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An orthogonal family of quincunx wavelets with continuously adjustable order

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3 Author(s)
Feilner, M. ; Biomed. Imaging Group, Swiss Fed. Inst. of Technol. Lausanne, Switzerland ; Van De Ville, D. ; Unser, M.

We present a new family of two-dimensional and three-dimensional orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order λ, which may be noninteger. We can also prove that they yield wavelet bases of L2(R2) for any λ>0. The wavelets are fractional in the sense that the approximation error at a given scale a decays like O(aλ); they also essentially behave like fractional derivative operators. To make our construction practical, we propose a fast Fourier transform-based implementation that turns out to be surprisingly fast. In fact, our method is almost as efficient as the standard Mallat algorithm for separable wavelets.

Published in:

Image Processing, IEEE Transactions on  (Volume:14 ,  Issue: 4 )