2011/11/30 by Martin Kleinsteuber, Hao Shen, Kleinsteuber, Martin +1
Chemistry · Computer Science · Mathematics · #Blind Source Separation Techniques #Spectroscopy and Chemometric Analyses #Speech and Audio Processing #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1111.7088
23 pages
arxiv created 2012/04/04 · arxiv updated 2012/04/05
Matrix Joint Diagonalization (MJD) is a powerful approach for solving the Blind Source Separation (BSS) problem. It relies on the construction of matrices which are diagonalized by the unknown demixing matrix. Their joint diagonalizer serves as a correct estimate of this demixing matrix only if it is uniquely determined. Thus, a critical question is under what conditions a joint diagonalizer is unique. In the present work we fully answer this question about the identifiability of MJD based BSS approaches and provide a general result on uniqueness conditions of matrix joint diagonalization. It unifies all existing results which exploit the concepts of non-circularity, non-stationarity, non-whiteness, and non-Gaussianity. As a corollary, we propose a solution for complex BSS, which can be formulated in a closed form in terms of an eigenvalue and a singular value decomposition of two matrices.