A higher order TV-type variational problem related to the denoising and inpainting of images

Abstract

We give a comprehensive survey on a class of higher order variational problems which are motivated by applications in mathematical imaging. The overall aim of this note is to investigate if and in which manner results from the first author's previous work on variants of the TV-regularization model (see e.g. [BF1], [BF2], [BF3] and [FT]) can be extended to functionals which involve higher derivatives. This seems to be not only of theoretical interest, but also relevant to applications since higher order TV-denoising appears to maintain the advantages of the classical model as introduced by Rudin, Osher and Fatemi in [ROF] while avoiding the unpleasant "staircasing" effect (see e.g. [BKP] or [LLT]). Our paper features results concerning generalized solutions in spaces of functions of higher order bounded variation, dual solutions as well as partial regularity of minimizers.

References in corpus (2)

• Existence and almost everywhere regularity of generalized minimizers for a class of variational problems with linear growth related to image inpainting
• A density result for Sobolev functions and functions of higher order bounded variation with additional integrability constraints

Cited by in corpus (3)

• On the solvability in Sobolev spaces and related regularity results for a variant of the TV-image recovery model: the vector-valued case
• Convex Regularization of Multi-Channel Images Based on Variants of the TV-Model
• Coupled variational problems of linear growth related to the denoising and inpainting of images