Translation-invariant shrinkage/thresholding of group sparse signals

Po Yu Chen, Ivan Selesnick

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)476-489
Number of pages14
JournalSignal Processing
Volume94
Issue number1
DOIs
StatePublished - 2014

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Cost functions
Signal denoising
Speech enhancement
Fourier transforms

Keywords

  • Convex optimization
  • Denoising
  • Group sparsity
  • L1 optimization
  • Speech enhancement
  • Translation-invariant denoising

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition

Cite this

Translation-invariant shrinkage/thresholding of group sparse signals. / Chen, Po Yu; Selesnick, Ivan.

In: Signal Processing, Vol. 94, No. 1, 2014, p. 476-489.

Research output: Contribution to journalArticle

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