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

Author:

Selesnick, Ivan W.   Parekh, Ankit   Bayram, Ilker  

Journal:

IEEE Signal Processing Letters

Issue Date:

2015

Abstract(summary):

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.

Page:

141-144