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

摘要

Reconstruction algorithm and its numerical examples of acoustical tomography based on the second-order Rytov transform perturbation approximation are presented. The Rytov transform reconstruction algorithms are different from ones based on the Born transform, because the generalized scattering wave is involved, and the Sommerfeld radiation conditions are not applicable to the differential form. Therefore, the Rytov transform must be introduced into the integral form instead of the differential form. The reconstruction algorithm in the first-order Rytov approximation is similar in form to one in the first-order Born approximation, but the algorithm in the second-order Rytov approximation is different in form from its counterpart. Also, comparisons of these reconstruction algorithms are given, and they show the differences between these algorithms.