3D inhomogeneous inversion for microwave imaging using distorted Born iterative method and BCG-FFT

Solving inverse scattering problem has many practical applications. For three dimensional problems, the computational complexity of model-based inversion algorithms has become a challenge. This paper addresses the computational efficiency in 3D microwave inversion by extending the idea of Chew and Liu (see IEEE Trans. on Geoscience and Remote Sensing, vol.32, no.4, p.878, 1994) for 2D problems to 3D vector fields. The method proposed is based on a fast computation algorithm for 3D dielectric scattered field. This fast algorithm combines the biconjugate gradient method with fast Fourier transform (BCG-FFT). A weighted mean square residual combined with a Tikhonov regularization is used to measure the goodness of the reconstructed results and the optimal solution is searched iteratively using a conjugate gradient procedure. The computational complexity of the inverse process is analyzed. Some computer simulation results demonstrate the efficiency of this algorithm, especially when the number of illumination angles is limited.