Open Access

ARTICLE

Multiquadric Radial Basis Function Approximation Scheme for Solution of Total Variation Based Multiplicative Noise Removal Model

by Mushtaq Ahmad Khan^1,*, Ahmed B. Altamimi², Zawar Hussain Khan³, Khurram Shehzad Khattak³, Sahib Khan^4,*, Asmat Ullah³, Murtaza Ali¹

1 University of Engineering and Technology, Mardan, 23200, Pakistan
2 University of Hail, Hail, Saudi Arabia
3 University of Engineering and Technology, Peshawar, 25000, Pakistan
4 Politecnico di Torino, Torino, 10129, Italy

* Corresponding Authors: Mushtaq Ahmad Khan. Email: ; Sahib Khan. Email:

Computer Modeling in Engineering & Sciences 2021, 126(1), 55-88. https://doi.org/10.32604/cmes.2021.011163

Received 23 April 2020; Accepted 19 August 2020; Issue published 22 December 2020

Abstract

This article introduces a fast meshless algorithm for the numerical solution nonlinear partial differential equations (PDE) by Radial Basis Functions (RBFs) approximation connected with the Total Variation (TV)-based minimization functional and to show its application to image denoising containing multiplicative noise. These capabilities used within the proposed algorithm have not only the quality of image denoising, edge preservation but also the property of minimization of staircase effect which results in blocky effects in the images. It is worth mentioning that the recommended method can be easily employed for nonlinear problems due to the lack of dependence on a mesh or integration procedure. The numerical investigations and corresponding examples prove the effectiveness of the recommended algorithm regarding the robustness and visual improvement as well as peak-signal-to-noise ratio (PSNR), signal-to-noise ratio (SNR), and structural similarity index (SSIM) corresponded to the current conventional TV-based schemes.

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Citations