Convex 1-D Total Variation Denoising with Non-convex Regularization

Selesnick I. W., Parekh A., Bayram I.

IEEE SIGNAL PROCESSING LETTERS, vol.22, no.2, pp.141-144, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 22 Issue: 2
  • Publication Date: 2015
  • Doi Number: 10.1109/lsp.2014.2349356
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.141-144
  • Istanbul Technical University Affiliated: No


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.