Minimizing Fusion Frame Potential

نویسندگان

  • Peter G. Casazza
  • Matthew Fickus
چکیده

Fusion frames are an emerging topic of frame theory, with applications to encoding and distributed sensing. However, little is known about the existence of tight fusion frames. In traditional frame theory, one method for showing that unit norm tight frames exist is to characterize them as the minimizers of an energy functional, known as the frame potential. We generalize the frame potential to the fusion frame setting. In particular, we introduce the fusion frame potential, and show how its minimization is equivalent to the minimization of the traditional frame potential over a particular domain. We then study this minimization problem in detail. Specifically, we show that if the fusion frame’s subspaces are large in number but small in dimension compared to the dimension of the underlying space, then fusion frames will always exists, with each being a minimizer of the fusion frame potential.

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تاریخ انتشار 2008