Physical laws governing finite tight frames

Peter G. Casazza, Matthew C. Fickus, Jelena Kovačević, Manuel T. Leon, Janet C. Tremain

Research output: Contribution to journalConference article

Abstract

We give a physical interpretation for finite tight frames along the lines of Columb's Law in Physics. This allows us to use results from classical mechanics to anticipate results in frame theory. As a consequence, we are able to classify those frames for an N-dimensional Hilbert space which are the closest to being tight (in the sense of minimizing potential energy) while having the norms of the frame vectors prescribed in advance. This also yields a fundamental inequality that all finite tight frames must satisfy.

Original languageEnglish (US)
Pages (from-to)371-380
Number of pages10
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume5207
Issue number1
StatePublished - Dec 1 2003
EventWavelets: Applications in Signal and Image Processing X - San Diego, CA, United States
Duration: Aug 4 2003Aug 8 2003

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering

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  • Cite this

    Casazza, P. G., Fickus, M. C., Kovačević, J., Leon, M. T., & Tremain, J. C. (2003). Physical laws governing finite tight frames. Proceedings of SPIE - The International Society for Optical Engineering, 5207(1), 371-380.