UWB Beam-Based Local Diffraction Tomography—Part II: The Inverse Problem

Abstract

This two-part article is concerned with the medium reconstruction using the beam-based tomographic inverse scattering. This Part II is based on the results of Part I that has dealt with the preprocessing phase. Specifically, we defined there the beam-frame representation of the scattered field and the corresponding processing windows that transform the scattering data to the beam domain. We have also derived the “local time-domain diffraction tomography” relation according to which the beam-domain data are directly related to the local Radon transform (LRT) of the medium. This local transform can be inverted and is used here for the local reconstruction of the medium via beam-domain filtered backpropagation. In this article, we define the filtered backpropagated beam waves and then reconstruct the medium in any sub-domain of interest (DoI) by aggregating the contributions of the backpropagated beams that pass in or near that DoI. Specifically, we use the class of isodiffracting beam waves, namely, the isodiffracting Gaussian beams (ID-GBs) and the isodiffracting pulse beams (ID-PBs) for the frequency- and time-domain formulations, respectively. Explicit expressions for the filtered backpropagated reconstruction kernels are given. The efficacy of the beam-domain approach for local backpropagation and reconstruction is demonstrated via numerical examples of the synthetic noisy data.