CN110335682B - Real part and imaginary part combined complex fMRI data sparse representation method - Google Patents

Real part and imaginary part combined complex fMRI data sparse representation method 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

A real part and imaginary part combined complex fMRI data sparse representation method belongs to the field of biomedical signal processing. Dividing fMRI complex data into a real part and an imaginary part to generate real part and imaginary part combined data; separating the combined data by using a sparse representation algorithm to obtain a series of SM components; selecting an interested component index based on a correlation coefficient absolute value maximization principle according to a spatial reference network of the interested component, and performing polarity correction; finally, the SM component of the component of interest is output. Compared with the widely applied sparse representation method of the amplitude fMRI data, the method can extract more meaningful activated voxels. For example, for 16 tested task state complex fMRI data, 87% more activated voxels are extracted from the estimated task related components of the invention. The invention can effectively analyze complete fMRI data, obtain more comprehensive brain function information and has good application prospect in the aspects of brain function research and brain disease diagnosis.

Description

Real part and imaginary part combined complex fMRI data sparse representation method
Technical Field
The invention relates to the field of biomedical signal processing, in particular to a method for sparse representation of fMRI (functional magnetic resonance imaging) data, wherein real parts and imaginary parts of the fMRI data are combined.
Background
fMRI is a non-invasive medical imaging technique that is very valuable in both scientific research and clinical fields. Because the brain is still perceived to a limited extent by people at present, a series of Spatial Map (SM) components and time series components thereof can be extracted from fMRI data by using a data-driven method such as sparse representation without any prior knowledge. The components belong to source signals and have important values in brain cognition and brain disease related research, such as brain function activation region positioning, the detection of brain function connection modes related to diseases by serving as nodes connected by a function network, the discrimination of healthy people from patients by serving as biomarkers (biomarker), and the like.
Sparse representation has yielded compelling success in amplitude fMRI data analysis, especially in brain network extraction and brain functional connectivity studies. The sparse representation method can extract more brain activation regions and interested components than an Independent Component Analysis (ICA) method, and is superior to the ICA method and the non-negative matrix decomposition method in classification accuracy and stability. However, complete fMRI data is complex, including both magnitude and phase components. Although the phase data is larger than the amplitude in terms of noise, the phase data contains unique brain function information with definite physiological significance which is not possessed by the amplitude data, and has fingerprint characteristics. Current studies indicate that more complete brain activation regions can be extracted from the complete fMRI complex data. Therefore, it is significant to adopt a sparse representation method to mine brain function information from complex fMRI data.
Disclosure of Invention
The invention aims to realize a sparse representation method of complete complex fMRI data by jointly analyzing real part data and imaginary part data of complex fMRI, and more activated voxels are extracted than amplitude fMRI data.
Firstly, dividing fMRI complex data into a real part and an imaginary part to generate real part and imaginary part combined data; then, separating the joint data by using a sparse representation algorithm, and estimating to obtain a series of SM components; then, according to a spatial reference network of the interested component, based on the principle of maximizing the absolute value of the correlation coefficient with the SM component, selecting the index of the interested component from all the components obtained by sparse representation estimation, and performing polarity correction; finally, the SM component of the component of interest is output. The method comprises the following concrete steps:
the first step is as follows: inputting single-subject complex fMRI data
Figure GDA0003842415890000021
Where T represents the number of time points and V represents the number of unidimensional intrabrain voxels.
The second step: real part and imaginary part joint data are generated. Dividing X into real part and imaginary part, and recording data in real part into
Figure GDA0003842415890000022
Imaginary part data of
Figure GDA0003842415890000023
The real-imaginary joint data is generated as follows:
Figure GDA0003842415890000024
the third step: and (5) sparse decomposition. Suppose real part data X of X re And imaginary data X im Sharing the coefficient matrix α, the model for sparse decomposition of Y is as follows:
Figure GDA0003842415890000025
wherein,
Figure GDA0003842415890000026
and
Figure GDA0003842415890000027
corresponding to the real part dictionary and the imaginary part dictionary respectively,
Figure GDA0003842415890000028
is an overcomplete dictionary matrix, i.e. 2T < M < V, coefficient matrix
Figure GDA0003842415890000029
Column vector α of i Is sparse, i =1, …, V.
According to the sparse decomposition model (2), the K-SVD algorithm (Aharon M, elad M, bruckstein A, K-SVD: an algorithm for designing over complex dictionary for sparse representation. IEEE Transactions on Signal Processing,4311-4322, 2006) is used to alternately solve D and alpha until the maximum number of iterations is reached. The objective functions of D and alpha are solved alternately as follows:
(1) Knowing D, the sparse coefficient α is solved, and the objective function is as follows:
Figure GDA00038424158900000210
where δ is a normal number, characterizing α i OfDegree, i =1, …, V. y is i Is the column vector of Y. In the K-SVD algorithm, the sparse coefficient α solution applies the OMP algorithm (Pati YC, rezaifiar R, krishnaprasad PS, original matching pursuit: correct function adaptation with applications to horizontal resolution. Proceedings of 27th Orthogonal Conference signals, systems and computers,40-44,1993).
(2) Knowing the sparse coefficient α, learning dictionary D, the objective function is as follows:
Figure GDA0003842415890000031
after the sparse representation algorithm converges, the row vector of alpha
Figure GDA0003842415890000032
I.e. SM components, j =1, …, M, i.e. there are M SM components.
The fourth step: and (4) selecting the interested component. Spatial reference network alpha with components of interest ref Based on the principle of maximizing absolute value of correlation coefficient, from M SM components
Figure GDA0003842415890000033
The index of the selected component of interest in (j =1, …, M) is as follows:
Figure GDA0003842415890000034
where "corr" represents a correlation coefficient.
The fifth step: and (5) polarity correction. SM component to component of interest
Figure GDA0003842415890000035
The polarity correction was performed as follows:
Figure GDA0003842415890000036
wherein "sign" indicates taking a sign.
And a sixth step: outputting SM component of the component of interest
Figure GDA0003842415890000037
Compared with the widely applied sparse representation method of the amplitude fMRI data, the method has the advantages that the complete fMRI data is utilized by combining the real part and imaginary part data, and more meaningful activated voxels can be extracted. For example, for complex fMRI data acquired under a task of tapping a finger on 16 subjects, with the number of active voxels of an acquired SM component and a correlation coefficient with a spatial reference (shown as (1) in fig. 2) of the component of interest) obtained by sparse decomposition as performance indexes, compared with an SM component (shown as (3) in fig. 2) obtained by a sparse representation method of amplitude fMRI data, the correlation coefficient of an estimated task-related (task) component (shown as (a) in fig. 2) of the invention is improved by 16%, 87% more active voxels are extracted, and the active voxels are mainly increased in a main motion region and an auxiliary motion region; the estimated default mode network DMN (default network) component (as shown in fig. 2 (B)) has similar correlation coefficient, but 28% more active voxels are extracted, mainly increasing in the hard-to-extract DMN sub-region ACC (adaptive threshold). Therefore, the invention can effectively analyze complete complex fMRI data, obtains more comprehensive brain function information than amplitude fMRI data sparse decomposition, and has good application prospect in brain function research and brain disease diagnosis.
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FIG. 1 is a flow chart of an implementation of the present invention.
FIG. 2 is a graph comparing SM components obtained by the method of the present invention with an amplitude fMRI sparse representation.
Detailed Description
An embodiment of the present invention is described in detail below with reference to the accompanying drawings.
Existing K =16 complex fMRI data acquired under a tapping finger task is tried. There were T =165 scans in the time dimension, each scan yielded 53 × 63 × 46 whole brain data, with a voxel count V =59610 in the brain. And (3) carrying out multi-test (16 test) analysis by adopting the single-test fMRI sparse representation method of the patent, and further obtaining a group average SM component. The method comprises the following concrete steps:
the first step is as follows: let k =1.
The second step is that: inputting tested k complex fMRI data
Figure GDA0003842415890000041
The third step: real part and imaginary part joint data are generated. Mixing X k Is divided into a real part and an imaginary part, wherein the real part data is
Figure GDA0003842415890000042
Imaginary data of
Figure GDA0003842415890000043
Substituting the formula (1) to generate the real part and imaginary part joint data of the tested k
Figure GDA0003842415890000044
The fourth step: for Y k And carrying out sparse decomposition. Let δ =20 and dictionary size M =400. Alternately solving overcomplete dictionary matrix by adopting K-SVD algorithm
Figure GDA0003842415890000045
Sum coefficient matrix
Figure GDA0003842415890000046
Until a maximum number of iterations 400 is reached. From alpha k Row vector of
Figure GDA0003842415890000047
And (3) extracting SM components, j =1, …,400, namely 400 SM components in total.
The fifth step: and (4) selecting the interested component. Assuming the task component and DMN component are two signals of interest, a 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 compound-value fMRI data. Journal of Neuroscience Methods,49-63,2017) is used for notationIs composed of
Figure GDA0003842415890000051
And
Figure GDA0003842415890000052
based on equation (5), the indexes of two interesting components are respectively obtained from 400 components, for example, when k =1, the task component j * =107,dmn component j * =178, and further, an SM component of the task component is obtained
Figure GDA0003842415890000053
And SM component of DMN component
Figure GDA0003842415890000054
And a sixth step: and (5) polarity correction. Substituting equation (6) for the SM component of the two components of interest
Figure GDA0003842415890000055
And
Figure GDA0003842415890000056
and carrying out polarity correction.
The seventh step: repeating the fourth step to the sixth step R =10 times, obtaining the best run by the method in "Kuang LD, lin QH, gong XF, cong F, sui J, calhoun VD. Model order efficiencies on ICA of stopping-state complex-value fMRI data: application to schizoopening. Journal of Neuroscience Methods 304,24-38,2018", and finally extracting SM component of two interested components
Figure GDA0003842415890000057
And
Figure GDA0003842415890000058
eighth step: k = k +1, if k >16, jumping to the eighth step; otherwise, repeating the second step to the eighth step.
The ninth step: outputting a group average SM component of the two components of interest
Figure GDA0003842415890000059
And
Figure GDA00038424158900000510
(as shown in (A) and (B) of FIG. 2).

Claims (1)

1. A real part and imaginary part combined complex fMRI data sparse representation method is characterized in that firstly, fMRI complex data are divided into a real part and an imaginary part to generate real part and imaginary part combined data; then, separating the joint data by using a sparse representation algorithm, and estimating to obtain a series of SM components; then, according to a spatial reference network of the interested component, based on the principle of maximizing the absolute value of the correlation coefficient with the SM component, selecting the index of the interested component from all the components obtained by sparse representation estimation, and performing polarity correction; finally, outputting the SM component of the interested component; the method specifically comprises the following steps:
the first step is as follows: inputting single-subject complex fMRI data
Figure FDA0002093068530000011
Wherein T represents the number of time points and V represents the number of one-dimensional endosomes;
the second step is that: generating real part and imaginary part joint data; dividing X into real part and imaginary part, and recording data in real part into
Figure FDA0002093068530000012
Imaginary data of
Figure FDA0002093068530000013
The real-imaginary joint data is generated as follows:
Figure FDA0002093068530000014
the third step: carrying out sparse decomposition; suppose real part data X of X re And imaginary data X im Sharing the coefficient matrix alpha, then performing sparse division on YThe solution is modeled as follows:
Figure FDA0002093068530000015
wherein,
Figure FDA0002093068530000016
and
Figure FDA0002093068530000017
corresponding to the real part dictionary and the imaginary part dictionary respectively,
Figure FDA0002093068530000018
for overcomplete dictionary matrices, i.e. 2T < M < V, coefficient matrices
Figure FDA0002093068530000019
Column vector α of i Is sparse, i =1, …, V;
according to the sparse decomposition model (2), alternately solving D and alpha by adopting a K-SVD algorithm until the maximum iteration number is reached; the objective functions of D and alpha are solved alternately as follows:
(1) Knowing D, the sparse coefficient α is solved, with the objective function as follows:
Figure FDA00020930685300000110
where δ is a normal number, characterizing α i I =1, …, V; y is i Is the column vector of Y; in the K-SVD algorithm, the OMP algorithm is applied to the sparse coefficient alpha solution;
(2) Knowing the sparse coefficient α, learning dictionary D, the objective function is as follows:
Figure FDA0002093068530000021
after the sparse representation algorithm converges, the row vector of alpha
Figure FDA0002093068530000022
I.e. SM component, j =1, …, M, i.e. there are M SM components;
the fourth step: selecting interested components; spatial reference network alpha with components of interest ref Based on the principle of maximizing absolute value of correlation coefficient, from M SM components
Figure FDA0002093068530000023
The index of the selected interesting components is as follows:
Figure FDA0002093068530000024
wherein "corr" represents a correlation coefficient;
the fifth step: correcting the polarity; SM component to component of interest
Figure FDA0002093068530000025
The polarity correction was performed as follows:
Figure FDA0002093068530000026
wherein, sign represents taking a sign;
and a sixth step: outputting SM component of the component of interest
Figure FDA0002093068530000027
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CN105342615A (en) * 2015-12-01 2016-02-24 中国科学院苏州生物医学工程技术研究所 Brain active region detection method and device
CN108903942A (en) * 2018-07-09 2018-11-30 大连理工大学 A method of utilizing plural number fMRI spatial source phase identification spatial diversity
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US20050085705A1 (en) * 2003-10-21 2005-04-21 Rao Stephen M. fMRI system for use in detecting neural abnormalities associated with CNS disorders and assessing the staging of such disorders
CN105342615A (en) * 2015-12-01 2016-02-24 中国科学院苏州生物医学工程技术研究所 Brain active region detection method and device
CN108903942A (en) * 2018-07-09 2018-11-30 大连理工大学 A method of utilizing plural number fMRI spatial source phase identification spatial diversity
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