Deep learning for waveform estimation in passive synthetic aperture radar

We propose Deep Learning (DL) as a framework for simultaneous waveform estimation and image reconstruction in passive synthetic aperture radar (SAR). We consider a passive imaging scenario where the scene is illuminated by source of opportunity with known position, but transmitting an unknown waveform. Image reconstruction is then posed as a machine learning task for which a recurrent neural network (RNN) can be constructed by unfolding the iterations of a proximal gradient descent algorithm. We separate the unknown waveform from the known components of the forward model and parameterize the network operator by the waveform coefficients. The image estimate generated by the RNN is then mapped back to the data space by a linear decoder stage, so that the waveform coefficients are refined in an unsupervised manner using passive SAR measurements as training data. As a result, network becomes a recurrent auto-encoder. In this architecture, forward propagation recovers scene reflectivity, and backpropagation solves for waveform coefficients. The non-convex training routine is initialized using the partially known SAR forward model, which helps ensure that the optimization problem converges to a satisfactory optimal point.

I. Introduction

Deep learning has been the catalyst of significant advancements in various fields of engineering [1]. Most applications of deep learning consist of finding complex decision boundaries in high dimensional parameter spaces relying on large amounts of training data. We instead utilize deep learning to estimate transmitted waveforms and reconstruct focused images from scattered field data obtained using passive radar. We take an optimization perspective to deep learning, and view the network as an inversion operator between measurement and image spaces, for which we can learn parameters through training.