Volterra Integral Equation Based Computational Technique for Fuzzy Transform in Image Denoising

The primary goal of the study is to apply the fuzzy transform (F-Transform) technique to numerically solve second-class Volterra integral equations using a symmetric kernel. The unknown function can be addressed by employing a series expansion, resulting in a solution that is more exact and precise. Firstly, the uniform fuzzy partition of the specified domain is utilized. Subsequently, the F-transform approach is employed to convert the equation into a collection of linear equations. Finally, the inverse fuzzy transform is used to obtain the estimated solution. The comparison between the precise and approximate answers has been simulated and done utilizing the mathematical software Mathematica. In order to verify the precision of the suggested algorithm, multiple numerical instances are examined. Moreover, the general example of suggested method is considered as an implementation of image denoising.