Passive synthetic aperture radar imaging based on low-rank matrix recovery

We present a novel image formation method for passive synthetic aperture radar (SAR) imaging. The method is an alternative to Time Difference of Arrival (TDOA) based backprojection method. The TDOA based backprojection works under the assumption that the scene is composed of a single or a few widely separated point targets. The new method overcomes this limitation and can reconstruct heterogenous scenes with extended targets. We assume that a scene of interest is illuminated by a stationary transmitter of opportunity with known illumination direction, but unknown location. We consider two airborne receivers collecting back-scattered data from the scene. We correlate the fast-time measurements from both receivers at each slow-time. The correlation process removes the transmitter dependency from the phase of the forward model under the small scene and far-field assumptions. We then define a linear model that maps the tensor product of the scene reflectivity with itself to the correlated measurements. The resulting inverse problem involves recovering a rank-one matrix from correlated measurements. We reconstruct the scene reflectivity by low-rank matrix recovery techniques. Numerical simulations show that the new method is superior to TDOA based backprojection for realistic SAR scenes.