A Coefficient Inverse Problem with a Single Measurement of Phaseless Scattering Data

Abstract

We present a reconstruction method for solving a 3D coefficient inverse problem with a single measurement of phaseless scattering data. These are multifrequency data generated by a single direction of the incident plane wave. Our method consists of two stages, each of which is challenging in its own right. The first stage is the problem of the reconstruction of the wave field itself on the measurement plane from the measured intensity. In this stage, we prove a uniqueness result and study a numerical method for this reconstruction. After obtaining the approximate scattered field on the measurement plane, in the second stage, we exploit our newly developed globally convergent numerical method to solve the coefficient inverse problem with the phased scattering data. Our two-stage method does not require any advanced information about the true solution of the phaseless coefficient inverse problem. Numerical examples are presented to demonstrate the performance of the method.