Total Variation Denoising Via the Moreau Envelope

Research output: Contribution to journalArticle

Abstract

Total variation denoising is a nonlinear filtering method well suited for the estimation of piecewise-constant signals observed in additive white Gaussian noise. The method is defined by the minimization of a particular nondifferentiable convex cost function. This letter describes a generalization of this cost function that can yield more accurate estimation of piecewise constant signals. The new cost function involves a nonconvex penalty (regularizer) designed to maintain the convexity of the cost function. The new penalty is based on the Moreau envelope. The proposed total variation denoising method can be implemented using forward-backward splitting.

Original languageEnglish (US)
Article number7807310
Pages (from-to)216-220
Number of pages5
JournalIEEE Signal Processing Letters
Volume24
Issue number2
DOIs
StatePublished - Feb 1 2017

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Moreau Envelope
Total Variation
Denoising
Cost functions
Cost Function
Penalty
Nonlinear filtering
Nonlinear Filtering
Gaussian White Noise
Convex function
Convexity

Keywords

  • Convex
  • denoising
  • sparse
  • total variation (TV)

ASJC Scopus subject areas

  • Signal Processing
  • Applied Mathematics
  • Electrical and Electronic Engineering

Cite this

Total Variation Denoising Via the Moreau Envelope. / Selesnick, Ivan.

In: IEEE Signal Processing Letters, Vol. 24, No. 2, 7807310, 01.02.2017, p. 216-220.

Research output: Contribution to journalArticle

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