Inverse problems arise from the need to interpret indirect and incomplete measurements. As
an area of contemporary mathematics, the field of inverse problems is strongly driven by …

This book presents the state of the art in sparse and multiscale image and signal processing,
covering linear multiscale transforms, such as wavelet, ridgelet, or curvelet transforms, and …

This paper introduces a new class of fractional-order anisotropic diffusion equations for
noise removal. These equations are Euler-Lagrange equations of a cost functional which is …

In this paper, we study alternating direction methods for solving constrained total-variation
image restoration and reconstruction problems. Alternating direction methods can be …

Can images be decomposed into the sum of a geometric part and a textural part? In a
theoretical breakthrough,[Y. Meyer, Oscillating Patterns in Image Processing and Nonlinear …

This thoroughly updated new edition presents state of the art sparse and multiscale image
and signal processing. It covers linear multiscale geometric transforms, such as wavelet …

The Cahn–Hilliard equation is a nonlinear fourth order diffusion equation originating in
material science for modeling phase separation and phase coarsening in binary alloys. The …

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 …

We propose a novel cartoon-texture separation model using a sparse low-rank
decomposition. Our texture model connects the separate ideas of robust principal …

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 …