Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus
of Variations | SpringerLink Skip to main content Advertisement Springer Nature Link Account …

Imaging is an interdisciplinary research area with profound applications in many areas of
science, engineering, technology, and medicine. The most primitive form of imaging is visual …

This paper explores various aspects of the image decomposition problem using modern
variational techniques. We aim at splitting an original image f into two components u and ρ …

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

This paper investigates the use of regularization functionals with nonlocal correlation terms
for the problem of image denoising and image deblurring. These functionals are expressed …

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 …

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 address the denoising of images contaminated with multiplicative noise, eg speckle
noise. Classical ways to solve such problems are filtering, statistical (Bayesian) methods …

The total variation model proposed by Rudin, Osher and Fatemi performs very well for
removing noise while preserving edges. However, it favors a piecewise constant solution in …

We propose a new class of models for image restoration and decomposition by functional
minimization. Following ideas of Y. Meyer in a total variation minimization framework of L …