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

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

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CN110335682B
CN110335682B CN201910509773.5A CN201910509773A CN110335682B CN 110335682 B CN110335682 B CN 110335682B CN 201910509773 A CN201910509773 A CN 201910509773A CN 110335682 B CN110335682 B CN 110335682B
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林秋华
张超颖
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Abstract

一种实部虚部联合的复数fMRI数据稀疏表示方法,属于生物医学信号处理领域。将fMRI复数数据分成实部和虚部两部分,生成实部虚部联合数据;利用稀疏表示算法分离联合数据,得到一系列SM成分;根据感兴趣成分的空间参考网络,基于相关系数绝对值最大化原则选取感兴趣成分索引,并做极性校正;最后,输出感兴趣成分的SM成分。与广泛应用的幅值fMRI数据稀疏表示方法相比,本发明能提取更多有意义的激活体素。例如,针对16被试任务态复数fMRI数据,本发明所估计的任务相关成分多提取了87%的激活体素。本发明能够有效分析完备的fMRI数据,获得更加全面的脑功能信息,在脑功能研究和脑疾病诊断方面有着良好的应用前景。

Figure 201910509773

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.

Figure 201910509773

Description

一种实部虚部联合的复数fMRI数据稀疏表示方法A Sparse Representation Method for Complex fMRI Data Based on the Combination of Real and Imaginary Parts

技术领域technical field

本发明涉及生物医学信号处理领域,涉及一种实部虚部联合的复数功能磁共振成像(functional magnetic resonance imaging,fMRI)数据稀疏表示方法。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.

背景技术Background technique

fMRI是一种在科研和临床领域都非常有价值的非侵入式医学影像技术。因为目前人们对大脑的认知程度仍然有限,利用数据驱动的方法如稀疏表示,不需要任何先验知识,就可以从fMRI数据中提取一系列空间激活脑区(spatial map,SM)成分及其时间序列成分。这些成分属于源信号,在脑认知和脑疾病相关的研究中有着重要的价值,如用于脑功能激活区域定位,作为功能网络连接的节点来考察与疾病相关的脑功能连接模式,以及作为生物标志物(biomarker)区分健康人与病人等。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.

稀疏表示已经在幅值fMRI数据分析中获得了引人注目的成果,尤其是在脑网络的提取和脑功能连接研究中。稀疏表示方法能比独立成分分析(independent componentanalysis,ICA)方法提取到更多的脑激活区和感兴趣成分,在分类精度和稳定性上优于ICA方法和非负矩阵分解方法。然而,完备的fMRI数据是复数的,包括幅值和相位两部分。相位数据虽然在噪声上大于幅值,但含有幅值数据所不具有的独特且生理意义明确的脑功能信息,同时具有指纹特性。现有研究表明,从完备的fMRI复数数据中可以提取到更为完整的脑激活区域。因此,采用稀疏表示方法从复数fMRI数据中挖掘脑功能信息具有重要意义。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.

发明内容Contents of the invention

本发明的目的在于,通过联合分析复数fMRI的实部和虚部数据,实现一种完备复数fMRI数据的稀疏表示方法,比幅值fMRI数据提取到更多的激活体素。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.

本发明的技术方案是,首先,将fMRI复数数据分成实部和虚部两部分,生成实部虚部联合数据;接着,利用稀疏表示算法分离联合数据,估计得到一系列SM成分;然后,根据感兴趣成分的空间参考网络,基于与SM成分相关系数绝对值最大化原则,从稀疏表示估计得到的所有成分中选取感兴趣成分索引,并做极性校正;最后,输出感兴趣成分的SM成分。具体实现步骤如下: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:

第一步:输入单被试复数fMRI数据

Figure GDA0003842415890000021
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
Figure GDA0003842415890000021
Where T represents the number of time points, and V represents the number of one-dimensional voxels in the brain.

第二步:生成实部虚部联合数据。将X分成实部和虚部两部分,记实部数据为

Figure GDA0003842415890000022
虚部数据为
Figure GDA0003842415890000023
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
Figure GDA0003842415890000022
The imaginary part data is
Figure GDA0003842415890000023
Generate the joint data of real part and imaginary part as follows:

Figure GDA0003842415890000024
Figure GDA0003842415890000024

第三步:稀疏分解。假设X的实部数据Xre和虚部数据Xim共享系数矩阵α,则对Y进行稀疏分解的模型如下: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:

Figure GDA0003842415890000025
Figure GDA0003842415890000025

其中,

Figure GDA0003842415890000026
Figure GDA0003842415890000027
分别对应实部字典和虚部字典,
Figure GDA0003842415890000028
为过完备字典矩阵,即2T<M<<V,系数矩阵
Figure GDA0003842415890000029
的列矢量αi是稀疏的,i=1,…,V。in,
Figure GDA0003842415890000026
and
Figure GDA0003842415890000027
Corresponding to the real part dictionary and the imaginary part dictionary respectively,
Figure GDA0003842415890000028
It is an over-complete dictionary matrix, that is, 2T<M<<V, and the coefficient matrix
Figure GDA0003842415890000029
The column vector α i of is sparse, i=1,...,V.

根据稀疏分解模型(2),采用K-SVD算法(Aharon M,Elad M,Bruckstein A,K-SVD:an algorithm for designing overcomplete dictionaries for sparserepresentation.IEEE Transactions on Signal Processing,4311-4322,2006)交替求解D和α,直到达到最大迭代次数。其中,交替求解D和α的目标函数分别如下: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)已知D,求解稀疏系数α,目标函数如下:(1) Knowing D, solve the sparse coefficient α, the objective function is as follows:

Figure GDA00038424158900000210
Figure GDA00038424158900000210

其中,δ是一个正常数,表征了αi的稀疏程度,i=1,…,V。yi是Y的列矢量。在K-SVD算法中,稀疏系数α求解应用了OMP算法(Pati YC,Rezaiifar R,Krishnaprasad PS,Orthogonal matching pursuit:recursive function approximation withapplications to wavelet decomposition.Proceedings of 27th Asilomar Conferenceon Signals,Systems and Computers,40-44,1993)。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)已知稀疏系数α,学习字典D,目标函数如下:(2) The sparse coefficient α is known, and the dictionary D is learned. The objective function is as follows:

Figure GDA0003842415890000031
Figure GDA0003842415890000031

稀疏表示算法收敛后,α的行矢量

Figure GDA0003842415890000032
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
Figure GDA0003842415890000032
That is, they are SM components, j=1,...,M, that is, there are M SM components in total.

第四步:感兴趣成分选取。利用感兴趣成分的空间参考网络αref,基于相关系数绝对值最大化原则,从M个SM成分

Figure GDA0003842415890000033
(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
Figure GDA0003842415890000033
The index of selecting the components of interest in (j=1,...,M) is as follows:

Figure GDA0003842415890000034
Figure GDA0003842415890000034

其中,“corr”表示相关系数。where "corr" represents the correlation coefficient.

第五步:极性校正。对感兴趣成分的SM成分

Figure GDA0003842415890000035
进行极性校正如下:Step 5: Polarity correction. SM component to the component of interest
Figure GDA0003842415890000035
Perform polarity correction as follows:

Figure GDA0003842415890000036
Figure GDA0003842415890000036

其中,“sign”表示取符号。Among them, "sign" means to take the sign.

第六步:输出感兴趣成分的SM成分

Figure GDA0003842415890000037
Step 6: Output the SM component of the component of interest
Figure GDA0003842415890000037

本发明所达到的效果和益处是,与广泛应用的幅值fMRI数据稀疏表示方法相比,通过联合实部虚部数据对完备的fMRI数据加以利用,能提取到更多有意义的激活体素。例如,针对16被试敲击手指任务下采集的复数fMRI数据,以稀疏分解所获取SM成分的激活体素数,以及与感兴趣成分空间参考(如附图2中的(1)所示)的相关系数为性能指标,较之幅值fMRI数据稀疏表示方法得到的SM成分(如附图2中的(3)所示),本发明所估计任务相关(task)成分(如附图2中的(A)所示)的相关系数提高了16%,多提取到了87%的激活体素,主要增加在主运动区和辅助运动区;所估计默认网络DMN(default mode network)成分(如附图2中的(B)所示)的相关系数相近,但多提取到了28%的激活体素,主要增加在难于提取的DMN子区域ACC(anterior cingulate cortex)。因此,本发明能够有效分析完备的复数fMRI数据,比幅值fMRI数据稀疏分解获得了更加全面的脑功能信息,在脑功能研究和脑疾病诊断方面有着良好的应用前景。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.

附图说明Description of drawings

图1是本发明实现流程图。Fig. 1 is the realization flow chart of the present invention.

图2是本发明方法与幅值fMRI稀疏表示方法得到的SM成分对比图。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.

具体实施方式Detailed ways

下面结合技术方案,详细叙述本发明的一个具体实施例。A specific embodiment of the present invention will be described in detail below in conjunction with the technical solution.

现有K=16被试在敲击手指任务下采集的复数fMRI数据。时间维度上有T=165次扫描,每次扫描都获得了53×63×46的全脑数据,脑内体素数V=59610。采用本专利的单被试fMRI稀疏表示方法进行多被试(16被试)分析,进而得到组平均SM成分。具体实现步骤如下: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:

第一步:令k=1。Step 1: Let k=1.

第二步:输入被试k复数fMRI数据

Figure GDA0003842415890000041
Step 2: Input subject k complex fMRI data
Figure GDA0003842415890000041

第三步:生成实部虚部联合数据。将Xk分成实部和虚部两部分,其中,实部数据为

Figure GDA0003842415890000042
虚部数据为
Figure GDA0003842415890000043
代入公式(1),生成被试k的实部虚部联合数据
Figure GDA0003842415890000044
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
Figure GDA0003842415890000042
The imaginary part data is
Figure GDA0003842415890000043
Substitute into formula (1) to generate the joint data of real and imaginary parts of subject k
Figure GDA0003842415890000044

第四步:对Yk进行稀疏分解。设δ=20,字典大小M=400。采用K-SVD算法交替求解过完备字典矩阵

Figure GDA0003842415890000045
和系数矩阵
Figure GDA0003842415890000046
直到达到最大迭代次数400。从αk的行矢量
Figure GDA0003842415890000047
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
Figure GDA0003842415890000045
and coefficient matrix
Figure GDA0003842415890000046
until the maximum number of iterations 400 is reached. The row vector from α k
Figure GDA0003842415890000047
Extract SM components from , j=1,...,400, that is, there are 400 SM components in total.

第五步:感兴趣成分选取。假设task成分和DMN成分为两个感兴趣信号,利用这两个感兴趣成分的空间参考网络(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),记为

Figure GDA0003842415890000051
Figure GDA0003842415890000052
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
Figure GDA0003842415890000053
以及DMN成分的SM成分
Figure GDA0003842415890000054
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
Figure GDA0003842415890000051
and
Figure GDA0003842415890000052
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
Figure GDA0003842415890000053
and the SM component of the DMN component
Figure GDA0003842415890000054

第六步:极性校正。代入公式(6),对两个感兴趣成分的SM成分

Figure GDA0003842415890000055
Figure GDA0003842415890000056
进行极性校正。Step 6: Polarity correction. Substituting into formula (6), the SM components of the two components of interest
Figure GDA0003842415890000055
and
Figure GDA0003842415890000056
Perform polarity correction.

第七步:重复第四步到第六步R=10次,采用“Kuang LD,Lin QH,Gong XF,Cong F,Sui J,Calhoun VD.Model order effects on ICA of resting-state complex-valuedfMRI data:application to schizophrenia.Journal of Neuroscience Methods 304,24–38,2018”中的方法获取best run,最终提取两个感兴趣成分的SM成分

Figure GDA0003842415890000057
Figure GDA0003842415890000058
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
Figure GDA0003842415890000057
and
Figure GDA0003842415890000058

第八步:k=k+1,若k>16,跳至第八步;否则,重复第二步到第八步。Step 8: k=k+1, if k>16, skip to step 8; otherwise, repeat steps 2 to 8.

第九步:输出两个感兴趣成分的组平均SM成分

Figure GDA0003842415890000059
Figure GDA00038424158900000510
(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
Figure GDA0003842415890000059
and
Figure GDA00038424158900000510
(As shown in (A) and (B) in accompanying drawing 2).

Claims (1)

1.一种实部虚部联合的复数fMRI数据稀疏表示方法,其特征在于,首先,将fMRI复数数据分成实部和虚部两部分,生成实部虚部联合数据;接着,利用稀疏表示算法分离联合数据,估计得到一系列SM成分;然后,根据感兴趣成分的空间参考网络,基于与SM成分相关系数绝对值最大化原则,从稀疏表示估计得到的所有成分中选取感兴趣成分索引,并做极性校正;最后,输出感兴趣成分的SM成分;具体包括以下步骤: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: 第一步:输入单被试复数fMRI数据
Figure FDA0002093068530000011
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
Figure FDA0002093068530000011
Where T represents the number of time points, and V represents the number of one-dimensional voxels in the brain;
第二步:生成实部虚部联合数据;将X分成实部和虚部两部分,记实部数据为
Figure FDA0002093068530000012
虚部数据为
Figure FDA0002093068530000013
生成实部虚部联合数据如下:
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
Figure FDA0002093068530000012
The imaginary part data is
Figure FDA0002093068530000013
Generate the joint data of real part and imaginary part as follows:
Figure FDA0002093068530000014
Figure FDA0002093068530000014
第三步:稀疏分解;假设X的实部数据Xre和虚部数据Xim共享系数矩阵α,则对Y进行稀疏分解的模型如下: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:
Figure FDA0002093068530000015
Figure FDA0002093068530000015
其中,
Figure FDA0002093068530000016
Figure FDA0002093068530000017
分别对应实部字典和虚部字典,
Figure FDA0002093068530000018
为过完备字典矩阵,即2T<M<<V,系数矩阵
Figure FDA0002093068530000019
的列矢量αi是稀疏的,i=1,…,V;
in,
Figure FDA0002093068530000016
and
Figure FDA0002093068530000017
Corresponding to the real part dictionary and the imaginary part dictionary respectively,
Figure FDA0002093068530000018
It is an over-complete dictionary matrix, that is, 2T<M<<V, and the coefficient matrix
Figure FDA0002093068530000019
The column vector α i of is sparse, i=1,...,V;
根据稀疏分解模型(2),采用K-SVD算法交替求解D和α,直到达到最大迭代次数;其中,交替求解D和α的目标函数分别如下: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)已知D,求解稀疏系数α,目标函数如下:(1) Knowing D, solve the sparse coefficient α, the objective function is as follows:
Figure FDA00020930685300000110
Figure FDA00020930685300000110
其中,δ是一个正常数,表征了αi的稀疏程度,i=1,…,V;yi是Y的列矢量;在K-SVD算法中,稀疏系数α求解应用了OMP算法;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)已知稀疏系数α,学习字典D,目标函数如下:(2) The sparse coefficient α is known, and the dictionary D is learned. The objective function is as follows:
Figure FDA0002093068530000021
Figure FDA0002093068530000021
稀疏表示算法收敛后,α的行矢量
Figure FDA0002093068530000022
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
Figure FDA0002093068530000022
It is the SM component, j=1,...,M, that is, there are M SM components in total;
第四步:感兴趣成分选取;利用感兴趣成分的空间参考网络αref,基于相关系数绝对值最大化原则,从M个SM成分
Figure FDA0002093068530000023
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 components of interest, based on the principle of maximizing the absolute value of the correlation coefficient, from M SM components
Figure FDA0002093068530000023
The index of selecting the components of interest in is as follows:
Figure FDA0002093068530000024
Figure FDA0002093068530000024
其中,“corr”表示相关系数;Among them, "corr" represents the correlation coefficient; 第五步:极性校正;对感兴趣成分的SM成分
Figure FDA0002093068530000025
进行极性校正如下:
Step 5: Polarity Correction; SM Components for Components of Interest
Figure FDA0002093068530000025
Perform polarity correction as follows:
Figure FDA0002093068530000026
Figure FDA0002093068530000026
其中,“sign”表示取符号;Among them, "sign" means to take the sign; 第六步:输出感兴趣成分的SM成分
Figure FDA0002093068530000027
Step 6: Output the SM component of the component of interest
Figure FDA0002093068530000027
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