Numerical method for the inverse interior scattering problem from phaseless data

Abstract

This paper is concerned with the inverse problem to determine the shape and location of an acoustically sound-soft cavity, or sound-hard cavity, or impedance cavity with known impedance function from phaseless data for one single source incidence. Based on representing scattered field by single-layer potential, a numerical method is presented for finding the unknown boundary of scatterers. Furthermore, we propose a Newton-type algorithm to recover a realvalued surface impedance from phaseless data. The efficient implementation of the method is described and the feasibility of the approach is illustrated by several numerical examples.

Uniqueness and numerical method for phaseless inverse diffraction grating problem with known superposition of incident point sources

“…It is worth mentioning that the data used in our numerical method requires much less information than in the uniqueness theorem. Numerical results for the inversion of various scattering profiles based on phaseless data can be found in recent papers [16,29,40] and references therein.…”