Reflectivity tomography using temporally truncated data

Ultrasonic reflectivity tomography is an imaging technique that aims to reconstruct a function that describes the reflectivity of an inhomogeneous object. Conventional reconstruction algorithms require that backscattered data be measured for all time 0 ≤ t < ∞ and at all source-receiver locations residing on a circle that encloses the object to be imaged. In this work, we examine the reconstruction problem using backscattered data that is temporally truncated. We reveal that, under certain conditions, an exact image can be reconstructed using temporally truncated data. We numerically validate our theoretical assertions.