Deep Learning Initialized Phase Retrieval

Raunak Manekar, Zhong Zhuang, Kshitij Tayal, Vipin Kumar, Ju Sun

Abstract:

Phase retrieval (PR) consists of estimating 2D or 3D objects from their Fourier
magnitudes and takes a central place in scientific imaging. At present, most iterative methods for PR work well only when the initialization is close enough to
the solution and fail otherwise. But there has been no general way of obtaining
desired initialization. In this paper, we show that a carefully designed deep learning
pipeline can consistently generate reliable initialization, so that the subsequent
iterative methods can solve the PR problem and produce high-quality solutions.
Technically, PR is an inverse problem containing three forward symmetries, and
naive deployment of end-to-end deep learning for PR yields poor initialization.
We explain why the symmetries cause the learning difficulty and propose a novel
strategy that substantially improves the estimation. Overall, the proposed method
solves PR in regimes not accessible by the previous methods, and our work synergizes deep learning and iterative methods to solve a difficult scientific inverse
problem.