Coupled variational problems of linear growth related to the denoising and inpainting of images

Abstract

In this note we present some results that were already conjectured in the work [9] by Bildhauer, Fuchs and Weickert, where they have investigated analytical aspects of coupled variational models with applications to mathematical imaging. Here we focus on variants of linear growth, which require a treatment in the framework of relaxation theory and convex analysis. Following basic ideas from [6] and [7], we establish existence and regularity of (dual-)solutions.