Constructing Finite Frames with a Given Spectrum

  • Matthew Fickus
  • Dustin G. Mixon
  • Miriam J. Poteet
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

Broadly speaking, frame theory is the study of how to produce well-conditioned frame operators, often subject to nonlinear application-motivated restrictions on the frame vectors themselves. In this chapter, we focus on one particularly well-studied type of restriction: having frame vectors of prescribed lengths. We discuss two methods for iteratively constructing such frames. The first method, called Spectral Tetris, produces special examples of such frames, and only works in certain cases. The second method combines the idea behind Spectral Tetris with the classical theory of majorization; this method can build any such frame in terms of a sequence of interlacing spectra, called eigensteps.

Keywords

Tight frames Schur-Horn Majorization Interlacing 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Matthew Fickus
    • 1
  • Dustin G. Mixon
    • 2
  • Miriam J. Poteet
    • 1
  1. 1.Department of MathematicsAir Force Institute of TechnologyWright-Patterson AFBUSA
  2. 2.Program in Applied and Computational MathematicsPrinceton UniversityPrincetonUSA

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