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Oblique and Biorthogonal Multi-Wavelet Bases with Fast-Filtering Algorithms

A. Aldroubi, J. McGowan

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing III, San Diego CA, USA, July 9-14, 1995, vol. 2569, part I, pp. 15-26.



We construct oblique multi-wavelets bases which encompass the orthogonal multi-wavelets and the biorthogonal uni-wavelets of Cohen, Deaubechies and Feauveau. These oblique multi-wavelets preserve the advantages of orthogonal and biorthogonal wavelets and enhance the flexibility of wavelet theory to accommodate a wider variety of wavelet shapes and properties. Moreover, oblique multi-wavelets can be implemented with fast vector filter-bank algorithms. We use the theory to derive a new construction of biorthogonal uni-wavelets.


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