Compressed sensing of streaming data

Nikolaos Freris, Orhan Ocal, Martin Vetterli

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

Abstract

We introduce a recursive scheme for performing Compressed Sensing (CS) on streaming data and analyze, both analytically and experimentally, the computational complexity and estimation error. The approach consists of sampling the input stream recursively via overlapping windowing and making use of the previous measurement in obtaining the next one. The signal estimate from the previous window is utilized in order to achieve faster convergence in an iterative optimization algorithm to decode the new window. To remove the bias of the estimator a two-step estimation procedure is proposed comprising support set detection and signal amplitude estimation. Estimation accuracy is enhanced by averaging estimates obtained from overlapping windows. The proposed method is shown to have asymptotic computational complexity O(nm3/2), where n is the window length, and m is the number of samples. The variance of normalized estimation error is shown to asymptotically go to 0 if k = O(n 1-∈) as n increases. The simulation results show speed up of at least ten times with respect to applying traditional CS on a stream of data while obtaining significantly lower reconstruction error under mild conditions on the signal magnitudes and the noise level.

Original languageEnglish (US)
Title of host publication2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013
PublisherIEEE Computer Society
Pages1242-1249
Number of pages8
ISBN (Print)9781479934096
DOIs
StatePublished - Jan 1 2013
Event51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013 - Monticello, IL, United States
Duration: Oct 2 2013Oct 4 2013

Other

Other51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013
CountryUnited States
CityMonticello, IL
Period10/2/1310/4/13

Fingerprint

Compressed sensing
Error analysis
Computational complexity
Set theory
Sampling

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Control and Systems Engineering

Cite this

Freris, N., Ocal, O., & Vetterli, M. (2013). Compressed sensing of streaming data. In 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013 (pp. 1242-1249). [6736668] IEEE Computer Society. https://doi.org/10.1109/Allerton.2013.6736668

Compressed sensing of streaming data. / Freris, Nikolaos; Ocal, Orhan; Vetterli, Martin.

2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013. IEEE Computer Society, 2013. p. 1242-1249 6736668.

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

Freris, N, Ocal, O & Vetterli, M 2013, Compressed sensing of streaming data. in 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013., 6736668, IEEE Computer Society, pp. 1242-1249, 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013, Monticello, IL, United States, 10/2/13. https://doi.org/10.1109/Allerton.2013.6736668
Freris N, Ocal O, Vetterli M. Compressed sensing of streaming data. In 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013. IEEE Computer Society. 2013. p. 1242-1249. 6736668 https://doi.org/10.1109/Allerton.2013.6736668
Freris, Nikolaos ; Ocal, Orhan ; Vetterli, Martin. / Compressed sensing of streaming data. 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013. IEEE Computer Society, 2013. pp. 1242-1249
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