Joint Blind Source Separation With Multivariate Gaussian Model: Algorithms and Performance Analysis

Abstract

In this paper, we consider the joint blind source separation (JBSS) problem and introduce a number of algorithms to solve the JBSS problem using the independent vector analysis (IVA) framework. Source separation of multiple datasets simultaneously is possible when the sources within each and every dataset are independent of one another and each source is dependent on at most one source within each of the other datasets. In addition to source separation, the IVA framework solves an essential problem of JBSS, namely the identification of the dependent sources across the datasets. We propose to use the multivariate Gaussian source prior to achieve JBSS of sources that are linearly dependent across datasets. Analysis within the paper yields the local stability conditions, nonidentifiability conditions, and induced Cramér-Rao lower bound on the achievable interference to source ratio for IVA with multivariate Gaussian source priors. Additionally, by exploiting a novel nonorthogonal decoupling of the IVA cost function we introduce both Newton and quasi-Newton optimization algorithms for the general IVA framework.Index Terms-Canonical correlation analysis, independent component analysis, independent vector analysis, joint blind source separation, permutation problem, second-order statistics.

Adaptive independent vector analysis for multi-subject complex-valued fMRI data

“…The first IVA algorithm for analyzing real-valued fMRI data was presented by Lee et al (2007a) using a multivariate Laplace distribution (Lee et al, 2007a(Lee et al, , 2008a called IVA-L. With the development of IVA-G using multivariate Gaussian distribution (Anderson et al, 2012a), an IVA algorithm called IVA-GL was implemented by utilizing IVA-G to initialize the de-mixing matrix and IVA-L to perform the subsequent separation. IVA-GL emphasizes both second-order and higher-order statistics (Anderson et al, 2012a), and thus tends to be more efficient than IVA-L and IVA-G for fMRI analysis.…”

“…The first IVA algorithm for analyzing real-valued fMRI data was presented by Lee et al (2007a) using a multivariate Laplace distribution (Lee et al, 2007a(Lee et al, , 2008a called IVA-L. With the development of IVA-G using multivariate Gaussian distribution (Anderson et al, 2012a), an IVA algorithm called IVA-GL was implemented by utilizing IVA-G to initialize the de-mixing matrix and IVA-L to perform the subsequent separation. IVA-GL emphasizes both second-order and higher-order statistics (Anderson et al, 2012a), and thus tends to be more efficient than IVA-L and IVA-G for fMRI analysis. IVA-GL was first tested using simulated fMRI data (Dea et al, 2011;Michael et al, 2014), and then applied to real-valued fMRI data for diverse applications: e.g., producing discriminative features for quantifying motor recovery after stroke (Laney et al, 2015a(Laney et al, , 2015b; finding dynamic changes in spatial functional network connectivity in healthy individuals and schizophrenic patients (Ma et al, 2014;Calhoun and Adali, 2016); showing the spatial variation in fMRI brain networks (Gopal et al, 2015; fusing multimodal data ; and removing the gradient artifact in concurrently collected electroencephalogram (EEG) and fMRI data (Acharjee et al, 2015).…”

Physiological parameter monitoring of drivers based on video data and independent vector analysis

“…Therefore, in this paper, we propose using more advanced facial landmark and pose estimator [9] to find more accurate facial sub-regions, and provide grouped color intensity signals for different facial subregions and color channels. Accordingly, Independent Vector Analysis (IVA) [10] is performed to extract common sources from different groups of mixed signals.…”

“…To estimate the mixing matrices {A [ ] } =1 for all groups of singles, [10] proposed to minimize the mutual information among the estimated source component vectors, by assuming that each latent source within a group is both related to a single latent source within each of the other groups and independent of all the other sources within the groups.…”

Independent vector analysis using subband and subspace nonlinearity

“…In recent years, independent vector analysis (IVA) was developed as an extension of ICA from univariate to multivariate components [13][14][15][16][17][18], and sources in the IVA model are considered as vectors instead of scalars. When IVA is used to perform source separation in the frequency domain, sources in different frequency bins are optimized together as vectors.…”