Beam-based time-domain tomographic inverse scattering

We present a novel beam-based theory for local time-dependent tomographic inverse scattering. The formulation is structured upon the recently introduced concept of “pulsed-beam frame” (PBF). The PBF is a properly constructed phase-space set of iso-diffracting pulsed-beam waves (ID-PB) that constitutes a frame everywhere in the propagation domain. As such, the PBF can be used not only for local expansion of the excitation sources, which is the common application of the beam frames [1], but also for local expansion of the medium inhomogeneities and of the induced sources [2]. In the present context of inverse scattering, the PBF is used to expand the time-dependent scattered fields (the data) and then to back-propagate this data and to locally reconstruct the medium.