We propose Deep Learning (DL) as a framework for performing simultaneous waveform estimation and image reconstruction in passive synthetic aperture radar (SAR). We interpret image reconstruction as a machine learning task for which a deep recurrent neural network (RNN) can be constructed by unfolding the iterations of a proximal gradient descent algorithm. We formulate the problem by representing the unknown waveform in a basis, and extend the recurrent auto-encoder architecture we proposed in<sup>1–3 </sup>by modifying the parameterization of the RNN to perform estimation of waveform coefficients, instead of unknown phase components in the forward model. Under a convex prior on the scene reflectivity, the constructed network serves as a convex optimizer in forward propagation, and a non-convex optimizer for the unknown waveform coefficients in backpropagation. With the auto-encoder architecture, the unknowns of the problem are estimated by operations only in the data domain, performed in an unsupervised manner. The highly non-convex problem of backpropagation is guided to a feasible solution over the parameter space by initializing the network with the known components of the SAR forward model. Moreover, prior information regarding the waveform can be incorporated during initialization. We validate the performance of our method with numerical simulations.
The recent success of deep learning has lead to growing interest in applying these methods to signal processing problems. This paper explores the applications of deep learning to synthetic aperture radar (SAR) image formation. We review deep learning from a perspective relevant to SAR image formation. Our objective is to address SAR image formation in the presence of uncertainties in the SAR forward model. We present a recurrent auto-encoder network architecture based on the iterative shrinkage thresholding algorithm (ISTA) that incorporates SAR modeling. We then present an off-line training method using stochastic gradient descent and discuss the challenges and key steps of learning. Lastly, we show experimentally that our method can be used to form focused images in the presence of phase uncertainties. We demonstrate that the resulting algorithm has faster convergence and decreased reconstruction error than that of ISTA.
In this paper we present a method for passive radar detection of ground moving targets using sparsely distributed apertures. We assume the scene is illuminated by a source of opportunity and measure the backscattered signal. We correlate measurements from two different receivers, then form a linear forward model that operates on a rank one, positive semi-definite (PSD) operator, formed by taking the tensor product of the phase-space reflectivity function with its self. Utilizing this structure, image formation and velocity estimation are defined in a constrained optimization framework. Additionally, image formation and velocity estimation are formulated as separate optimization problems, this results in computational savings. Position estimation is posed as a rank one PSD constrained least squares problem. Then, velocity estimation is performed as a cardinality constrained least squares problem, solved using a greedy algorithm. We demonstrate the performance of our method with numerical simulations, demonstrate improvement over back-projection imaging, and evaluate the effect of spatial diversity.