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

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

IEEE SIGNAL PROCESSING LETTERS, cilt.22, sa.2, ss.141-144, 2015 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Konu: 2
  • Basım Tarihi: 2015
  • Doi Numarası: 10.1109/lsp.2014.2349356
  • Sayfa Sayıları: ss.141-144


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.