indicator, compared with the SM component (as shown in (3) in the accompanying drawing 2) that the amplitude fMRI data sparse representation method obtains, the task-related (task) component (as shown in the accompanying drawing 2) estimated by the present invention (as shown in the accompanying drawing 2 The correlation coefficient (shown in (A)) has increased by 16%, and 87% more activated voxels have been extracted, mainly in the main motor area and auxiliary motor area; the estimated default network DMN (default mode network) component (as shown in the attached figure The correlation coefficient shown in (B) in 2) is similar, but 28% more activation voxels are extracted, mainly in the difficult-to-extract DMN sub-region ACC (anterior cingulate cortex). Therefore, the present invention can effectively analyze complete complex fMRI data, obtain more comprehensive brain function information than the sparse decomposition of amplitude fMRI data, and has good application prospects in brain function research and brain disease diagnosis.

Description of drawings

Fig. 1 is the realization flow chart of the present invention.

Fig. 2 is a comparison diagram of SM components obtained by the method of the present invention and the sparse representation method of amplitude fMRI.

Detailed ways

A specific embodiment of the present invention will be described in detail below in conjunction with the technical solution.

There are complex fMRI data collected by K=16 subjects under the finger tapping task. There are T=165 scans in the time dimension, each scan has obtained whole brain data of 53×63×46, and the number of voxels in the brain is V=59610. The single-subject fMRI sparse representation method of this patent is used for multi-subject (16 subjects) analysis, and then the group average SM component is obtained. The specific implementation steps are as follows:

Step 1: Let k=1.

Step 2: Input subject k complex fMRI data

虚部数据为

代入公式(1)，生成被试k的实部虚部联合数据

Step 3: Generate joint data of real part and imaginary part. Divide X ^k into two parts, the real part and the imaginary part, where the real part data is

The imaginary part data is

Substitute into formula (1) to generate the joint data of real and imaginary parts of subject k

和系数矩阵

直到达到最大迭代次数400。从α^k的行矢量

中提取SM成分，j＝1,…,400，即共有400个SM成分。Step 4: Sparsely decompose Y ^k . Let δ=20 and the dictionary size M=400. Using K-SVD Algorithm to Alternately Solve Overcomplete Dictionary Matrix

and coefficient matrix

until the maximum number of iterations 400 is reached. The row vector from α ^k

Extract SM components from , j=1,...,400, that is, there are 400 SM components in total.

和

基于公式(5)，从400个成分中分别求取两个感兴趣成分的索引，如k＝1时，task成分j^*＝107，DMN成分j^*＝178，进而获取task成分的SM成分

以及DMN成分的SM成分

Step 5: Selection of components of interest. Assuming that the task component and the DMN component are two signals of interest, using the spatial reference network of the two components of interest (Kuang LD, Lin QH, Gong XF, Cong FY, Calhoun VD, Adaptive independent vector analysis for multi-subject complex- valued fMRIdata.Journal of Neuroscience Methods, 49-63, 2017), recorded as

and

Based on the formula (5), the indexes of the two components of interest are obtained from the 400 components. For example, when k=1, the task component j ^* = 107, the DMN component j ^* = 178, and then obtain the SM component of the task component

and the SM component of the DMN component

与

进行极性校正。Step 6: Polarity correction. Substituting into formula (6), the SM components of the two components of interest

and

Perform polarity correction.

和

Step 7: Repeat steps 4 to 6 R=10 times, using "Kuang LD, Lin QH, Gong XF, Cong F, Sui J, Calhoun VD. Model order effects on ICA of resting-state complex-valued fMRI data :application to schizophrenia.Journal of Neuroscience Methods 304,24–38,2018" to obtain the best run, and finally extract the SM components of the two components of interest

and

Step 8: k=k+1, if k>16, skip to step 8; otherwise, repeat steps 2 to 8.

和

(如附图2中的(A)和(B)所示)。Step 9: Output the group-averaged SM components of the two components of interest

and

(As shown in (A) and (B) in accompanying drawing 2).

Claims (1)

1. A sparse representation method for complex fMRI data of a combination of real and imaginary parts, characterized in that, at first, the fMRI complex data is divided into two parts, real and imaginary, to generate the joint data of real and imaginary parts; then, use the sparse representation algorithm Separate the joint data and estimate a series of SM components; then, according to the spatial reference network of the components of interest, based on the principle of maximizing the absolute value of the correlation coefficient with the SM components, select the component of interest index from all the components estimated by the sparse representation, and Do polarity correction; finally, output the SM component of the component of interest; specifically include the following steps: Step 1: Input single-subject complex fMRI data

Where T represents the number of time points, and V represents the number of one-dimensional voxels in the brain; Step 2: Generate the joint data of the real part and the imaginary part; divide X into two parts, the real part and the imaginary part, and record the data of the real part as

The imaginary part data is

Generate the joint data of real part and imaginary part as follows:

The third step: sparse decomposition; assuming that the real part data X _re and the imaginary part data X _{im of} X share the coefficient matrix α, the model of sparse decomposition of Y is as follows:

in,

and

Corresponding to the real part dictionary and the imaginary part dictionary respectively,

It is an over-complete dictionary matrix, that is, 2T<M<<V, and the coefficient matrix

The column vector α _i of is sparse, i=1,...,V; According to the sparse decomposition model (2), the K-SVD algorithm is used to alternately solve D and α until the maximum number of iterations is reached; among them, the objective functions for alternately solving D and α are as follows: (1) Knowing D, solve the sparse coefficient α, the objective function is as follows:

Among them, δ is a normal number, representing the degree of sparsity of α _i , i=1,...,V; y _i is the column vector of Y; in the K-SVD algorithm, the sparse coefficient α is solved using the OMP algorithm; (2) The sparse coefficient α is known, and the dictionary D is learned. The objective function is as follows:

After the sparse representation algorithm converges, the row vector of α

It is the SM component, j=1,...,M, that is, there are M SM components in total; Step 4: Selection of components of interest; using the spatial reference network α _ref of the components of interest, based on the principle of maximizing the absolute value of the correlation coefficient, from M SM components

The index of selecting the components of interest in is as follows:

Among them, "corr" represents the correlation coefficient; Step 5: Polarity Correction; SM Components for Components of Interest

Perform polarity correction as follows:

Among them, "sign" means to take the sign; Step 6: Output the SM component of the component of interest

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