Analysis of Kirchhoff migration and direct sampling method within far-field approximation: from the multi-static to the mono-static configuration

Abstract : A recently developed direct sampling method (DSM) is studied in the framework of multi-and mono-static configurations within the far-field hypothesis. A full analysis of the behavior of the DSM has not been provided yet in both cases even if, due to a lack of information compared to multi-static data, the mono-static configurations need an adapted analysis. Thanks to the theoretical analysis based on the asymptotic formula for far-field patterns and small obstacles hypothesis, the behavior of DSM is explained and the reason for which it failed in the mono-static configuration is identified. A modified DSM is then proposed and compared to the classical Kirchhoff migration technique (KM) in order to improve the imaging efficiency of the DSM approach. The theoretical results are supported by numerical experiments with synthetic data.