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A globally well‐posed nonlinear nonlocal diffusion
Author(s) -
Guidotti Patrick
Publication year - 2007
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200700568
Subject(s) - regularization (linguistics) , nonlinear system , context (archaeology) , mathematics , diffusion , variety (cybernetics) , mathematical optimization , computer science , econometrics , calculus (dental) , artificial intelligence , statistics , physics , geography , quantum mechanics , thermodynamics , medicine , archaeology , dentistry
Nonlinear diffusions have successfully been employed to perform a variety of tasks in image processing. In the context of denoising, the Perona‐Malik equation is a particularly successful example. In spite of its cherished qualities, it is mathematically ill‐posed and has some practical short‐comings. In this short paper a new nonlocal nonlinear diffusion is reported upon, which is globally well‐posed and shares with Perona‐Malik all its qualities even improving on its weaknesses. It can be viewed as a new kind of regularization. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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