A primal-dual approach for a total variation Wasserstein flow

TL;DR

This paper introduces an implicit primal-dual scheme for a nonlinear fourth-order diffusion equation used in image density denoising, incorporating a penalty term for dual variable constraints, with numerical demonstrations of its effectiveness.

Contribution

It presents a novel primal-dual method with penalty relaxation for total variation Wasserstein flows, enhancing computational stability and efficiency.

Findings

Effective denoising demonstrated through numerical examples

The penalty term improves dual variable constraint handling

The scheme shows promising stability and convergence properties

Abstract

We consider a nonlinear fourth-order diffusion equation that arises in denoising of image densities. We propose an implicit time-stepping scheme that employs a primal-dual method for computing the subgradient of the total variation seminorm. The constraint on the dual variable is relaxed by adding a \emph{penalty term}, depending on a parameter that determines the weight of the penalisation. The paper is furnished with some numerical examples showing the denoising properties of the model considered.