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ISS2: An Extension of Iterative Source Steering Algorithm for Majorization-Minimization-Based Independent Vector Analysis
Rintaro Ikeshita, Tomohiro Nakatani
A majorization-minimization (MM) algorithm for independent vector analysis optimizes a separation matrix W = [w₁, …, wₘ]ʰ ∈ℂ^(m ×m) by minimizing a surrogate function of the form ℒ(W) = ∑_(i = 1)ᵐ wᵢʰ Vᵢ wᵢ - log| W |², where m ∈ℕ is the number of sensors and positive definite matrices V₁,…,Vₘ ∈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 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.
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