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

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

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...

On a class of variational problems with linear growth related to image inpainting

In this article, we investigate a modification of the total variation image inpainting method and improve the partial regularity results previously established in [8] to C 1,α interior differentiability of solutions of this new variational problem using De Giorgi type arguments.

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

In our note we discuss some strongly elliptic modifications of the total variation inpainting model formulated in the space BV(Ω) and investigate the corresponding dual variational problems. Remarkable features are the uniqueness of the dual solution and the uniqueness of the absolutely continuous part ∇ a u of the gradient of BV-solutions u on the whole domain. Additionally, any BV-minimizer u...

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. ...