Acoustical tomography based on the second-order born transform perturbation approximation

In this paper, reconstruction algorithms and their numerical examples of acoustical tomography based on the second-order Born transform perturbation approximation are presented, The reconstruction algorithms in the second-order Born approximation are similar in form to those in the first-order Born approximation, Replacing the angular spectrum of the scattered wave in the first-order case by the result of applying a first-order operator to the angular spectrum of the scattered wave or applying a second-order operator to the angular spectrum of the incident wave leads to the second-order reconstruction algorithms, Also, comparisons of reconstruction algorithms of the first- and second-order Born approximations are given, and they show that the second-order Born approximation algorithms have a distinct advantage over the first-order approximations in many cases.