Accelerating the iterative inverse scattering algorithms by using the fast recursive aggregate T-matrix algorithm

A review and a convergence analysis of the Born and distorted Born iterative methods are given. The fast recursive aggregate T-matrix algorithm is reviewed and then applied to the solution of the direct scattering part in the iterative inverse scattering algorithms. Together with the conjugate gradient method in the inversion part of the iterative inverse scattering algorithms, the overall computational complexity for the iterative inverse scattering algorithms is reduced from O(N³) to O(N²), representing a significant reduction of their computational complexity. The resulting distorted Born iterative algorithm is demonstrated to have a high-resolution ability of reconstructing one- or two-pixel pulse objects.