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Title
Abstract
Introduction
Multiresolution Analysis
Conclusions
References
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Computer Science
Computer Vision

Separable and Nonseparable Multiwavelets in Multiple Dimensions

Profile image of Heinrich RoderHeinrich Roder

2002, Journal of Computational Physics

https://doi.org/10.1006/JCPH.2001.6743
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35 pages

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Abstract

We report on a method of constructing multidimensional biorthogonal interpolating multiwavelets. The approach is based upon polynomial interpolation in R d (C. de Boor and A. Ron, Math. Comput. 58, 198 (1997)) and an extension of the lifting scheme (J. Kovačević and W. Sweldens, IEEE Trans. Image Process. 9, No. 3, 480 (2000)). The constructed wavelets have compact support, are nearly isotropic, and retain partial scale invariance leading to a fast and efficient multidimensional wavelet transform. We demonstrate an implementation for these wavelets of variable polynomial order up to four dimensions. Finally, we show that these wavelets have a much sparser representation of discontinuous functions as compared to tensor product wavelets, which allows for a more compact and efficient representation.

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