Locally adapted hierarchical basis preconditioning
ACM SIGGRAPH 2006 Papers
Design of optimal quincunx filter banks for image coding
EURASIP Journal on Applied Signal Processing
Biorthogonal wavelets based on gradual subdivision of quadrilateral meshes
Computer Aided Geometric Design
Frequency-domain design of overcomplete rational-dilation wavelet transforms
IEEE Transactions on Signal Processing
Wavelet steerability and the higher-order Riesz transform
IEEE Transactions on Image Processing
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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 λ0. 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.