Image representation and denoising using squared eigenfunctions of Schrodinger operator

TL;DR

This paper introduces a novel 2D image processing method based on semi-classical analysis of the Schrödinger operator, utilizing eigenfunctions for image reconstruction and denoising, with a focus on parameter effects and numerical validation.

Contribution

It extends semi-classical Schrödinger operator analysis to two dimensions for image processing, providing a new approach for image reconstruction and denoising.

Findings

Effective image reconstruction demonstrated

Parameter effects on convergence analyzed

Numerical examples validate the method

Abstract

This paper extends to two dimensions the recent signal analysis method based on the semi-classical analysis of the Schrodinger operator. The generalization uses the separation of variables technique when writing the eigenfunctions of the Schrodinger operator. The algorithm is described and the effect of some parameters on the convergence of this method are numerically studied. Some examples on image reconstruction and denosing are illustrated.