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The fundamental limits of stable recovery in compressed sensing

Publication ,  Journal Article
Reeves, G
Published in: IEEE International Symposium on Information Theory - Proceedings
January 1, 2014

Compressed sensing has shown that a wide variety of structured signals can be recovered from a limited number of noisy linear measurements. This paper considers the extent to which such recovery is robust to signal and measurement uncertainty. The main result is a non-asymptotic upper bound on the reconstruction error in terms of two key quantities: the best approximation error of the signal (with respect to a user-defined approximation set) and the measurement error. We assume a random Gaussian sensing matrix but place no restrictions on the signal or the noise. This result provides a simple and yet powerful framework for analyzing the fundamental limits of stable recovery, allowing us to sharpen existing results as well as derive new ones. © 2014 IEEE.

Duke Scholars

Published In

IEEE International Symposium on Information Theory - Proceedings

DOI

ISSN

2157-8095

Publication Date

January 1, 2014

Start / End Page

3017 / 3021
 

Citation

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Reeves, G. (2014). The fundamental limits of stable recovery in compressed sensing. IEEE International Symposium on Information Theory - Proceedings, 3017–3021. https://doi.org/10.1109/ISIT.2014.6875388
Reeves, G. “The fundamental limits of stable recovery in compressed sensing.” IEEE International Symposium on Information Theory - Proceedings, January 1, 2014, 3017–21. https://doi.org/10.1109/ISIT.2014.6875388.
Reeves G. The fundamental limits of stable recovery in compressed sensing. IEEE International Symposium on Information Theory - Proceedings. 2014 Jan 1;3017–21.
Reeves, G. “The fundamental limits of stable recovery in compressed sensing.” IEEE International Symposium on Information Theory - Proceedings, Jan. 2014, pp. 3017–21. Scopus, doi:10.1109/ISIT.2014.6875388.
Reeves G. The fundamental limits of stable recovery in compressed sensing. IEEE International Symposium on Information Theory - Proceedings. 2014 Jan 1;3017–3021.

Published In

IEEE International Symposium on Information Theory - Proceedings

DOI

ISSN

2157-8095

Publication Date

January 1, 2014

Start / End Page

3017 / 3021