On the Information-Theoretic Limits of Noisy Sparse Phase Retrieval

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Truong, LV 
Scarlett, J 

The support recovery problem consists of determining a sparse subset of variables that is relevant in generating a set of observations. In this paper, we study the support recovery problem in the phase retrieval model consisting of noisy phaseless measurements, which arises in a diverse range of settings such as optical detection, X-ray crystallography, electron microscopy, and coherent diffractive imaging. Our focus is on informationtheoretic fundamental limits under an approximate recovery criterion, with Gaussian measurements and a simple discrete model for the sparse non-zero entries. Our bounds provide sharp thresholds with near-matching constant factors in several scaling regimes on the sparsity and signal-to-noise ratio.

46 Information and Computing Sciences, 4006 Communications Engineering, 40 Engineering, 4603 Computer Vision and Multimedia Computation
Journal Title
2019 IEEE Information Theory Workshop, ITW 2019
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2019 IEEE Information Theory Workshop (ITW)
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