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

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Abstract

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.
Original languageEnglish
Title of host publicationProceedings IEEE International Conference on Acoustics, Speech and Signal Processing.
Number of pages4
PublisherIEEE Press
Publication dateMar 2012
Pages3609-3612
ISBN (Print)978-1-4673-0045-2
ISBN (Electronic)978-1-4673-0044-5
DOIs
Publication statusPublished - Mar 2012
Event2012 IEEE International Conference on Acoustics, Speech and Signal Processing - Kyoto, Japan
Duration: 25 Mar 201230 Mar 2012

Conference

Conference2012 IEEE International Conference on Acoustics, Speech and Signal Processing
CountryJapan
CityKyoto
Period25/03/201230/03/2012
SeriesI E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings
ISSN1520-6149

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Compressed sensing
Glossaries
Atoms
Benchmarking
Sampling

Cite this

Nielsen, J. K., Christensen, M. G., & Jensen, S. H. (2012). On Compressed Sensing and the Estimation of Continuous Parameters From Noisy Observations. In 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
Nielsen, Jesper Kjær ; Christensen, Mads Græsbøll ; Jensen, Søren Holdt. / On Compressed Sensing and the Estimation of Continuous Parameters From Noisy Observations. Proceedings IEEE International Conference on Acoustics, Speech and Signal Processing. . IEEE Press, 2012. pp. 3609-3612 (I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings).
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Nielsen, JK, Christensen, MG & Jensen, SH 2012, On Compressed Sensing and the Estimation of Continuous Parameters From Noisy Observations. in 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.

Proceedings IEEE International Conference on Acoustics, Speech and Signal Processing. . IEEE Press, 2012. p. 3609-3612 (I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

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Nielsen JK, Christensen MG, Jensen SH. On Compressed Sensing and the Estimation of Continuous Parameters From Noisy Observations. In Proceedings IEEE International Conference on Acoustics, Speech and Signal Processing. . IEEE Press. 2012. p. 3609-3612. (I E E E International Conference on Acoustics, Speech and Signal Processing. Proceedings). https://doi.org/10.1109/ICASSP.2012.6288697