A novel inverse scattering method using localized incidence with enhanced imaging resolution

This paper is concerned with reconstructing the shape of an acoustic obstacle from near-field measurements. Based on the use of the locally focusing waves with very narrow widths illuminating the obstacle, the boundary of the obstacle is reconstructed by a direct imaging algorithm. The stability of the imaging scheme is mathematically analyzed. Unlike the incident plane waves or point sources, the narrow-banded focusing wave combined with the direct imaging method brings several benefits in inverse scattering: (ⅰ) Focusing property. A focusing wave illuminates only a local part of the obstacle's boundary, which generates a spike-type imaging indicator for each incident direction; (ⅱ) High resolution. Reconstructing the boundary points within each beam illumination improves the quality of some well-known algorithms; (ⅲ) Fast and easy implementation. The imaging indicator can be formulated directly, without a solver for forward scattering or iterative updates. These promising features can be observed through our numerical experiments.