ISS2: An Extension of Iterative Source Steering Algorithm for Majorization-Minimization-Based Independent Vector Analysis

A majorization-minimization (MM) algorithm for independent vector analysis optimizes a separation matrix W = [w1, ldots, wm]h ∈ mathbbCm × m by minimizing a surrogate function of the form L(W) = sumi = 1m wih Vi wi - log | det W |2, where m ∈ mathbbN is the number of sensors and positive definite matrices V1,ldots,Vm ∈ mathbbCm × m are constructed in each MM iteration. For m ≥ 3, no algorithm has been found to obtain a global minimum of L(W). Instead, block coordinate descent (BCD) methods with closed-form update formulas have been developed for minimizing L(W) and shown to be effective. One such BCD is called iterative projection (IP) that updates one or two rows of W in each iteration. Another BCD is called iterative source steering (ISS) that updates one column of the mixing matrix A = W-1 in each iteration. Although the time complexity per iteration of ISS is m times smaller than that of IP, the conventional ISS converges slower than the current fastest IP (called IP2) that updates two rows of W in each iteration. We here extend this ISS to ISS2 that can update two columns of A in each iteration while maintaining its small time complexity. To this end, we provide a unified way for developing new ISS type methods from which ISS2 as well as the conventional ISS can be immediately obtained in a systematic manner. Numerical experiments to separate reverberant speech mixtures show that our ISS2 converges in fewer MM iterations than the conventional ISS, and is comparable to IP2.