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

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.