Uniqueness of two phaseless inverse acoustics problems in 3-d

TL;DR

This paper proves the uniqueness of determining the sound speed in 3D inverse acoustic problems using only the magnitude of the scattered wave field, without phase information, which is a significant advancement in inverse problems.

Contribution

It introduces a novel uniqueness result for 3D inverse acoustic problems with phaseless measurements, expanding the understanding of inverse problems with limited data.

Findings

Proves uniqueness of sound speed reconstruction with phaseless data

Demonstrates that only the modulus of the scattered wave field suffices for unique determination

Advances inverse acoustic theory by relaxing measurement requirements

Abstract

Uniqueness is proven for two 3-d inverse problems of the determination of the spatially distributed sound speed in the frequency dependent acoustic PDE. The main new point is the assumption that only the modulus of the scattered complex valued wave field is measured on a certain set.