A regularization of nonlinear diffusion equations in a multiresolution framework

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 res...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 31; no. 5; pp. 575 - 587
Main Authors: Teschke, Gerd, Zhariy, Mariya, Soares, Maria Joana
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 25.03.2008
Wiley
Teubner
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
nonlinear diffusion
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
operator-adapted refinable functions
regularization
Sciences and techniques of general use
nonlinear diffusion
Numerical linear algebra
Mathematical method
Algorithm
Discretization method
Non linear equation
Regularization method
Scaling function
Numerical analysis
Applied mathematics
Non linear model
operator-adapted refinable functions
Diffusion equation
Ill posed problem
Regularization
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary: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.
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content type line 23
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.926