Convex 1-D total variation denoising with non-convex regularization

Ivan W. Selesnick, Ankit Parekh, Ilker Bayram

Research output: Contribution to journalArticlepeer-review


Total variation (TV) denoising is an effective noise suppression method when the derivative of the underlying signal is known to be sparse. TV denoising is defined in terms of a convex optimization problem involving a quadratic data fidelity term and a convex regularization term. A non-convex regularizer can promote sparsity more strongly, but generally leads to a non-convex optimization problem with non-optimal local minima. This letter proposes the use of a non-convex regularizer constrained so that the total objective function to be minimized maintains its convexity. Conditions for a non-convex regularizer are given that ensure the total TV denoising objective function is convex. An efficient algorithm is given for the resulting problem.

Original languageEnglish (US)
Article number6880761
Pages (from-to)141-144
Number of pages4
JournalIEEE Signal Processing Letters
Issue number2
StatePublished - Feb 2015


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

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering
  • Applied Mathematics


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