Image reconstruction of reflectivity from short scan data

In reflectivity tomography, a weakly reflecting object that is immersed in an acoustically homogeneous background medium is interrogated with an infinitesimally short ultrasonic pulse and the corresponding reflected signal is measured at the source location as a function of time. The goal of reflectivity tomography is to reconstruct a function that describes the reflectivity of an inhomogeneous object, from knowledge of the reflected signal measured at different source-receiver positions. In this work, we identify symmetries in the reflectivity tomography data function and demonstrated that they can be exploited to reduce the amount of data that needs to be measured in order to accurately reconstruct the reflectivity function, propose and numerically investigate reconstruction algorithms for reconstructing the reflectivity function from a π-scheme data set.