Total Variation Denoising via the Moreau Envelope

TL;DR

This paper introduces a generalized total variation denoising method using a non-convex penalty based on the Moreau envelope, which improves estimation accuracy while maintaining convexity, and can be implemented with forward-backward splitting.

Contribution

It proposes a novel non-convex regularizer based on the Moreau envelope for total variation denoising, enhancing accuracy without losing convexity.

Findings

Improved estimation accuracy for piecewise-constant signals.

Maintains convexity of the cost function with a non-convex penalty.

Efficient implementation via forward-backward splitting.

Abstract

Total variation denoising is a nonlinear filtering method well suited for the estimation of piecewise-constant signals observed in additive white Gaussian noise. The method is defined by the minimization of a particular non-differentiable convex cost function. This paper describes a generalization of this cost function that can yield more accurate estimation of piecewise constant signals. The new cost function involves a non-convex penalty (regularizer) designed to maintain the convexity of the cost function. The new penalty is based on the Moreau envelope. The proposed total variation denoising method can be implemented using forward-backward splitting.