Young measure solutions and instability of the one-dimensional Perona-Malik equation

Taheri, Shahnez, Tang, Qi and Zhang, Kewei (2005) Young measure solutions and instability of the one-dimensional Perona-Malik equation. Journal of Mathematical Analysis and Applications, 308 (2). pp. 467-490. ISSN 0022-247X

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Abstract

We apply a variational approach to the one-dimensional version of the widely used Perona-Malik equation in image processing. We rephrase the problem into the one related to the quasiconvex hull of a graph in the space of 2 x 2 matrices M-2x2. We then use the solutions of some heat equations as the centre of the mass for the Young measure-valued solutions to construct the approximate solutions by using simple laminates. The approximate solutions can be viewed as solutions of a perturbation problem by W--1,W- p (or W--1,W- infinity) functions. The sequences of the approximate solutions generates Young measure-valued solutions. Our results also show that the solutions of the one-dimensional Perona-Malik equation are unstable under small W--1,W- infinity perturbations.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Qi Tang
Date Deposited: 06 Feb 2012 20:29
Last Modified: 01 May 2012 15:19
URI: http://sro.sussex.ac.uk/id/eprint/26129
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