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On the role of diversity in sparsity estimation

Publication ,  Journal Article
Reeves, G; Gastpar, M
Published in: IEEE International Symposium on Information Theory - Proceedings
October 26, 2011

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. © 2011 IEEE.

Duke Scholars

Published In

IEEE International Symposium on Information Theory - Proceedings

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Publication Date

October 26, 2011

Start / End Page

119 / 123
 

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Reeves, G., & Gastpar, M. (2011). On the role of diversity in sparsity estimation. IEEE International Symposium on Information Theory - Proceedings, 119–123. https://doi.org/10.1109/ISIT.2011.6033723
Reeves, G., and M. Gastpar. “On the role of diversity in sparsity estimation.” IEEE International Symposium on Information Theory - Proceedings, October 26, 2011, 119–23. https://doi.org/10.1109/ISIT.2011.6033723.
Reeves G, Gastpar M. On the role of diversity in sparsity estimation. IEEE International Symposium on Information Theory - Proceedings. 2011 Oct 26;119–23.
Reeves, G., and M. Gastpar. “On the role of diversity in sparsity estimation.” IEEE International Symposium on Information Theory - Proceedings, Oct. 2011, pp. 119–23. Scopus, doi:10.1109/ISIT.2011.6033723.
Reeves G, Gastpar M. On the role of diversity in sparsity estimation. IEEE International Symposium on Information Theory - Proceedings. 2011 Oct 26;119–123.

Published In

IEEE International Symposium on Information Theory - Proceedings

DOI

Publication Date

October 26, 2011

Start / End Page

119 / 123