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

Abstract

The computational efficiency in 3D microwave inversion is addressed by extending the idea in a recent paper for 2D problems to 3D vector fields. The method proposed here is based on recently developed fast computation algorithm for 3D dielectric scattered field. This fast algorithm combines biconjugate gradient method with fast Fourier transform (BCG-FFT). A weighted mean square residual combined with 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 when the BCG-FFT algorithm is used to implement the operations of the Frechet derivative operator. Some computer simulation results demonstrate the efficiency of this algorithm, especially when the number of illumination angles is limited.