Title :
On the role of diversity in sparsity estimation
Author :
Reeves, Galen ; Gastpar, Michael
Author_Institution :
Dept. of Electr. Eng. & Comput. Sci., Univ. of California, Berkeley, CA, USA
fDate :
July 31 2011-Aug. 5 2011
Abstract :
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.
Keywords :
signal processing; statistical analysis; diversity; noise uncertainty; nonzero value uncertainty; signal processing; sparsity pattern estimation; Compressed sensing; Estimation; Joints; Signal to noise ratio; Upper bound; Vectors;
Conference_Titel :
Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on
Conference_Location :
St. Petersburg
Print_ISBN :
978-1-4577-0596-0
Electronic_ISBN :
2157-8095
DOI :
10.1109/ISIT.2011.6033723