Non-convex Total Variation Regularization for Convex Denoising of Signals

Ivan Selesnick, Alessandro Lanza, Serena Morigi, Fiorella Sgallari

Research output: Contribution to journalArticlepeer-review


Total variation (TV) signal denoising is a popular nonlinear filtering method to estimate piecewise constant signals corrupted by additive white Gaussian noise. Following a ‘convex non-convex’ strategy, recent papers have introduced non-convex regularizers for signal denoising that preserve the convexity of the cost function to be minimized. In this paper, we propose a non-convex TV regularizer, defined using concepts from convex analysis, that unifies, generalizes, and improves upon these regularizers. In particular, we use the generalized Moreau envelope which, unlike the usual Moreau envelope, incorporates a matrix parameter. We describe a novel approach to set the matrix parameter which is essential for realizing the improvement we demonstrate. Additionally, we describe a new set of algorithms for non-convex TV denoising that elucidate the relationship among them and which build upon fast exact algorithms for classical TV denoising.

Original languageEnglish (US)
Pages (from-to)825-841
Number of pages17
JournalJournal of Mathematical Imaging and Vision
Issue number6-7
StatePublished - Jul 1 2020


  • Convex non-convex regularization
  • Forward-backward splitting algorithm
  • Signal denoising
  • Total variation regularization

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics


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