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Exploiting Group Sparsity in Nonlinear Acoustic Echo Cancellation by Adaptive Proximal Forward-Backward Splitting
Hiroki KURODA Shunsuke ONO Masao YAMAGISHI Isao YAMADA
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2013/10/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Sparsity-aware Signal Processing)
group sparsity, nonlinear acoustic echo cancellation (NLAEC), adaptive Volterra filter, weighted group l1 norm, adaptive proximal forward-backward splitting (APFBS),
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In this paper, we propose a use of the group sparsity in adaptive learning of second-order Volterra filters for the nonlinear acoustic echo cancellation problem. The group sparsity indicates sparsity across the groups, i.e., a vector is separated into some groups, and most of groups only contain approximately zero-valued entries. First, we provide a theoretical evidence that the second-order Volterra systems tend to have the group sparsity under natural assumptions. Next, we propose an algorithm by applying the adaptive proximal forward-backward splitting method to a carefully designed cost function to exploit the group sparsity effectively. The designed cost function is the sum of the weighted group l1 norm which promotes the group sparsity and a weighted sum of squared distances to data-fidelity sets used in adaptive filtering algorithms. Finally, Numerical examples show that the proposed method outperforms a sparsity-aware algorithm in both the system-mismatch and the echo return loss enhancement.