Beam Domain Formulation for Tomographic Inverse Scattering. Part II: The Inverse Problem

We present a local UWB inverse scattering approach using pulsed-beam wave processing. The theory utilizes a phase-space set of shifted titled and delayed pulse-beams which has been shown previously to constitute a frame at any z= canst. plane, thus providing a local alternative to the plane-wave spectrum. This pulsed-beam frame (PBF) is used here to expend the scattering data and then back-propagate it for local reconstruction of the medium. In this paper we explore the beam-domain representation of the scattered fields and show, within the Born approximation, that the beam-domain data correspond to local Radon transform (LRT) of the medium. This result will be used in Part II of this paper for local reconstruction within this subdomain.