Blind Source Separation Methods For Group Analyses Of Multi-Subject Complex-Valued FMRI Data

Functional magnetic resonance imaging(fMRI),with high spatial resolution and non-intrusion,is a vital medical imaging technology and has been widely applied to brain science.The group analysis of multi-subject fMRI data can capture inter-subject common or variability information,and can provide group-level features for brain function study and brain disease diagnosis.Blind sourse separation(BSS),a data-driven technique,can estimate source signals and their mixing process with the only knowledge of observed signals.Thus,it is suitable for analyzing fMRI data with limited brain cognition.There are three popular BSS methods-independent component analysis(ICA),independent vector analysis(IVA)and tensor decomposition,which provide complementary spatial map and time course information representing average,specific and shared features from multiple subjects,respectively.However,the fMRI data are initially acquired as complex-valued images,multi-subject fMRI data exhibit higher spatial and temporal inter-subject variability,and the model order effect on multi-subject complex-valued fMRI data is unknown.These problems limit the performance of existing methods.To solve these problems,this dissertation contributes in the following three aspects:(1)The challenges of IVA applied to complex-valued fMRI data include the large variability of the source component vector distribution,the extremely noisy nature and the non-circularity property.To address these challenges,a novel complex-valued fixed-point IVA algorithm based on multivariate generalized Gaussian distribution was proposed.First,a nonlinear function based on multivariate generalized Gaussian distribution was constructed,and its shape parameter was updated by maximum likelihood estimation to adaptively match varying source component vector distributions.Second,to achieve the de-noising goal,the nonlinear function was employed in the dominant subspace of source component vector.Lastly,the pseudo covariance matrix of fMRI data was incorporated into the update of unmixing matrix to emphasize the noncircularity of complex-valued fMRI data.Results from simulated and actual fMRI data showed that the proposed approach exhibited significant improvements over existing complex-valued IVA algorithms,especially for fMRI data with higher noise levels and larger spatial and temporal changes.Compared with magnitude-only analysis,the proposed algorithm detected more interesting voxels(three times for both task-related and default mode network components).An adaptive phase range detection method was proposed to solve the problem of fixed phase range of an existing post-processing phase denoising strategy.This method was based on the prior spatial information and maximal correlation,was suitable for the post-processing phase denoising of both task-related and resting-state fMRI data,and verified the correctness of fixed phase range ±π/4 for denoising.(2)As existing tensor decomposition can not simultaneously solve the inter-subject spatiotemporal variability,two new algorithms were proposed.On one hand,an improved method by combing shift-invariant canonical polyadic decomposition(CPD)and ICA was proposed.Shift-invariant CPD and ICA were separately used to incorporate inter-subject temporal variability and spatial variability.ICA was firstly performed on multi-subject magnitude-only fMRI data to obtain the aggregating mixing matrix,and then shift-invariant rank-one approximation was conducted on aggregating mixing matrix to estimate shared TCs with subject-dependent delays and intensities.Shared SMs were finally estimated by a least-squares fit using reconstructed aggregating mixing matrix.On the other hand,a novel complex-valued shift-invariant CPD algorithm with source phase maps sparsity was proposed.Real-valued shift-invariant CPD was extended into the complex-valued domain to deal with the inter-subject temporal variability.According to the small phase property of complex-valued spatial components,a smoothed ’0 norm function was utilized to add sparsity constraints on the voxels of spatial maps with large phase values,and the inter-subject spatial variability was thus relaxed.The simulated and actual fMRI data experiments both showed that these two proposed methods had better separation performance than existing methods,in particular for cases with larger time delays and higher noise levels.Compared with magnitude-only method,the complex-valued method detected more about two times task-related voxels.(3)This dissertation investigated model order effects on group analysis of complex-valued fMRI data and explores underlying causes.First of all,an improved best run selection method was proposed by combining subject averaging and one-sample t-test.Results from actual fMRI data showed that the proposed method was better than existing methods at all model orders.Secondly,based on the proposed best run selection method,model order effect on group analysis of complex-valued fMRI data was investigated.Results show that complex-valued intact networks existed from lower model order to higher model order.This is distinguished from component splitting of magnitude-only networks.In addition,the cause of complex-valued intact networks was explored,the model order effect on phase fMRI analysis and eigenvalues of phase data were analyzed.Results indicated that the incorporation of phase data appears to play a complementary role in preserving integrity of brain networks.Finally,when compared with magnitude-only analysis,the intact DMN components obtained in complex-valued analysis at higher model orders exhibited highly significant subject-level differences between healthy controls and patients with schizophrenia,indicating the potential of intact components at higher model orders as biomarkers for schizophrenia.