Unrolled Wirtinger Flow with Deep Decoding Priors for Phaseless Imaging

TL;DR

This paper presents a deep learning approach that unrolls the Wirtinger Flow algorithm with a learned decoding prior for phaseless imaging, providing theoretical guarantees and demonstrating improved sample efficiency in synthetic aperture imaging.

Contribution

It introduces a novel deep unrolled Wirtinger Flow method with learned encoding and decoding networks, along with an exact recovery theory for intensity-only imaging.

Findings

Guarantees exact recovery under certain conditions.

Shows improved sample complexity in synthetic aperture imaging.

Establishes relation between Lipschitz constants and convergence rate.

Abstract

We introduce a deep learning (DL) based network and an associated exact recovery theory for imaging from intensity-only measurements. The network architecture uses a recurrent structure that unrolls the Wirtinger Flow (WF) algorithm with a deep decoding prior that enables performing the algorithm updates in a lower dimensional encoded image space. We use a separate deep network (DN), referred to as the encoding network, for transforming the spectral initialization used in the WF algorithm to an appropriate initial value for the encoded domain. The unrolling scheme models a fixed number of iterations of the underlying optimization algorithm into a recurrent neural network (RNN). Furthermore, it facilitates simultaneous learning of the parameters of the decoding and encoding networks and the RNN. We establish a sufficient condition to guarantee exact recovery under deterministic forward models. Additionally, we demonstrate the relation between the Lipschitz constants of the trained decoding prior and encoding networks to the convergence rate of the WF algorithm. We show the practical applicability of our method in synthetic aperture imaging using high fidelity simulation data from the PCSWAT software. Our numerical study shows that the decoding prior and the encoding network facilitate improvements in sample complexity.