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

Yin Ding, Ivan Selesnick

Research output: Contribution to journalArticle

Abstract

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
Volume22
Issue number9
DOIs
StatePublished - Sep 1 2015

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Wavelet Denoising
Convex optimization
Convex Optimization
Regularization
Wavelets
Denoising
Sparsity
Signal denoising
Wavelet Thresholding
Total Variation Regularization
Parameter Selection
Regularization Parameter
Penalty Function
Total Variation
Fast Algorithm
Penalty
Convexity
Objective function
Oscillation

Keywords

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

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing
  • Applied Mathematics

Cite this

Artifact-Free Wavelet Denoising : Non-convex Sparse Regularization, Convex Optimization. / Ding, Yin; Selesnick, Ivan.

In: IEEE Signal Processing Letters, Vol. 22, No. 9, 7047778, 01.09.2015, p. 1364-1368.

Research output: Contribution to journalArticle

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