Journal
SIGNAL PROCESSING
Volume 94, Issue -, Pages 476-489Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.sigpro.2013.06.011
Keywords
L1 optimization; Group sparsity; Denoising; Speech enhancement; Convex optimization; Translation-invariant denoising
Categories
Funding
- NSF [CCF-1018020]
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1018020] Funding Source: National Science Foundation
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This paper addresses signal denoising when large-amplitude coefficients form clusters (groups). The L1-norm and other separable sparsity models do not capture the tendency of coefficients to cluster (group sparsity). This work develops an algorithm, called 'overlapping group shrinkage' (OGS), based on the minimization of a convex cost function involving a group-sparsity promoting penalty function. The groups are fully overlapping so the denoising method is translation-invariant and blocking artifacts are avoided. Based on the principle of majorization-minimization (MM), we derive a simple iterative minimization algorithm that reduces the cost function monotonically. A procedure for setting the regularization parameter, based on attenuating the noise to a specified level, is also described. The proposed approach is illustrated on speech enhancement, wherein the OGS approach is applied in the short-time Fourier transform (STFT) domain. The OGS algorithm produces denoised speech that is relatively free of musical noise. (C) 2013 Elsevier B.V. All rights reserved.
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