A Direct Sampling Method for Inverse Scattering Using Far-field Data

This work is concerned with a direct sampling method (DSM) for inverse acoustic scattering problems using far-field data. Using one or few incident waves, the DSM provides quite reasonable profiles of scatterers in timeharmonic inverse acoustic scattering without a priori knowledge of either the physical properties or the number of disconnected components of the scatterer. We shall first present a novel derivation of the DSM using far-field data, then carry out a systematic evaluation of the performances and distinctions of the DSM using both near-field and far-field data. A new interpretation from the physical perspective is provided based on some numerical observations. It is shown from a variety of numerical experiments that the method has several interesting and promising potentials: a) ability to identify not only medium scatterers, but also obstacles, and even cracks, using measurement data from one or few incident directions, b) robustness with respect to large noise, and c) computational efficiency with only inner products involved. MSC (AMS 2010): 35R30, 41A27, 78A46