Some recent developments in the unique determinations in phaseless inverse acoustic scattering theory

Abstract

This article is an overview on some recent advances in the inverse scattering problems with phaseless data. Based upon our previous studies on the uniqueness issues in phaseless inverse acoustic scattering theory, this survey aims to briefly summarize the relevant rudiments comprising prototypical model problems, major results therein, as well as the rationale behind the basic techniques. We hope to sort out the essential ideas and shed further lights on this intriguing field.

Uniqueness in phaseless inverse electromagnetic scattering problem with known superposition of incident electric dipoles

“…Utilizing the reference sphere technique to prove the uniqueness was introduced for inverse acoustic scattering problems with phaseless far-field data in [32], and phaseless near-field data [33][34][35]. Recently, the reference sphere method was applied to other types of inverse scattering problems, such as the electromagnetic wave scattering [36], the elastic wave scattering [37], the acoustic-elastic coupling scattering [38].…”

A direct imaging method for the exterior and interior inverse scattering problems

“…Recently, inverse scattering problems without the phase information receive great interests. Some uniqueness results and numerical methods on the exterior inverse scattering problems with phaseless data can be found in [2,4,7,14,15,16,17,27,30,31].…”