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

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