Wavelets Centered on a Knot Sequence: Theory, Construction, and Applications

We develop a general notion of orthogonal wavelets ‘centered’ on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these schemes and apply them to a data set extracted from an ocelot i...

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Bibliographic Details
Published in:The Journal of fourier analysis and applications 2015-06, Vol.21 (3), p.509-553
Main Authors: Anderson, Bruce W., Bruff, Derek O., Geronimo, Jeffrey S., Hardin, Douglas P.
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Approximations and Expansions
Fourier Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Partial Differential Equations
Signal processing
Signal,Image and Speech Processing
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Summary:We develop a general notion of orthogonal wavelets ‘centered’ on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these schemes and apply them to a data set extracted from an ocelot image. As another application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi-crystal lattice consisting of the τ -integers where τ is the golden ratio. The resulting spaces then generate a multiresolution analysis of L 2 ( R ) with scaling factor τ .
ISSN:1069-5869
1531-5851
DOI:10.1007/s00041-014-9375-9