A Fully Polarimetric Multilevel Fast Spectral Domain Algorithm for 3-D Imaging With Irregular Sample Locations

A fully polarimetric frequency-wavenumber domain algorithm for 3-D imaging using the synthetic aperture radar technique with irregular sample locations is introduced. At its core, the algorithm works with a multilevel plane-wave representation and relies on some of the concepts of the multilevel fast multipole method (MLFMM). By utilizing a recursive segmentation scheme, the presented algorithm efficiently handles irregular observation locations, which can vary along all three dimensions in space. The basic idea is to divide the observation region into subdomains of decreasing size, until the calculation of the spectral domain representation of the observation data in the individual subdomains by a discrete Fourier transform (DFT) without further acceleration is feasible. The overall uniformly sampled spectral representation of the observation data is then obtained by hierarchical aggregation of the subdomain spectra. The probe influence is fully compensated by the combined processing of several polarizations and solving small linear systems of equations related to the frequency-wavenumber samples on the coarsest level. The focused image is finally computed by fast Fourier transforms (FFTs). This approach, as opposed to conventional coherent back-projection algorithms (BPAs), allows for a fully polarimetric description of the scattering object and achieves good efficiency without loss of accuracy. To show the effectiveness of the algorithm, imaging results obtained from numerical simulations as well as from the evaluation of measured field data are presented and discussed.