Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9502891 | Journal of Mathematical Analysis and Applications | 2005 | 24 Pages |
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 2Ã2 matrices M2Ã2. 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 Wâ1,p (or Wâ1,â) 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 Wâ1,â perturbations.
Keywords
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Shahnaz Taheri, Qi Tang, Kewei Zhang,