Artifact-Free Wavelet Denoising: Non-convex Sparse Regularization, Convex Optimization

Research output: Contribution to journalArticlepeer-review


Algorithms for signal denoising that combine wavelet-domain sparsity and total variation (TV) regularization are relatively free of artifacts, such as pseudo-Gibbs oscillations, normally introduced by pure wavelet thresholding. This paper formulates wavelet-TV (WATV) denoising as a unified problem. To strongly induce wavelet sparsity, the proposed approach uses non-convex penalty functions. At the same time, in order to draw on the advantages of convex optimization (unique minimum, reliable algorithms, simplified regularization parameter selection), the non-convex penalties are chosen so as to ensure the convexity of the total objective function. A computationally efficient, fast converging algorithm is derived.

Original languageEnglish (US)
Article number7047778
Pages (from-to)1364-1368
Number of pages5
JournalIEEE Signal Processing Letters
Issue number9
StatePublished - Sep 1 2015


  • Convex optimization
  • non-convex regularization
  • total variation denoising
  • wavelet denoising

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics


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