Total Variation Denoising Via the Moreau Envelope

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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
Issue number2
StatePublished - Feb 2017


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

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics


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