A Khatri–Rao subspace approach to blind identification of mixtures of quasi-stationary sources

Abstract

Blind identification (BID) of mixtures of quasi-stationary sources (QSS) is a vital approach for blind speech or audio source separation, and has attracted much interest for more than a decade. In general, BID-QSS is formulated, and then treated, under either the parallel factor analysis or joint diagonalization framework. This paper describes a Khatri–Rao (KR) subspace formulation of BID-QSS. Like subspace techniques founded in sensor array processing, the KR subspace formulation enables us to decompose the BID problem into a per-source decoupled BID problem. By exploring this new opportunity, we derive an overdetermined BID algorithm that solves BID-QSS in a successive and algebraically simple manner. Analysis shows that under an ideal data setting, the decoupled solutions of the proposed overdetermined BID algorithm yield very fast convergence. We also tackle the underdetermined case by proposing a two-stage strategy where the decoupled solutions are used to warm-start another BID algorithm. Simulation results show that the proposed BID algorithms yield competitive mean-square error and runtime performance in comparison to the state-of-the-arts in BID-QSS.