Orthogonal Quincunx Wavelets with Fractional Orders

M. Feilner, M. Jacob, M. Unser

Proceedings of the 2001 Eighth IEEE International Conference on Image Processing (ICIP'01), Θεσσαλονίκη (Thessaloniki), Ελληνική Δημοκρατία (Hellenic Republic), October 7-10, 2001, vol. I, pp. 606–609.

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We present a new family of 2D 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 α, which may be non-integer. The wavelets have good isotropy properties. We can also prove that they yield wavelet bases of L₂(ℜ²) for any α > 0. The wavelets are fractional in the sense that the approximation error at a given scale a decays like O(a^α); they also essentially behave like fractional derivative operators. To make our construction practical, we propose an FFT-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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DOI: 10.1109/ICIP.2001.959118