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2019 The stochastic geometry of unconstrained one-bit data compression
François Baccelli, Eliza O’Reilly
Electron. J. Probab. 24: 1-27 (2019). DOI: 10.1214/19-EJP389


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 $\mathbb{R} ^{n}$ or a stationary Poisson point process in $\mathbb{R} ^{n}$. 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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François Baccelli. Eliza O’Reilly. "The stochastic geometry of unconstrained one-bit data compression." Electron. J. Probab. 24 1 - 27, 2019.


Received: 25 April 2019; Accepted: 5 November 2019; Published: 2019
First available in Project Euclid: 3 December 2019

zbMATH: 07142932
MathSciNet: MR4040998
Digital Object Identifier: 10.1214/19-EJP389

Primary: 60D05
Secondary: 52A22, 68P30, 94A34


Vol.24 • 2019
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