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A New Family of Rotation-Covariant Wavelets on the Hexagonal Lattice

L. Condat, B. Forster-Heinlein, D. Van De Ville

Proceedings of the SPIE Optics and Photonics 2007 Conference on Mathematical Methods: Wavelet XII, San Diego CA, USA, August 26-29, 2007, vol. 6701, pp. 67010B-1/67010B-9.



We present multiresolution spaces of complex rotation-covariant functions, deployed on the 2-D hexagonal lattice. The designed wavelets, which are complex-valued, provide an important phase information for image analysis, which is missing in the discrete wavelet transform with real wavelets. Moreover, the hexagonal lattice allows to build wavelets having a more isotropic magnitude than on the Cartesian lattice. The associated filters, fully characterized in the Fourier domain, yield an efficient FFT-based implementation.


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