A New Well-posed Nonlocal Perona-Malik Type Equation
偏微分方程分析
2018-08-14 v1 动力系统
摘要
A modification of the Perona-Malik equation is proposed for which the local nonlinear diffusion term is replaced by a nonlocal term of slightly reduced ``strength''. The new equation is globally well-posed (in spaces of classical regularity) and possesses desirable properties from the perspective of image processing. It admits characteristic functions as (formally linearly ``stable'') stationary solutions and can therefore be reliably employed for denoising keeping blurring in check. Its numerical implementation is stable, enhances some of the features of Perona-Malik, and avoids problems known to affect the latter.
引用
@article{arxiv.math/0702715,
title = {A New Well-posed Nonlocal Perona-Malik Type Equation},
author = {Patrick Guidotti},
journal= {arXiv preprint arXiv:math/0702715},
year = {2018}
}