Random noise attenuation on finite-difference wave propagation using fuzzy transform

TL;DR

This paper introduces a fuzzy transform-based finite-difference method for solving the acoustic wave equation, effectively reducing random and periodic noise in noisy initial conditions.

Contribution

It applies F-transform to finite-difference wave propagation, demonstrating noise attenuation capabilities in solving the acoustic wave equation.

Findings

F-transform can remove periodic noise effectively.

F-transform significantly reduces random noise in wave simulations.

The method improves the accuracy of wave propagation models with noisy data.

Abstract

Fuzzy Transform (F-transform) has been introduced as an approximation method which encompasses both classical transforms and approximation methods studied in fuzzy modeling and fuzzy control. It has been proved that, under some conditions, F-transform can remove a periodical noise and it can significantly reduce random noise. In this work we apply the F-transform methodology to propose a finite-difference approach to solving the acoustic wave equation with noisy initial conditions.