The stochastic geometry of unconstrained one-bit data compression
- Creators
- Baccelli, François
- O'Reilly, Eliza
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.
Additional Information
© 2019 Institute of Mathematical Statistics. Creative Commons Attribution 4.0 International License. Received: 25 April 2019; Accepted: 5 November 2019; First available in Project Euclid: 3 December 2019. The first and second author were supported by a grant of the Simons Foundation (#197982 to UT Austin) and the second author was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1110007.Attached Files
Published - euclid.ejp.1575342533.pdf
Submitted - 1810.06095.pdf
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Additional details
- Eprint ID
- 101654
- Resolver ID
- CaltechAUTHORS:20200302-133608411
- 197982
- Simons Foundation
- DGE-1110007
- NSF Graduate Research Fellowship
- Created
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2020-03-02Created from EPrint's datestamp field
- Updated
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2023-03-16Created from EPrint's last_modified field