Abstract
Proximal methods are an important tool in signal processing applications, where many problems can be characterized by the minimization of an expression involving a smooth fitting term and a convex regularization term – for example the classic ℓ1-Lasso. Such problems can be solved using the relevant proximal operator. Here we consider the use of proximal operators for the ℓp-quasinorm where 0 ≤ p ≤ 1. Rather than seek a closed form solution, we develop an iterative algorithm using a Majorization-Minimization procedure which results in an inexact operator. Experiments on image denoising show that for p ≤ 1 the algorithm is effective in the high-noise scenario, outperforming the Lasso despite the inexactness of the proximal step.