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 in1–3 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.
Bariscan Yonel, Eric Mason, and Birsen Yazici, "Deep learning for waveform estimation in passive synthetic aperture radar imaging," Proc. SPIE 10647, Algorithms for Synthetic Aperture Radar Imagery XXV, 106470E (Presented at SPIE Defense + Security: April 19, 2018; Published: 27 April 2018); https://doi.org/10.1117/12.2305882.
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