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

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 behaviors of the indicator functions. Several numerical examples are presented to show the effectiveness of the proposed method.