### Abstract

Original language | English |
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Title of host publication | Proceedings IEEE International Conference on Acoustics, Speech and Signal Processing. |

Number of pages | 4 |

Publisher | IEEE Press |

Publication date | Mar 2012 |

Pages | 3609-3612 |

ISBN (Print) | 978-1-4673-0045-2 |

ISBN (Electronic) | 978-1-4673-0044-5 |

DOIs | |

Publication status | Published - Mar 2012 |

Event | 2012 IEEE International Conference on Acoustics, Speech and Signal Processing - Kyoto, Japan Duration: 25 Mar 2012 → 30 Mar 2012 |

### Conference

Conference | 2012 IEEE International Conference on Acoustics, Speech and Signal Processing |
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Country | Japan |

City | Kyoto |

Period | 25/03/2012 → 30/03/2012 |

Series | I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings |
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ISSN | 1520-6149 |

### Fingerprint

### Cite this

*Proceedings IEEE International Conference on Acoustics, Speech and Signal Processing.*(pp. 3609-3612). IEEE Press. I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings https://doi.org/10.1109/ICASSP.2012.6288697

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*Proceedings IEEE International Conference on Acoustics, Speech and Signal Processing. .*IEEE Press, I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings, pp. 3609-3612, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing, Kyoto, Japan, 25/03/2012. https://doi.org/10.1109/ICASSP.2012.6288697

**On Compressed Sensing and the Estimation of Continuous Parameters From Noisy Observations.** / Nielsen, Jesper Kjær; Christensen, Mads Græsbøll; Jensen, Søren Holdt.

Research output: Contribution to book/anthology/report/conference proceeding › Article in proceeding › Research › peer-review

TY - GEN

T1 - On Compressed Sensing and the Estimation of Continuous Parameters From Noisy Observations

AU - Nielsen, Jesper Kjær

AU - Christensen, Mads Græsbøll

AU - Jensen, Søren Holdt

PY - 2012/3

Y1 - 2012/3

N2 - Compressed sensing (CS) has in recent years become a very popular way of sampling sparse signals. This sparsity is measured with respect to some known dictionary consisting of a finite number of atoms. Most models for real world signals, however, are parametrised by continuous parameters corresponding to a dictionary with an infinite number of atoms. Examples of such parameters are the temporal and spatial frequency. In this paper, we analyse how CS affects the estimation performance of any unbiased estimator when we assume such infinite dictionaries. We base our analysis on the Cramer-Rao lower bound (CRLB) which is frequently used for benchmarking the estimation accuracy of unbiased estimators. For the popular sensing matrices such as the Gaussian sensing matrix, our analysis shows that compressed sensing on average degrades the estimation accuracy by at least the down-sample factor.

AB - Compressed sensing (CS) has in recent years become a very popular way of sampling sparse signals. This sparsity is measured with respect to some known dictionary consisting of a finite number of atoms. Most models for real world signals, however, are parametrised by continuous parameters corresponding to a dictionary with an infinite number of atoms. Examples of such parameters are the temporal and spatial frequency. In this paper, we analyse how CS affects the estimation performance of any unbiased estimator when we assume such infinite dictionaries. We base our analysis on the Cramer-Rao lower bound (CRLB) which is frequently used for benchmarking the estimation accuracy of unbiased estimators. For the popular sensing matrices such as the Gaussian sensing matrix, our analysis shows that compressed sensing on average degrades the estimation accuracy by at least the down-sample factor.

UR - http://www.scopus.com/inward/record.url?scp=84867612879&partnerID=8YFLogxK

U2 - 10.1109/ICASSP.2012.6288697

DO - 10.1109/ICASSP.2012.6288697

M3 - Article in proceeding

SN - 978-1-4673-0045-2

T3 - I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings

SP - 3609

EP - 3612

BT - Proceedings IEEE International Conference on Acoustics, Speech and Signal Processing.

PB - IEEE Press

ER -