A solution to the inverse problem of non-coherent image propagation

TL;DR

This paper derives a Fourier-based formula for non-coherent wave field propagation, providing a theoretical solution to the inverse problem, but highlights practical challenges due to noise amplification in numerical implementations.

Contribution

It introduces a Fourier-based theoretical solution to the inverse problem of non-coherent image propagation and discusses the limitations caused by noise in numerical solutions.

Findings

Theoretical solution derived using Fourier transformation.

Numerical solutions face rapid SNR decrease.

Numerical examples illustrate the phenomena.

Abstract

We derive a formula for the non-coherent wave field propagation in terms of the Fourier transformation. As a result, we find a theoretical solution of the inverse problem of image propagation in non-coherent case. However, the practical solution of the inverse problem in a numerical way leads to rapidly decreasing SNR. We also discuss origin and behavior of that phenomenon. Some numerical examples are presented.