Imaging of location and geometry for extended targets using the response matrix

In this paper, we study how to image both the location and the shape of extended targets using the response matrix obtained from inter-element response of an active array of transducers. In particular, the time reversal technique is used for efficient initial localization of the target and the level set method is used for shape reconstruction. We then show how to couple the location estimation and shape reconstruction in a complementary way to improve accuracy for range estimation. Resolution analysis for active arrays in remote sensing regime is also presented. We illustrate with numerical experiments which show that the method is capable of imaging objects with complicated shapes and that the method is robust with respect to noisy data.