Three-dimensional microwave imaging by local shape function method with CGFFT

This paper proposes the local shape function method (LSF) with CGFFT T-matrix method to reconstruct object permittivity in three dimensions. The algorithm accounts for multiple scattering by casting the inverse problem into a minimization problem, and iteratively minimizing the difference between the measured and calculated fields from the current object profile. In 3D scattering, the dyadic Green's function singularity needs a more cautious treatment, while LSF avoids the singularity problem by matching the boundary condition at the surface of each subscatterer instead of at the center, which yields a less nonlinear inverse problem compared with other techniques. At each step of the minimization process, numerous forward problems corresponding to different transmitters have to be solved efficiently. Thus, CGFFT T-matrix method is chosen to achieve this end, and the computational cost of the algorithms can be O(N_TN log N), where N_T and N are the number of transmitters and that of discretized cells, respectively. Some numerical examples are presented to show that LSF can reconstruct the permittivity with high fidelity.