Point-wise behavior of the Geman-McClure and the Hebert Leahy image restoration models - UTU Research Portal

A1 Refereed original research article in a scientific journal

Point-wise behavior of the Geman-McClure and the Hebert Leahy image restoration models

Authors: Harjulehto P, Hasto P, Tiirola J

Publisher: Amer Inst Mathematical Sciences

Publication year: 2015

Journal:Inverse Problems and Imaging

Journal name in sourceINVERSE PROBLEMS AND IMAGING

Journal acronym: Inverse Probl Imag

Volume: 9

Issue: 3

First page : 835

Last page: 851

Number of pages: 17

ISSN: 1930-8337

DOI: https://doi.org/10.3934/ipi.2015.9.83577

Abstract

We present new continuous variants of the Geman-McClure model and the Hebert-Leahy model for image restoration, where the energy is given by the nonconvex function x bar right arrow x(2)/(1+x(2)) or x bar right arrow log(1+x(2)), respectively. In addition to studying these models' Gamma-convergence, we consider their point-wise behaviour when the scale of convolution tends to zero. In both cases the limit is the Mumford-Shah functional.