Blind source recovery for non-minimum phase surroundings

Abstract

This paper revisits the issue of Blind Source Recovery (BSR) of non-minimum phase linear MIMO systems and provides a new rigorous derivation of the proposed state space algorithms [4,6,7,9]. Using state space representation for both the mixing and convolving (or reverberative) surrounding environment and the recovery (or demixing and deconvolving) networks, we systematically derive update laws based on the minimization of Kullback-Liebler divergence using the theory of optimization and the calculus of variations along the Riemannian contra-variant (or the natural) gradient. A simulation example for recovery of signals from a challenging non-minimum environment is also included in this paper.