4,424 research outputs found
Analysis of Fisher Information and the Cram\'{e}r-Rao Bound for Nonlinear Parameter Estimation after Compressed Sensing
In this paper, we analyze the impact of compressed sensing with complex
random matrices on Fisher information and the Cram\'{e}r-Rao Bound (CRB) for
estimating unknown parameters in the mean value function of a complex
multivariate normal distribution. We consider the class of random compression
matrices whose distribution is right-orthogonally invariant. The compression
matrix whose elements are i.i.d. standard normal random variables is one such
matrix. We show that for all such compression matrices, the Fisher information
matrix has a complex matrix beta distribution. We also derive the distribution
of CRB. These distributions can be used to quantify the loss in CRB as a
function of the Fisher information of the non-compressed data. In our numerical
examples, we consider a direction of arrival estimation problem and discuss the
use of these distributions as guidelines for choosing compression ratios based
on the resulting loss in CRB.Comment: 12 pages, 3figure
Adaptive Compressed Sensing for Support Recovery of Structured Sparse Sets
This paper investigates the problem of recovering the support of structured
signals via adaptive compressive sensing. We examine several classes of
structured support sets, and characterize the fundamental limits of accurately
recovering such sets through compressive measurements, while simultaneously
providing adaptive support recovery protocols that perform near optimally for
these classes. We show that by adaptively designing the sensing matrix we can
attain significant performance gains over non-adaptive protocols. These gains
arise from the fact that adaptive sensing can: (i) better mitigate the effects
of noise, and (ii) better capitalize on the structure of the support sets.Comment: to appear in IEEE Transactions on Information Theor
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