Synthetic Aperture Imaging and Motion Estimation Using Tensor Methods

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 subapertures. We then apply a tensor robust principal component analysis (TRPCA) to the tensor data which separates it into the parts coming from the stationary and moving reflectors. A key feature of the proposed algorithm is the use of a Fourier-based tensor nuclear norm which is well adapted to the SAR data structure. Images are then 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.