Passive Synthetic Aperture Radar Imaging Using Low-Rank Matrix Recovery Methods

We present a novel image formation method for passive synthetic aperture radar (SAR) imaging. The method is an alternative to widely used time difference of arrival (TDOA) or correlation-based backprojection method. These methods work 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 heterogeneous scenes with extended targets. We assume that the scene of interest is illuminated by a stationary transmitter of opportunity with known illumination direction, but unknown location. We consider two airborne receivers and correlate the fast-time bistatic measurements at each slow-time. This correlation process maps the tensor product of the scene reflectivity with itself to the correlated measurements. Since this tensor product is a rank-one positive semi-definite operator, the image formation lends itself to low-rank matrix recovery techniques. Taking into account additive noise in bistatic measurements, we formulate the estimation of the rank-one operator as a convex optimization with rank constrain. We present a gradient-descent based iterative reconstruction algorithm and analyze its computational complexity. Extensive numerical simulations show that the new method is superior to correlation-based backprojection in reconstructing extended and distributed targets with better geometric fidelity, sharper edges, and better noise suppression.