An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order

M. Feilner, D. Van De Ville, M. Unser

IEEE Transactions on Image Processing, vol. 14, no. 4, pp. 499–510, April 2005.

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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(a^λ); they also essentially behave like fractional derivative operators. To make our construction practical, we propose an 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.

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AUTHOR="Feilner, M. and Van De Ville, D. and Unser, M.",
TITLE="An Orthogonal Family of Quincunx Wavelets with
	Continuously Adjustable Order",
JOURNAL="{IEEE} Transactions on Image Processing",
YEAR="2005",
volume="14",
number="4",
pages="499--510",
month="April",
note="")

DOI: 10.1109/TIP.2005.843754