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The stochastic geometry of unconstrained one-bit data compression

François Baccelli 1 Eliza O’reilly 2
1 DYOGENE - Dynamics of Geometric Networks
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique : UMR 8548, Inria de Paris
Abstract : A stationary stochastic geometric model is proposed for analyzing the data compression method used in one-bit compressed sensing. The data set is an unconstrained stationary set, for instance all of R^n or a stationary Poisson point process in R^n. It is compressed using a stationary and isotropic Poisson hyperplane tessellation, assumed independent of the data. That is, each data point is compressed using one bit with respect to each hyperplane, which is the side of the hyperplane it lies on. This model allows one to determine how the intensity of the hyperplanes must scale with the dimension n to ensure sufficient separation of different data by the hyperplanes as well as sufficient proximity of the data compressed together. The results have direct implications in compressed sensing and in source coding.
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Submitted on : Friday, December 20, 2019 - 9:07:33 PM
Last modification on : Tuesday, May 4, 2021 - 2:06:02 PM

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François Baccelli, Eliza O’reilly. The stochastic geometry of unconstrained one-bit data compression. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2019, 24, ⟨10.1214/19-EJP389⟩. ⟨hal-02422200⟩



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