EPFL | Biomedical Imaging Group

An Orthogonal Family of Quincunx Wavelets with Continuously-Adjustable Order

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

IEEE Transactions on Image Processing, in press.

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We present a new family of 2D and 3D 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 non-integer. 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 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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