On some perturbations of the total variation image inpainting method. Part II: relaxation and dual variational formulation

On some perturbations of the total variation image inpainting method. Part I: regularity theory

In this article we investigate some modifications of the total variation inpainting model and discuss the existence as well as the smoothness of solutions to these new variational problems. We emphasize that our variant of a linear growth regulariza-tion is completely discussed in the Sobolev space W 1 1 without passing to a relaxed version in the space of functions with bounded variation.

On some perturbations of the total variation image inpainting method. Part III: minimization among sets with finite perimeter

Existence of generalized minimizers and of dual solutions for a class of variational problems with linear growth related to image recovery

We continue the analysis of some modifications of the total variation image inpainting method formulated on the space BV (Ω) in the sense that we generalize some of the main results of [13] to the case of vectorvalued images where now we do not impose any structure condition on our density F and the dimension of the domain Ω is arbitrary. Precisely we discuss existence of generalized solutions ...

Image Restoration by Variable Splitting based on Total Variant Regularizer

The aim of image restoration is to obtain a higher quality desired image from a degraded image. In this strategy, an image inpainting method fills the degraded or lost area of the image by appropriate information. This is performed in such a way so that the obtained image is undistinguishable for a casual person who is unfamiliar with the original image. In this paper, different images are degr...

Existence and almost everywhere regularity of generalized minimizers for a class of variational problems with linear growth related to image inpainting

We continue the analysis of some modifications of the total variation image inpainting method formulated on the space BV (Ω) in the sense that we generalize the main results of [32] to the case that a more general data fitting term is involved. As in [32] we deal with vector-valued images, we do not impose any structure condition on our density F and the dimension of the domain Ω is arbitrary. ...