On the role of diversity in sparsity estimation


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Reeves, G; Gastpar, M

Published Date

  • October 26, 2011

Published In

  • Ieee International Symposium on Information Theory Proceedings

Start / End Page

  • 119 - 123

Digital Object Identifier (DOI)

  • 10.1109/ISIT.2011.6033723

Citation Source

  • Scopus