  We study synthetic aperture radar (SAR) imaging and motion estimation of
complex scenes consisting of stationary and moving targets. We use the classic
SAR setup with a single antenna emitting signals and receiving the echoes from
the scene. The known motion estimation methods for such setups work only in
simple cases, with one or a few targets in the same motion. We propose to
extend the applicability of these methods to complex scenes, by complementing
them with a data pre-processing step intended to separate the echoes from the
stationary targets and the moving ones. We present two approaches. The first is
an iteration designed to subtract the echoes from the stationary targets one by
one. It estimates the location of each stationary target from a preliminary
image, and then uses it to define a filter that removes its echo from the data.
The second approach is based on the robust principle component analysis (PCA)
method. The key observation is that with appropriate pre-processing and
windowing, the discrete samples of the stationary target echoes form a low rank
matrix, whereas the samples of a few moving target echoes form a high rank
sparse matrix. The robust PCA method is designed to separate the low rank from
the sparse part, and thus can be used for the SAR data separation. We present a
brief analysis of the two methods and explain how they can be combined to
improve the data separation for extended and complex imaging scenes. We also
assess the performance of the methods with extensive numerical simulations.
