On the Information-Theoretic Limits of Noisy Sparse Phase Retrieval
2019 IEEE Information Theory Workshop, ITW 2019
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Truong, L., & Scarlett, J. (2019). On the Information-Theoretic Limits of Noisy Sparse Phase Retrieval. 2019 IEEE Information Theory Workshop, ITW 2019 https://doi.org/10.1109/ITW44776.2019.8989363
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.
External DOI: https://doi.org/10.1109/ITW44776.2019.8989363
This record's URL: https://www.repository.cam.ac.uk/handle/1810/301725
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