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 backprojection 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 semidefinite 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.1932-4553 (c)
We introduce a deep learning (DL) framework for inverse problems in imaging, and demonstrate the advantages and applicability of this approach in passive synthetic aperture radar (SAR) image reconstruction. We interpret image reconstruction as a machine learning task and utilize deep networks as forward and inverse solvers for imaging. Specifically, we design a recurrent neural network (RNN) architecture as an inverse solver based on the iterations of proximal gradient descent optimization methods. We further adapt the RNN architecture to image reconstruction problems by transforming the network into a recurrent auto-encoder, thereby allowing for unsupervised training. Our DL based inverse solver is particularly suitable for a class of image formation problems in which the forward model is only partially known. The ability to learn forward models and hyper parameters combined with unsupervised training approach establish our recurrent auto-encoder suitable for real world applications.We demonstrate the performance of our method in passive SAR image reconstruction. In this regime a source of opportunity, with unknown location and transmitted waveform, is used to illuminate a scene of interest. We investigate recurrent autoencoder architecture based on the 1 and 0 constrained leastsquares problem. We present a projected stochastic gradient descent based training scheme which incorporates constraints of the unknown model parameters. We demonstrate through extensive numerical simulations that our DL based approach out performs conventional sparse coding methods in terms of computation and reconstructed image quality, specifically, when no information about the transmitter is available.
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