Direct Imaging of Layered Media with SISO Data Using Reduced Order Models

We present a direct nonlinear imaging scheme for layered media with single-input single-output (SISO) data. This scheme is based on the reduced order model (ROM) approach, which transforms the measured data into its corresponding single scattering component. To construct ROMs with only SISO data, we enrich the SISO data by adding auxiliary sensors and estimating their measurements with the assumption that the measurements for different sensors only differ in arrival time and amplitude. The feasibility of this scheme is validated with a 2D numerical example.