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.
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