Concentration of Measure for Block Diagonal Measurement Matrices (bibtex)
by , , and
Abstract:
Concentration of measure inequalities are at the heart of much theoretical analysis of randomized compressive operators. Though commonly studied for dense matrices, in this paper we derive a concentration of measure bound for block diagonal matrices where the nonzero entries along the main diagonal blocks are i.i.d. subgaussian random variables. Our main result states that the concentration exponent, in the best case, scales as that for a fully dense matrix. We also identify the role that the energy distribution of the signal plays in distinguishing the best case from the worst. We illustrate these phenomena with a series of experiments.
Reference:
Concentration of Measure for Block Diagonal Measurement MatricesM.B. Wakin, J.Y. Park, H.L. Yap and C.J. Rozell. In Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP), March 2010.
Bibtex Entry:
@InProceedings{wakin.10,
  author = 	 {Wakin, M.B. and Park, J.Y. and Yap, H.L. and Rozell, C.J.},
  title = 	 {Concentration of Measure for Block Diagonal Measurement Matrices},
  booktitle =	 {{Proceedings of the International Conference on Acoustics, Speech, and Signal Processing (ICASSP)}},
  year =	 2010,
  month = {March},
  address =	 {Dallas, TX},
abstract = {Concentration of measure inequalities are at the heart of much
theoretical analysis of randomized compressive operators. Though
commonly studied for dense matrices, in this paper we derive a
concentration of measure bound for block diagonal matrices where the
nonzero entries along the main diagonal blocks are i.i.d.
subgaussian random variables. Our main result states that the
concentration exponent, in the best case, scales as that for a fully
dense matrix. We also identify the role that the energy distribution
of the signal plays in distinguishing the best case from the worst.
We illustrate these phenomena with a series of experiments.},
url =          {http://siplab.gatech.edu/pubs/wakinICASSP2010.pdf}
}
Powered by bibtexbrowser