A quasi-backscattering problem for inverse acoustic scattering in the Born regime

We consider the problem of detecting three-dimensional inclusions from quasi-backscattering far field data generated by an incident field of time-harmonic fixed frequency plane waves modeled with the Born approximation. We assume only partial far field data is known and use a sampling-type method to reconstruct small obstacles and extended spherical obstacles. In particular, at the location of a device transmitting an incident wave, we assume far field data is collected only along a line extending a short distance from the transmitting device. Several numerical examples are provided to demonstrate the effectiveness of the approach.