Shrinkage for Redundant Representations?
November 17th, 2005
SPARS05', IRISA - INRIA, Rennes, France.

Shrinkage is a well known and appealing denoising technique. The use of shrinkage is known to be optimal for Gaussian white noise, provided that the sparsity on the signal’s representation is enforced using a unitary transform. Still, shrinkage is also practiced successfully with non-unitary, and even redundant representations. In this lecture we shed some light on this behavior. We show that simple shrinkage could be interpreted as the first iteration of an algorithm that solves the basis pursuit denoising (BPDN) problem. Thus, this work leads to a sequential shrinkage algorithm that can be considered as a novel and effective pursuit method. We demonstrate this algorithm, both synthetically, and for the image denoising problem, showing in both cases its superiority over several popular alternatives..