An orthogonal family of quincunx wavelets with continuously adjustable order.
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 lamda, which may be noninteger. We can also prove that they yield wavelet bases of L2(R2) for any lambda > 0. The wavelets are fractional in the sense that the approximation error at a given scale a decays like O(a(lamda)); 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.
Feilner
Manuela
M
Biomedical Imaging Group, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
van de Ville
Dimitri
D
D000465:Algorithms; D001185:Artificial Intelligence; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted