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

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.