Practical Phase Retrieval: Low-Photon Holography with Untrained Priors

Hannah Lawrence, David Barmherzig, Henry Li, Michael Eickenberg, Marylou Gabrié

Keywords: inverse problems, phase retrieval, generative priors, holography, coherent diffraction imaging

Abstract: Phase retrieval is the inverse problem of recovering a signal from magnitude-only Fourier measurements, and underlies numerous imaging modalities, such as Coherent Diffraction Imaging (CDI). A variant of this setup, known as holography, includes a reference object that is placed adjacent to the specimen of interest before measurements are collected. The resulting inverse problem, known as holographic phase retrieval, is well-known to have improved problem conditioning relative to the original. This innovation, i.e. Holographic CDI, becomes crucial at the nanoscale, where imaging specimens such as viruses, proteins, and crystals require low-photon measurements. This data is highly corrupted by Poisson shot noise, and often lacks low-frequency content as well. In this work, we introduce a dataset-free deep learning framework for holographic phase retrieval adapted to these challenges. The key ingredients of our approach are the explicit and flexible incorporation of the physical forward model into the automatic differentiation procedure, the Poisson log-likelihood objective function, and an optional untrained deep image prior. We perform extensive evaluation under realistic conditions. Compared to competing classical methods, our method recovers signal from higher noise levels and is more resilient to suboptimal reference design, as well as to large missing regions of low-frequencies in the observations. To the best of our knowledge, this is the first work to consider a dataset-free machine learning approach for holographic phase retrieval.

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One-sentence Summary: We propose a method for holographic phase retrieval with a deep image prior, and improve reconstruction under challenging experimental conditions, including high noise and missing data.

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