Joint Matrices Decompositions and Blind Source Separation: A survey of methods, identification, and applications

Author

Chabriel, Gilles ; Kleinsteuber, Martin ; Moreau, Eric ; Hao Shen ; Tichavsky, Petr ; Yeredor, Arie

Author_Institution

Univ. of Toulon, La Garde, France

Volume

31

Issue

3

fYear

2014

fDate

May-14

Firstpage

34

Lastpage

43

Abstract

Matrix decompositions such as the eigenvalue decomposition (EVD) or the singular value decomposition (SVD) have a long history in signal processing. They have been used in spectral analysis, signal/noise subspace estimation, principal component analysis (PCA), dimensionality reduction, and whitening in independent component analysis (ICA). Very often, the matrix under consideration is the covariance matrix of some observation signals. However, many other kinds of matrices can be encountered in signal processing problems, such as time-lagged covariance matrices, quadratic spatial time-frequency matrices [21], and matrices of higher-order statistics.

Keywords

covariance matrices; independent component analysis; principal component analysis; singular value decomposition; source separation; EVD; ICA; PCA; SVD; blind source separation; covariance matrix; dimensionality reduction; eigenvalue decomposition; higher-order statistics; independent component analysis; joint matrices decompositions; principal component analysis; quadratic spatial time-frequency matrices; signal processing; singular value decomposition; spectral analysis; time-lagged covariance matrices; Context awareness; Covariance matrices; Eigenvalues and eigenfunctions; Matrix decomposition; Principle component analysis; Source separation; Symmetric matrices;

fLanguage

English

Journal_Title

Signal Processing Magazine, IEEE

Publisher

ieee

ISSN

1053-5888

Type

jour

DOI

10.1109/MSP.2014.2298045

Filename

6784078