This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …

In this paper we study a variational problem in the space of functions of bounded Hessian.
Our model constitutes a straightforward higher-order extension of the well known ROF …

Total variation methods and similar approaches based on regularizations with ℓ 1-type
norms (and seminorms) have become a very popular tool in image processing and inverse …

Higher order equations, when applied to image inpainting, have certain advantages over
second order equations, such as continuation of both edge and intensity information over …

Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning
dynamical systems that can be modelled by ordinary differential equations. In this paper, we …

Wavelet inpainting problem consists of filling in missed data in the wavelet domain. In [17],
Chan, Shen, and Zhou proposed an efficient method to recover piecewise constant or …

Image Inpainting is the art of filling in missing data in an image. The purpose of in painting is
to reconstruct missing regions in a visually plausible manner so that it seems reasonable to …

Image inpainting is the process of recovering the damage areas in the images in an
undetectable way, it is considered the important one of the subjects in image processing …

The Cahn--Hilliard equation provides a simple and fast tool for binary image inpainting. By
now, two generalizations to gray value images exist: bitwise binary inpainting and TV-H ^-1 …

In this paper, we propose a fast local image inpainting algorithm based on the Allen–Cahn
model. The proposed algorithm is applied only on the inpainting domain and has two …