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

Code

• github.com/tky823/ssspy
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Abstract

A majorization-minimization (MM) algorithm for independent vector analysis optimizes a separation matrix W = [w_1, , w_m]^h C^m m by minimizing a surrogate function of the form L(W) = _i = 1^m w_i^h V_i w_i - | W |^2, where m N is the number of sensors and positive definite matrices V_1,,V_m C^m 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 IP_2) that updates two rows of W in each iteration. We here extend this ISS to ISS_2 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 ISS_2 as well as the conventional ISS can be immediately obtained in a systematic manner. Numerical experiments to separate reverberant speech mixtures show that our ISS_2 converges in fewer MM iterations than the conventional ISS, and is comparable to IP_2.

Reproductions