  We consider a synthetic aperture imaging configuration, such as synthetic
aperture radar (SAR), where we want to first separate reflections from moving
targets from those coming from a stationary background, and then to image
separately the moving and the stationary reflectors. For this purpose, we
introduce a representation of the data as a third order tensor formed from data
coming from partially overlapping sub-apertures. We then apply a tensor robust
principal component analysis (TRPCA) to the tensor data which separates them
into the parts coming from the stationary and moving reflectors. Images are
formed with the separated data sets. Our analysis shows a distinctly improved
performance of TRPCA, compared to the usual matrix case. In particular, the
tensor decomposition can identify motion features that are undetectable when
using the conventional motion estimation methods, including matrix RPCA. We
illustrate the performance of the method with numerical simulations in the
X-band radar regime.
