A Fast Algorithm of Cross-Correlated Contrast Source Inversion in Homogeneous Background Media

Nonlinear iterative inversion methods are computationally expensive, which leads to limited applications. In this article, a fast algorithm of the cross-correlated contrast source inversion (CC-CSI) method is proposed. By assuming a homogeneous background medium, the task of solving systems of linear equations, the most time-consuming part of the CC-CSI method, has been efficiently implemented with several fast Fourier transforms (FFTs) and inverse FFTs (IFFTs) for transverse magnetic (TM), transverse electric (TE), and 3-D inversion, respectively. Theoretical analysis and real experiments demonstrate that the inversion efficiency of CC-CSI has been improved dramatically in comparison to the strategies of LU decomposition and the Biconjugate gradient (Bicg) algorithm. Specifically, the inversion speed of the proposed fast CC-CSI algorithm is at least one order of magnitude higher than using the latter two approaches in 3-D inversion, while the memory requirement of the proposed algorithm is intermediary and acceptable. Furthermore, the proposed fast scheme is also applicable to all the inversion methods which are related to computing the electric fields directly from the contrast sources in homogeneous background media.