Reconstructing sparse signals from their zero crossings

Petros T. Boufounos, Richard G. Baraniuk

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

14 Scopus citations

Abstract

Classical sampling records the signal level at pre-determined time instances, usually uniformly spaced. An alternative implicit sampling model is to record the timing of pre-determined level crossings. Thus the signal dictates the sampling times but not the sampling levels. Logan's theorem provides sufficient conditions for a signal to be recoverable, within a scaling factor, from only the timing of its zero crossings. Unfortunately, recovery from noisy observations of the timings is not robust and usually fails to reproduce the original signal. To make the reconstruction robust this paper introduces the additional assumption that the signal is sparse in some basis. We reformulate the reconstruction problem as a minimization of a sparsity inducing cost function on the unit sphere and provide an algorithm to compute the solution. While the problem is not convex, simulation studies indicate that the algorithm converges in typical cases and produces the correct solution with very high probability.

Original languageEnglish (US)
Title of host publication2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
Pages3361-3364
Number of pages4
DOIs
StatePublished - 2008
Event2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP - Las Vegas, NV, United States
Duration: Mar 31 2008Apr 4 2008

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
ISSN (Print)1520-6149

Other

Other2008 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP
CountryUnited States
CityLas Vegas, NV
Period3/31/084/4/08

Keywords

  • Implicit sampling
  • Level-crossing problems
  • Sparse reconstruction

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Signal Processing
  • Acoustics and Ultrasonics

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