On the structures of Grassmannian frames

Preprint English OPEN
Haas IV, John I.; Casazza, Peter G.;
(2017)
  • Subject: 42C15, 52C35 | Mathematics - Functional Analysis

A common criterion in the design of finite Hilbert space frames is minimal coherence, as this leads to error reduction in various signal processing applications. Frames that achieve minimal coherence relative to all unit-norm frames are called Grassmannian frames, a cla... View more
  • References (27)
    27 references, page 1 of 3

    [1] I. Daubechies, A. Grossmann, and Y. Meyer, “Painless nonorthogonal expansions,” J. Math. Phys., vol. 27, no. 5, pp. 1271-1283, 1986. [Online]. Available: http://dx.doi.org.ezproxy.lib.uh.edu/10.1063/1.527388

    [2] N. Strawn, “Optimization over finite frame varieties and structured dictionary design,” Appl. Comput. Harmon. Anal., vol. 32, no. 3, pp. 413-434, 2012. [Online]. Available: http://dx.doi.org.ezproxy.lib.uh.edu/10.1016/j.acha.2011.09.001

    [3] R. Vale and S. Waldron, “Tight frames and their symmetries,” Constr. Approx., vol. 21, no. 1, pp. 83-112, 2005. [Online]. Available: http://dx.doi.org.ezproxy.lib.uh.edu/10.1007/s00365-004-0560-y [4]

    [5] V. K. Goyal, M. Vetterli, and N. T. Thao, “Quantized overcomplete expansions in RN : analysis, synthesis, and algorithms,” IEEE Trans. Inform. Theory, vol. 44, no. 1, pp. 16-31, 1998. [Online]. Available: http://dx.doi.org.ezproxy.lib.uh.edu/10.1109/18.650985

    [6] R. B. Holmes and V. I. Paulsen, “Optimal frames for erasures,” Linear Algebra Appl., vol. 377, pp. 31-51, 2004. [Online]. Available: http://dx.doi.org.ezproxy.lib.uh.edu/10.1016/j.laa.2003.07.012

    [7] G. Zauner, Quantendesigns - Grundzu¨ge einer nichtkommutativen Designtheorie, 1999, dissertation (Ph.D.)-University Wien (Austria).

    [8] A. J. Scott and M. Grassl, “Symmetric informationally complete positive-operator-valued measures: a new computer study,” J. Math. Phys., vol. 51, no. 4, pp. 042 203, 16, 2010. [Online]. Available: http://dx.doi.org.ezproxy.lib.uh.edu/10.1063/1.3374022

    [9] T. Strohmer and R. W. Heath, Jr., “Grassmannian frames with applications to coding and communication,” Appl. Comput. Harmon. Anal., vol. 14, no. 3, pp. 257-275, 2003. [Online]. Available: http://dx.doi.org.ezproxy.lib.uh.edu/10.1016/S1063-5203(03)00023-X

    [10] I. S. Dhillon, R. W. Heath, Jr., T. Strohmer, and J. A. Tropp, “Constructing packings in Grassmannian manifolds via alternating projection,” Experiment. Math., vol. 17, no. 1, pp. 9-35, 2008. [Online]. Available: http://projecteuclid.org.ezproxy.lib.uh.edu/euclid.em/1227031894

    [11] D. Mixon, C. Quinn, N. Kiyavash, and M. Fickus, “Equiangular tight frame fingerprinting codes,” in Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on, May 2011, pp. 1856-1859.

  • Similar Research Results (5)
  • Metrics
Share - Bookmark