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

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KHATOON ABADI A.; YAHYA K.; AMINI M.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

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Journal: Journal of Sciences, Islamic Republic of Iran Year:2018 | Volume:29 | Issue:4 Page(s): 361-368

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Title

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

Author(s)

KHATOON ABADI A. | YAHYA K. | AMINI M. | Issue Writer Certificate

Keywords

Adaptive wavelet method

Radial basis functions

Perona-Malik equation

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.

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APA: Copy

KHATOON ABADI, A., YAHYA, K., & AMINI, M.. (2018). Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, 29(4), 361-368. SID. https://sid.ir/paper/718159/en

Vancouver: Copy

KHATOON ABADI A., YAHYA K., AMINI M.. Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation. JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN[Internet]. 2018;29(4):361-368. Available from: https://sid.ir/paper/718159/en

IEEE: Copy

A. KHATOON ABADI, K. YAHYA, and M. AMINI, “Adopting the Multiresolution Wavelet Analysis in Radial Basis Functions to Solve the Perona-Malik Equation,” JOURNAL OF SCIENCES ISLAMIC REPUBLIC OF IRAN, vol. 29, no. 4, pp. 361–368, 2018, [Online]. Available: https://sid.ir/paper/718159/en

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