Squeezable bases: local orthogonal bases on nonuniform grids

Douglas P. Hardin; Jeffrey S. Geronimo

doi:10.1117/12.449712

5 December 2001 Squeezable bases: local orthogonal bases on nonuniform grids

Douglas P. Hardin, Jeffrey S. Geronimo

Proceedings Volume 4478, Wavelets: Applications in Signal and Image Processing IX; (2001) https://doi.org/10.1117/12.449712
Event: International Symposium on Optical Science and Technology, 2001, San Diego, CA, United States

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.

Citation Download Citation

Douglas P. Hardin and Jeffrey S. Geronimo "Squeezable bases: local orthogonal bases on nonuniform grids", Proc. SPIE 4478, Wavelets: Applications in Signal and Image Processing IX, (5 December 2001); https://doi.org/10.1117/12.449712

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