  This study concentrates on advancing mathematical and computational
methodology for radar tomography imaging in which the unknown volumetric
velocity distribution of a wave within a bounded domain is to be reconstructed.
Our goal is to enable effective simulation and inversion of a large amount of
full-wave data within a realistic 2D or 3D geometry. For propagating and
inverting the wave, we present a rigorous multigrid-based forward approach
which utilizes the finite-difference time-domain method and a nested finite
element grid structure. Based on the multigrid approach, we introduce and
validate a multiresolution algorithm which allows regularization of the unknown
distribution through a coarse-to-fine inversion scheme. In this approach,
sparse signals can be effectively inverted, as the coarse fluctuations are
reconstructed before the finer ones. Furthermore, the number of nonzero entries
in the system matrix can be compressed and thus the inversion procedure can be
speeded up. As a test scenario we investigate satellite-based asteroid interior
reconstruction. We use both full-wave and projected wave data and estimate the
accuracy of the inversion under different error sources: noise and positioning
inaccuracies. The results suggest that the present full-wave inversion approach
allows recovering the interior with a single satellite recording backscattering
data. It seems that robust results can be achieved, when the peak-to-peak
signal-to-noise ratio is above 10 dB. Furthermore, it seems that reconstructing
the deep interior can be enhanced if two satellites can be utilized in the
measurements.
