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Solving Phase Retrieval with a Learned Reference

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Computer Vision – ECCV 2020 (ECCV 2020)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12375))

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Abstract

Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by leveraging some prior knowledge about the structure of the unknown image. The inherent ambiguities about shift and flip in the Fourier measurements make this problem especially difficult; and most of the existing methods use several random restarts with different permutations. In this paper, we assume that a known (learned) reference is added to the signal before capturing the Fourier amplitude measurements. Our method is inspired by the principle of adding a reference signal in holography. To recover the signal, we implement an iterative phase retrieval method as an unrolled network. Then we use back propagation to learn the reference that provides us the best reconstruction for a fixed number of phase retrieval iterations. We performed a number of simulations on a variety of datasets under different conditions and found that our proposed method for phase retrieval via unrolled network and learned reference provides near-perfect recovery at fixed (small) computational cost. We compared our method with standard Fourier phase retrieval methods and observed significant performance enhancement using the learned reference.

R. Hyder and Z. Cai—Equal contribution.

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Acknowledgment

The first two authors contributed equally in this work. This research was supported in parts by an ONR grant N00014-19-1-2264, DARPA REVEAL Program, and a Google Faculty Award.

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Authors and Affiliations

  1. University of California, Riverside, CA, 92521, USA

    Rakib Hyder, Zikui Cai & M. Salman Asif

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  1. Rakib Hyder
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  2. Zikui Cai
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  3. M. Salman Asif
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Correspondence to M. Salman Asif .

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Editors and Affiliations

  1. University of Oxford, Oxford, UK

    Andrea Vedaldi

  2. Graz University of Technology, Graz, Austria

    Horst Bischof

  3. University of Freiburg, Freiburg im Breisgau, Germany

    Thomas Brox

  4. University of North Carolina at Chapel Hill, Chapel Hill, NC, USA

    Jan-Michael Frahm

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Hyder, R., Cai, Z., Asif, M.S. (2020). Solving Phase Retrieval with a Learned Reference. In: Vedaldi, A., Bischof, H., Brox, T., Frahm, JM. (eds) Computer Vision – ECCV 2020. ECCV 2020. Lecture Notes in Computer Science(), vol 12375. Springer, Cham. https://doi.org/10.1007/978-3-030-58577-8_26

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  • DOI: https://doi.org/10.1007/978-3-030-58577-8_26

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