Application of the Multiplicative Regularized Gauss-Newton Algorithm for Three-Dimensional Microwave Imaging

We apply the so-called multiplicative regularized Gauss-Newton inversion algorithm for solving three-dimensional electromagnetic microwave inverse problems. This inversion algorithm automatically adjusts the regularization parameter and when combined with the total variation type regularization function, it can provide inversion results with excellent edge-preserving characteristics. In addition, in order to deal with an extensive memory requirement for the Gauss-Newton method, we employ an implicit Jacobian calculation scheme. By using this scheme we do not have to explicitly store the Jacobian matrix. Hence, we are able to significantly reduce the memory requirement of the Gauss-Newton method albeit at an additional computational overhead. Furthermore, in order to be able to handle a large scale computational problem, both the forward and the inversion algorithms are parallelized using the MPI library, where we obtain a nearly linear speedup factor. We demonstrate efficiency and robustness of this algorithm by inverting synthetic data, Fresnel experimental data, and biomedical experimental data.