MULTIPLICATIVE UPDATES AND JOINT DIAGONALIZATION BASED ACCELERATION FOR UNDER-DETERMINED BSS USING A FULL-RANK SPATIAL COVARIANCE MODEL

Abstract

Here we introduce multiplicative update rules for full-rank spatial covariance analysis (FCA), a blind source separation (BSS) method proposed by Duong et al. [Under-determined reverberant audio source separation using a full-rank spatial covariance model, IEEE Trans. ASLP, vol. 18, no. 7, pp. 1830–1840, Sept. 2010]. In the FCA, source separation is performed by multichannel Wiener filtering with the covariance matrix of each source signal estimated by the expectation-maximization (EM) algorithm. A drawback of this EM algorithm is that it does not necessarily yield good covariance matrix estimates within a feasible number of iterations. In contrast, the proposed multiplicative update rules tend to give covariance matrix estimates that result in better source separation performance than the EM algorithm. Furthermore, we propose joint diagonalization based acceleration of the multiplicative update rules, which leads to signifi-cantly reduced computation time per iteration. In a BSS experiment, the proposed multiplicative update rules resulted in higher source separation performance than the conventional EM algorithm overall. Moreover, the joint diagonalization based accelerated algorithm was up to 200 times faster than the algorithm without acceleration, which is realized without much degradation in the source separation performance.