Deep Phaseless Imaging via Wirtinger Flow with Decoding Prior

We introduce a deep learning (DL) based network for imaging from intensity-only measurements using low dimensional encoded representations. Phaseless imaging constitutes a non-convex and ill-posed problem that is relevant to a wide range of applications, where accurate measurement of phase information is challenging. State-of-the-art methods solve the original non-convex optimization problem using sophisticated initialization schemes that lead to locally benign loss function topographies. However, these are commonly contingent upon high sample complexity and restrictive conditions on the forward maps, which limit their practical applicability. To circumvent fundamental limitations, we utilize a model-based deep network for phaseless imaging that implements a fixed-step size realization of gradient descent directly on the lower dimensional encoded representation domain. Accordingly, the iterative algorithm is combined with a non-linear encoder-decoder pair that govern the mapping between low dimensional representations and the image manifold of our interest. This results in feasible regimes beyond those dictated by the standard sufficient conditions of the exact recovery theory used in non-convex optimization. We empirically demonstrate the effectiveness of our lower dimensional formulation of signal recovery through numerical simulations on a number of practical deterministic imaging geometries at reduced sample complexities.