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Bounds for smoothness of refinable functions

✍ Scribed by Henning Thielemann

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
244 KB
Volume
391
Category
Article
ISSN
0024-3795

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✦ Synopsis

The VILLEMOES machine can be used to compute the SOBOLEV smoothness of a refinable function. We start with presenting this technique. It involves the computation of the spectral radius of a special matrix which has at least quadratic time complexity with respect to the refinement mask size. For the one-dimensional case we deduce by linear algebra some simple estimates which require only a few basic operations on the mask coefficients with a total of linear time complexity. For orthogonal DAUBECHIES and biorthogonal CDF wavelet generators the estimates are compared to the known regularities.

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