An Equivalent Distorted Born Iterative Method to Solve Inverse Scattering Problem Without Updating the Green's Function

Abstract

In this paper, an equivalent distorted Born iteration method (DBIM) is proposed to solve inverse scattering problem based on volume integral equation (VIE) method. For its forward problem, the object region is regarded as the scatterer and free space is considered to be the background, which relates to a free space Green's function. The equivalent DBIM inversion model is constructed base on the forward model which has the same convergent rate with the conventional DBIM. Differently, the integration kernel, the free space Green's function, remains unchanged in the equivalent DBIM while that of the conventional DBIM need to be computed and updated in every iterations. In this way, the computational complexity of the DBIM has been reduced remarkably, and it is easy to be employed in solving three-dimensional (3-D) inverse problem.