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Oblique Multiwavelet Bases: Examples

A. Aldroubi

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing IV, Denver CO, USA, August 6-9, 1996, vol. 2825, part I, pp. 54-64.



Orthogonal, semiorthogonal and biorthogonal wavelet bases are special cases of oblique multiwavelet bases. One of the advantage of oblique multiwavelets is the flexibility they provide for constructing bases with certain desired shapes and/or properties. The decomposition of a signal in terms of oblique wavelet bases is still a perfect reconstruction filter bank. In this paper, we present several examples that show the similarity and differences between the oblique and other types of wavelet bases. We start with the Haar multiresolution to illustrate several examples of oblique wavelet bases, and then use the Cohen-Daubechies-Plonka multiscaling function to construct several oblique multiwavelets.


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