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

Ivan W. Selesnick, Ankit Parekh, Ilker Bayram

Research output: Contribution to journalArticlepeer-review

101 Scopus citations


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


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


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