Intrinsic Newton’s Method on Oblique Manifolds for Overdetermined Blind Source Separation

This paper studies the problem of Overdetermined Blind Source Separation (OdBSS), a challenging problem in signal processing. It aims to recover desired sources from outnumbered observations without knowing either the source distributions or the mixing process. It is well-known that performance of standard BSS algorithms, which usually utilize a whitening step as a pre-process to reduce the dimensionality of observations, might be seriously limited due to its blind trust on the data covariance matrix. In this paper, we develop efficient OdBSS algorithms without dimensionality reduction. In particular, our algorithms solve a problem of simultaneous diagonalization of a set of symmetric matrices. By exploiting the appropriate underlying manifold, namely the so-called oblique manifold, intrinsic Newton’s method is developed to optimize two popular cost functions for the simultaneous diagonalization of symmetric matrices, i.e., the off-norm function and the log- likelihood function. Performance of the proposed algorithms is investigated by several numerical experiments.     «

This paper studies the problem of Overdetermined Blind Source Separation (OdBSS), a challenging problem in signal processing. It aims to recover desired sources from outnumbered observations without knowing either the source distributions or the mixing process. It is well-known that performance of standard BSS algorithms, which usually utilize a whitening step as a pre-process to reduce the dimensionality of observations, might be seriously limited due to its blind trust on the data covariance m...     »