A Coupled Variational Problem of Linear Growth Related to the Denoising and Inpainting of Images

Abstract

We present some results conjectured by Bildhauer, Fuchs, and Weickert who investigated analytical aspects of coupled variational models with applications to mathematical imaging. We focus on variants of linear growth, which require a treatment within the framework of relaxation theory and convex analysis. We establish existence and regularity of (dual-) solutions.