Physical laws governing finite tight frames

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

doi:10.1117/12.503746

Physical laws governing finite tight frames

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

Electrical and Computer Engineering

Research output: Contribution to journal › Conference article › peer-review

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 language	English (US)
Pages (from-to)	371-380
Number of pages	10
Journal	Proceedings of SPIE - The International Society for Optical Engineering
Volume	5207
Issue number	1
DOIs	https://doi.org/10.1117/12.503746
State	Published - 2003
Event	Wavelets: Applications in Signal and Image Processing X - San Diego, CA, United States Duration: Aug 4 2003 → Aug 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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10.1117/12.503746

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AU - Leon, Manuel T.

AU - Tremain, Janet C.

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T2 - Wavelets: Applications in Signal and Image Processing X

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Physical laws governing finite tight frames

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