Image Reconstruction Using the sinc Kernel Function

Abstract

This study is devoted to address the challenge of solving ill-posed integral equations for image restoration. The integral equation is widely recognized as an ill-posed problem [1]. Our study demonstrates that utilizing a two- dimensional function as a kernel function in the integral equation leads to stable solutions, by establishing a consistent dependence between the solutions and the input data (images). We were able to obtain solutions for the integral equation without employing a regularization process, which significantly reduces the duration of the calculation process.