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Proceedings Paper

Squeezable bases: local orthogonal bases on nonuniform grids
Author(s): Douglas P. Hardin; Jeffrey S. Geronimo
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Paper Abstract

We describe a method for adapting local shift-invariant bases to non-uniform grids via what we call a squeeze map. When the shift-invariant basis is orthogonal there is a squeeze map such that the nonuniform basis is orthogonal and has the same smoothness and same approximation order as the shift-invariant basis. When the smoothness or approximation order is large enough the squeeze map is uniquely determined and may be calculated locally in terms of the ratios of adjacent intervals. Therefore a basis may be rapidly generated for a given grid. Furthermore local changes in a grid (for example knot insertion or deletion) only affect a few of the basis functions. When starting with a refinable scaling vector the squeeze map machinery gives a procedure for generating orthogonal wavelets on semi-regular grids (that is, an arbitrary non-uniform coarse space with uniform refinements) with the same polynomial reproduction and smoothness as the shift-invariant space.

Paper Details

Date Published: 5 December 2001
PDF: 8 pages
Proc. SPIE 4478, Wavelets: Applications in Signal and Image Processing IX, (5 December 2001); doi: 10.1117/12.449712
Show Author Affiliations
Douglas P. Hardin, Vanderbilt Univ. (United States)
Jeffrey S. Geronimo, Georgia Institute of Technology (United States)

Published in SPIE Proceedings Vol. 4478:
Wavelets: Applications in Signal and Image Processing IX
Andrew F. Laine; Michael A. Unser; Akram Aldroubi, Editor(s)

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