Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation
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 pape...
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| Format: | Article |
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University of Tehran
2018-10-01
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| Series: | Journal of Sciences, Islamic Republic of Iran |
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| Online Access: | https://jsciences.ut.ac.ir/article_67447_882ae755221799e32f4a9635764db7fb.pdf |
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| author | A. Khatoon Abadi K. Yahya M. Amini |
| author_facet | A. Khatoon Abadi K. Yahya M. Amini |
| author_sort | A. Khatoon Abadi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-169c0ebfa4d945feaea46f514a94097d |
| institution | Kabale University |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2018-10-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-169c0ebfa4d945feaea46f514a94097d2025-08-20T03:53:52ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142018-10-0129436136810.22059/jsciences.2018.6744767447Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik EquationA. Khatoon Abadi0K. Yahya1M. Amini2Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Islamic Republic of IranFaculty of Informatics, Chemnitz University of Technology, Straße der Nationen 62Department of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Islamic Republic of IranWavelets 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.https://jsciences.ut.ac.ir/article_67447_882ae755221799e32f4a9635764db7fb.pdfadaptive wavelet methodradial basis functionsperona-malik equation |
| spellingShingle | A. Khatoon Abadi K. Yahya M. Amini Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation Journal of Sciences, Islamic Republic of Iran adaptive wavelet method radial basis functions perona-malik equation |
| title | Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation |
| title_full | Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation |
| title_fullStr | Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation |
| title_full_unstemmed | Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation |
| title_short | Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation |
| title_sort | adopting the multiresolution wavelet analysis in radial basis functions to solve the perona malik equation |
| topic | adaptive wavelet method radial basis functions perona-malik equation |
| url | https://jsciences.ut.ac.ir/article_67447_882ae755221799e32f4a9635764db7fb.pdf |
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