Deep Learning Initialized Phase Retrieval
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 inverse problems 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 traditional approaches to solve difficult scientific inverse problems.
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