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Support Recovery in the Phase Retrieval Model: Information-Theoretic Fundamental Limit | IEEE Journals & Magazine | IEEE Xplore

Support Recovery in the Phase Retrieval Model: Information-Theoretic Fundamental Limit


Abstract:

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 suppor...Show More

Abstract:

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 information-theoretic fundamental limits under an approximate recovery criterion, considering both discrete and Gaussian models for the sparse non-zero entries, along with Gaussian measurement matrices. In both cases, our bounds provide sharp thresholds with near-matching constant factors in several scaling regimes on the sparsity and signal-to-noise ratio. As a key step towards obtaining these results, we develop new concentration bounds for the conditional information content of log-concave random variables, which may be of independent interest.
Published in: IEEE Transactions on Information Theory ( Volume: 66, Issue: 12, December 2020)
Page(s): 7887 - 7910
Date of Publication: 14 October 2020

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