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conference paper

On the role of diversity in sparsity estimation

Reeves, Galen
•
Gastpar, Michael  
2011
2011 IEEE International Symposium on Information Theory Proceedings
2011 IEEE International Symposium on Information Theory - ISIT

A major challenge in sparsity pattern estimation is that small modes are difficult to detect in the presence of noise. This problem is alleviated if one can observe samples from multiple realizations of the nonzero values for the same sparsity pattern. We will refer to this as “diversity”. Diversity comes at a price, however, since each new realization adds new unknown nonzero values, thus increasing uncertainty. In this paper, upper and lower bounds on joint sparsity pattern estimation are derived. These bounds, which improve upon existing results even in the absence of diversity, illustrate key tradeoffs between the number of measurements, the accuracy of estimation, and the diversity. It is shown, for instance, that diversity introduces a tradeoff between the uncertainty in the noise and the uncertainty in the nonzero values. Moreover, it is shown that the optimal amount of diversity significantly improves the behavior of the estimation problem for both optimal and computationally efficient estimators.

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Type
conference paper
DOI
10.1109/ISIT.2011.6033723
Author(s)
Reeves, Galen
Gastpar, Michael  
Date Issued

2011

Publisher

IEEE

Published in
2011 IEEE International Symposium on Information Theory Proceedings
Start page

119

End page

123

Editorial or Peer reviewed

NON-REVIEWED

Written at

EPFL

EPFL units
LINX  
Event nameEvent placeEvent date
2011 IEEE International Symposium on Information Theory - ISIT

St. Petersburg, Russia

31 07 - 5 08 2011

Available on Infoscience
November 14, 2013
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/97045
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