Simultaneous recovery of an obstacle and its excitation sources from near-field scattering data

TL;DR

This paper introduces a combined optimization and sampling approach to simultaneously identify obstacles and their incident sources from near-field scattering data, supported by theoretical analysis and numerical validation.

Contribution

It proposes a novel two-step sampling scheme with indicator functions and an optimization method for joint obstacle and source recovery, with proven convergence properties.

Findings

Effective obstacle and source recovery demonstrated through numerical examples.

The proposed method provides accurate initial guesses for the inverse problem.

Theoretical analysis confirms convergence and indicator behavior.

Abstract

This paper is concerned with the inverse problem of determining an obstacle and the corresponding incident point sources in the Helmholtz equation from near-field scattering data. An optimization method is proposed to simultaneously recover both the obstacle and source locations. Moreover, a two-step sampling scheme with novel indicator functions is proposed to produce a good initial guess for solving the optimization problem. Theoretically, we analyze the convergence properties of the optimization method and the indicating behaviors of the indicator functions. Several numerical examples are presented to show the effectiveness of the proposed method.