Reconstruction algorithms of an inverse source problem for the Helmholtz equation

Abstract

In this paper, we study an inverse source problem for the Helmholtz equation from measurements. The purpose of this paper is to reconstruct the salient features of the hidden sources within a body. We propose three stable reconstruction algorithms to detect the number, the location, the size, and the shape of the hidden sources along with compact support from a single measurement of near-field Cauchy data on the external boundary. This problem is nonlinear and ill-posed; thus, we should consider regularization techniques in reconstruction algorithms. We give several numerical experiments to demonstrate the viability of our proposed reconstruction algorithms.