Deep Learning based Phaseless SAR without Born Approximation

In this paper, we present a phase retrieval approach from intensity measurements using a Deep Learning (DL) based Wirtinger Flow (WF) algorithm for the case where the measurement model is non-linear, and this non-linearity depends on the unknown signal. In the context of synthetic aperture radar (SAR), this is relevant to the image reconstruction problem for the scenario where the Born approximation is no longer valid which results in multi-scattering effect within the extended target being imaged. Since we are adopting WF for DL based imaging, the underlying optimization problem is non-convex. However, unlike the WF algorithm, the unknown image is estimated from the measurement intensities in a learned encoding space with the goal of achieving effective reconstruction performance. The overall DL network is composed of an encoding network for determining a suitable initial value in the transformed space, a recurrent neural network (RNN) that models the steps of a gradient descent algorithm for an optimization problem, and a decoding network that can incorporate the generative image prior and transforms the encoded estimation from the RNN output to the original image space. Numerical results are included to verify feasibility of the proposed approach.