### 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(nm^{3/2}), 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 language | English (US) |
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Title of host publication | 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013 |

Publisher | IEEE Computer Society |

Pages | 1242-1249 |

Number of pages | 8 |

ISBN (Print) | 9781479934096 |

DOIs | |

State | Published - Jan 1 2013 |

Event | 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013 - Monticello, IL, United States Duration: Oct 2 2013 → Oct 4 2013 |

### Other

Other | 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013 |
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Country | United States |

City | Monticello, IL |

Period | 10/2/13 → 10/4/13 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Networks and Communications
- Control and Systems Engineering

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Compressed sensing of streaming data

AU - Freris, Nikolaos

AU - Ocal, Orhan

AU - Vetterli, Martin

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84897741562&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897741562&partnerID=8YFLogxK

U2 - 10.1109/Allerton.2013.6736668

DO - 10.1109/Allerton.2013.6736668

M3 - Conference contribution

AN - SCOPUS:84897741562

SN - 9781479934096

SP - 1242

EP - 1249

BT - 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013

PB - IEEE Computer Society

ER -