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 quitereasonable profiles of scatterers in time-harmonic inverse acousticscattering without a priori knowledge of either the physical propertiesor the number of disconnected components of the scatterer. We shallfirst present a novel derivation of the DSM using far-field data,then carry out a systematic evaluation of the performances and distinctionsof the DSM using both near-field and far-field data. A newinterpretation from the physical perspective is provided based on somenumerical observations.It is shown from a variety of numerical experiments that the methodhas 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 efficiencywith only inner products involved.