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The value of redundant measurement in compressed sensing

Publication ,  Journal Article
Kostina, V; Duarte, MF; Jafarpour, S; Calderbank, R
Published in: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
August 18, 2011

The aim of compressed sensing is to recover attributes of sparse signals using very few measurements. Given an overall bit budget for quantization, this paper demonstrates that there is value to redundant measurement. The measurement matrices considered here are required to have the property that signal recovery is still possible even after dropping certain subsets of D measurements. It introduces the concept of a measurement matrix that is weakly democratic in the sense that the amount of information about the signal carried by each of the designated D-subsets is the same. Examples of deterministic measurement matrices that are weakly democratic are constructed by exponentiating codewords from the binary second order Reed Muller code. The value in rejecting D measurements that are on average larger, is to be able to provide a finer grid for vector quantization of the remaining measurements, even after discounting the original budget by the bits used to identify the reject set. Simulation results demonstrate that redundancy improves recovery SNR, sometimes by a wide margin. Optimum performance occurs when a significant fraction of measurements are rejected. © 2011 IEEE.

Duke Scholars

Published In

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

DOI

ISSN

1520-6149

Publication Date

August 18, 2011

Start / End Page

3656 / 3659
 

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Kostina, V., Duarte, M. F., Jafarpour, S., & Calderbank, R. (2011). The value of redundant measurement in compressed sensing. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, 3656–3659. https://doi.org/10.1109/ICASSP.2011.5947143
Kostina, V., M. F. Duarte, S. Jafarpour, and R. Calderbank. “The value of redundant measurement in compressed sensing.” ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, August 18, 2011, 3656–59. https://doi.org/10.1109/ICASSP.2011.5947143.
Kostina V, Duarte MF, Jafarpour S, Calderbank R. The value of redundant measurement in compressed sensing. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2011 Aug 18;3656–9.
Kostina, V., et al. “The value of redundant measurement in compressed sensing.” ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Aug. 2011, pp. 3656–59. Scopus, doi:10.1109/ICASSP.2011.5947143.
Kostina V, Duarte MF, Jafarpour S, Calderbank R. The value of redundant measurement in compressed sensing. ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings. 2011 Aug 18;3656–3659.

Published In

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

DOI

ISSN

1520-6149

Publication Date

August 18, 2011

Start / End Page

3656 / 3659