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Proceedings Paper

Physical laws governing finite tight frames
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Paper 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.

Paper Details

Date Published: 13 November 2003
PDF: 10 pages
Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); doi: 10.1117/12.503746
Show Author Affiliations
Peter G. Casazza, Univ. of Missouri/Columbia (United States)
Matthew C. Fickus, Cornell Univ. (United States)
Jelena Kovacevic, XWaveforms (United States)
Manuel T. Leon, Univ. of Missouri/Columbia (United States)
Janet C. Tremain, Univ. of Missouri/Columbia (United States)

Published in SPIE Proceedings Vol. 5207:
Wavelets: Applications in Signal and Image Processing X
Michael A. Unser; Akram Aldroubi; Andrew F. Laine, Editor(s)

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