Method of Formal Parameter Expansion for Acoustical Inverse Scattering Problems

Abstract

In acoustical diffraction tomography, the inverse scattering perturbation theory, especially the first-order Born perturbation approximation has its advantages: comparatively simple calculations. That is why it has been used in diffraction tomography in many fields, such as in medical and seismic imaging ¹⁻². But this method has its disadvantages: severe limitations on scatterers, i.e., objects to be imaged³⁻⁵. These limitations are impracticable in the most cases, such as in medical imaging and petroleum exploration. The use of high-order, for example, second-order Born perturbation algorithms can reduce these limitations to a certain extent. But they also failed to reconstruct the object with good accuracy in many cases ⁵. In such cases, the third- or even higher-order Born approximation must be taken into ac- count. This will result in more and more tedious calculations. Can and how do we find a method which needs comparatively simple calculations and has not severe limitations on objects?