Total Variation-Based Model For Signal Restoration Using Local Meshless Algorithm

Danyal Ahmad; Mushtaq Ahmad Khan; Abdul Kabir; Muhammad Atif; Tawab Khan

Author(s)

Danyal Ahmad Department of Natural Sciences and Humanities, University of Engineering and Technology Mardan, Mardan 23200, Pakistan

Mushtaq Ahmad Khan Department of Natural Sciences and Humanities, University of Engineering and Technology Mardan, Mardan 23200, Pakistan

Abdul Kabir Department of Natural Sciences and Humanities, University of Engineering and Technology Mardan, Mardan 23200, Pakistan

Muhammad Atif Department of Natural Sciences and Humanities, University of Engineering and Technology Mardan, Mardan 23200, Pakistan

Tawab Khan Department of Natural Sciences and Humanities, University of Engineering and Technology Mardan, Mardan 23200, Pakistan

Abstract

A noisy signal is transformed into another signal that exhibits fluctuations, called signal fluctuation. This fluctuation is a common challenge in signal processing. In this article, we present a mesh-free Local Meshless Scheme (LMC) for numerically solving the Euler-Lagrange Partial Differential Equation (EL-PDE) associated with the Total Variation (TV)-based model designed to remove additive noise from given data signals. This method employs the Multi-quadric Radial Basis Function (MQ-RBF) as its basis function. The features of this approach effectively eliminate fluctuations from the noisy signals by leveraging meshless applications. Experimental results demonstrate that the proposed LMC exhibits superior performance in terms of Signal to Noise Ratio (SNR) when compared to conventional methods and the Global Meshless Scheme (GMS), across various basis functions. Moreover, the results indicate that the LMCA is faster regarding computation time (CUP time) and requires fewer iterations for convergence than both the conventional method and the GMS.

Publication Details

Page(s) 120-147

DOI DOI not available

Published Journal: The Sciencetech, Volume: 5, Issue: 4, Year: 2024

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Keywords

Global Meshless Scheme, Local Meshless Scheme, Total Variation-Regularization, Signal to Noise Ratio, Additive Noise, Euler Lagrange Partial Differential Equation, Multi-quadric Radial Basis Function, Radial Basis Function Interpolation

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