Localization of small obstacles from back-scattered data at limited incident angles with full-waveform inversion

We investigate numerically the inverse problem of locating small circular obstacles in a homogeneous medium from multi-frequency back-scattered data limited to four angles of incidence. The main novelty of our paper is working with the position of the obstacles as parameter space in the frame work of full-waveform inversion (FWI) procedure. The computational cost of FWI is lowered by using a method based on single-layer potential. Reconstruction results are shown up to twenty-four obstacles, from initial guesses allowed to be far from the target. In experiments with six obstacles, we supplement the reconstruction with an analysis of the performance of the nonlinear conjugate gradient and quasi-Newton methods, in used with various line search algorithms.