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A Physical Interpretation for Finite Tight Frames (2003)
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BibTeX
@MISC{Casazza03aphysical,
author = {P. G. Casazza and M. Fickus and J. Kovačević and M. T. Leon and J. C. Tremain},
title = {A Physical Interpretation for Finite Tight Frames},
year = {2003}
}
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Abstract
Though finite tight frames arise in many applications, they have often proved difficult to understand and construct. We investigate the nonlinear problem of finding a tight frame for which the lengths of the frame elements have been prescribed in advance. Borrowing several ideas from Classical Mechanics, we show that this problem has a natural, intuitive interpretation. In particular, we show that such frames may be characterized as the minimizers of a potential energy function, and justify their interpretation as “maximally orthogonal” sequences. By exploiting this idea, we are able toshowthat such frames always exist, provided the requisite lengths satisfy a “fundamental inequality.” In so doing, we characterize those sequences of nonnegative numbers which arise as the lengths of a tight frame’s elements.
Keyphrases
finite tight frame physical interpretation fundamental inequality nonlinear problem tight frame element nonnegative number many application orthogonal sequence classical mechanic frame element tight frame requisite length intuitive interpretation potential energy function borrowing several idea
