Renormalized Born Inversion

Abstract

Typical ultrasound B-scan processing relies on 1D Born inversion. That is, the images displayed represent grey-scale maps of Born inversion profiles: impedance changes are proportional to backscattered amplitude, and depth x=c/sub 0/t/2. These approximations yield useful images. By systematically exploiting the implicit assumptions that underlie the success of traditional imaging, however, significant improvements can be made to better image quality with little or no additional processing expense. In the context of perturbation theory, Born inversion represents a regular perturbation expansion in powers of epsilon , the scale of medium inhomogeneity. Such an expansion, however, is nonuniform in distance and time. It is this nonuniformity that can be easily corrected to yield a method that is both simple and accurate. The approach we shall explore is renormalization. We redefine the order zero operator to remove nonuniformity from the expansion. The first term is as simple to obtain as in regular Born scattering, but the approximation is uniformly valid in space and time. Of course, iterating the process might improve the approximation further, but we are concerned here with methods that can be applied in real-time. The renormalization that we choose is consistent with the WKB ansatz. After renormalization, our order zero operator depends implicitly on the unknown sound speed c(x). In order to evaluate this dependence, we must assume that changes in c(x) are directly correlated to changes in the impedance. Soft tissue data shows such a correlation