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Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation

Document Type : Final File

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Islamic Republic of Iran

2 Faculty of Informatics, Chemnitz University of Technology, Straße der Nationen 62

3 R. B216, 09111 Chemnitz, Germany

Abstract

Wavelets and radial basis functions (RBF) have ubiquitously proved very successful to solve different forms of partial differential equations (PDE) using shifted basis functions, and as with the other meshless methods, they have been extensively used in scattered data interpolation. The current paper proposes a framework that successfully reconciles RBF and adaptive wavelet method to solve the Perona-Malik equation in terms of locally shifted functions. We take advantage of the scaling functions that span multiresolution subspaces to provide resilient grid comprising centers. At the next step, the derivatives are computed and summed over these local feature collocations to generate the solution. We discuss the stability of the solution and depict how convergence could be granted in this context. Finally, the numerical results are provided to illustrate the accuracy and efficiency of the proposed method.

Keywords

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Journal of Sciences, Islamic Republic of Iran
Volume 29, Issue 4
October 2018
Pages 361-368
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