A coefficient inverse problem with a single measurement of phaseless scattering data

TL;DR

This paper introduces a two-stage numerical method for a 3D coefficient inverse problem using single-measurement phaseless scattering data, involving reconstruction of the scattered field and a globally convergent inverse algorithm.

Contribution

It develops a novel two-stage approach combining phase retrieval and a globally convergent inverse method for phaseless data in 3D scattering problems.

Findings

Successful numerical reconstruction of scattered fields from intensity data.

Effective solution of the inverse problem with demonstrated numerical examples.

Validation that the method can approximate electric fields under certain conditions.

Abstract

This paper is concerned with a numerical method for a 3D coefficient inverse problem with phaseless scattering data. These are multi-frequency data generated by a single direction of the incident plane wave. Our numerical procedure consists of two stages. The first stage aims to reconstruct the (approximate) scattered field at the plane of measurements from its intensity. We present an algorithm for the reconstruction process and prove a uniqueness result of this reconstruction. After obtaining the approximate scattered field, we exploit a newly developed globally convergent numerical method to solve the coefficient inverse problem with the phased scattering data. The latter is the second stage of our algorithm. Numerical examples are presented to demonstrate the performance of our method. Finally, we present a numerical study which aims to show that, under a certain assumption, the solution of the scattering problem for the 3D scalar Helmholtz equation can be used to approximate the component of the electric field which was originally incident upon the medium.