Translation-invariant shrinkage/thresholding of group sparse signals

Po Yu Chen, Ivan W. Selesnick

Research output: Contribution to journalArticlepeer-review


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
Issue number1
StatePublished - 2014


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

ASJC Scopus subject areas

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


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