Uniqueness of a phaseless inverse scattering problem for the generalized 3-D Helmholtz equation

TL;DR

This paper proves a uniqueness theorem for a 3-D inverse scattering problem where only the magnitude of the scattered wave is measured, addressing the challenge of phase retrieval in wave-based imaging.

Contribution

It establishes the first uniqueness result for the phaseless inverse scattering problem for the generalized 3-D Helmholtz equation.

Findings

Proved uniqueness of the solution with phaseless data

Addressed the phase retrieval challenge in inverse scattering

Contributed to wave-based imaging theory

Abstract

An inverse scattering problems for the 3-D generalized Helmholtz equation is considered. Only the modulus of the complex valued scattered wave field is assumed to be measured and the phase is not measured. Uniqueness theorem is proved.