On coupled regularization for non-convex variational image enhancement

Abstract

A natural continuation from conventional convex methods for image enhancement is the transition to non-convex formulations. However, strictly non-convex models do not admit traditional tools from convex optimization to be used. To resolve this drawback, non-convex problems are often cast into convex formulations by relaxing stringent assumptions on model properties. In this work we present an alternative approach. We study when an energy functional is convex given a non-convex penalty term. Key to our formulation is the introduction of a novel coupling between the discretization scheme and a non-local weight function in the data term. We interpret the non-local weights for the finite difference operators. In a denoising application we study a class of non-convex ℓp-norms. The resulting energies are globally minimized using the popular ADMM.