1-Bit compressive sensing

Petros T. Boufounos, Richard G. Baraniuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution

488 Scopus citations

Abstract

Compressive sensing is a new signal acquisition technology with the potential to reduce the number of measurements required to acquire signals that are sparse or compressible in some basis. Rather than uniformly sampling the signal, compressive sensing computes inner products with a randomized dictionary of test functions. The signal is then recovered by a convex optimization that ensures the recovered signal is both consistent with the measurements and sparse. Compressive sensing reconstruction has been shown to be robust to multi-level quantization of the measurements, in which the reconstruction algorithm is modified to recover a sparse signal consistent to the quantization measurements. In this paper we consider the limiting case of 1-bit measurements, which preserve only the sign information of the random measurements. Although it is possible to reconstruct using the classical compressive sensing approach by treating the 1-bit measurements as ±1 measurement values, in this paper we reformulate the problem by treating the 1-bit measurements as sign constraints and further constraining the optimization to recover a signal on the unit sphere. Thus the sparse signal is recovered within a scaling factor. We demonstrate that this approach performs significantly better compared to the classical compressive sensing reconstruction methods, even as the signal becomes less sparse and as the number of measurements increases.

Original languageEnglish (US)
Title of host publicationCISS 2008, The 42nd Annual Conference on Information Sciences and Systems
Pages16-21
Number of pages6
DOIs
StatePublished - 2008
EventCISS 2008, 42nd Annual Conference on Information Sciences and Systems - Princeton, NJ, United States
Duration: Mar 19 2008Mar 21 2008

Publication series

NameCISS 2008, The 42nd Annual Conference on Information Sciences and Systems

Other

OtherCISS 2008, 42nd Annual Conference on Information Sciences and Systems
CountryUnited States
CityPrinceton, NJ
Period3/19/083/21/08

ASJC Scopus subject areas

  • Computer Science Applications
  • Information Systems
  • Control and Systems Engineering

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