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.

I. Introduction

IN recent years, the growing availability of radio frequency sources of opportunity, such as radio, television and cell phone transmission stations, have lead to an increasing interest in passive radar applications [1]–[8]. Removing the need to have a dedicated transmitter, passive radar systems offer many advantages such as stealth, simplicity and lowered cost.