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A regularization of nonlinear diffusion equations in a multiresolution framework
Author(s) -
Teschke Gerd,
Zhariy Mariya,
Soares Maria Joana
Publication year - 2007
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.926
Subject(s) - regularization (linguistics) , discretization , mathematics , nonlinear system , diffusion , mathematical analysis , algorithm , mathematical optimization , computer science , artificial intelligence , physics , quantum mechanics , thermodynamics
We develop a regularization technique for Perona–Malik diffusion equations that relies on multiresolution techniques. The main result of this paper is to show that the chosen discretization overcomes the ill posedness of the nonlinear Perona–Malik model. The resulting algorithm is tested and the results are compared with pixel‐based methods. Copyright © 2007 John Wiley & Sons, Ltd.