Design of dyadic wavelets
Maarten Jansen · 2022
The design of dyadic wavelet bases on equispaced knots is driven by two main objectives: orthogonality and symmetry. Within the class of wave- lets with compact support, the Haar wavelet is the only basis that com- bines both properties. Since the Haar basis offers limited smoothness, many applications require a choice to be made between the two prop- erties. Daubechies’ maxflat and symmlet wavelets combine orthogonal- ity and sparsity through vanishing moments. The symmlets minimise the asymmetry using the left over degrees of freedom. Another wavelet family proposed by Daubechies are coiflets. This family invests part of the de- grees of freedom in the facilitation of linear approximation. In the class of symmetric wavelets, the equispaced B-spline wavelets take a prominent position. Known as Cohen-Daubechies-Feauveay wavelets in the equis- paced setting, their design forms the starting point for variations including the so-call symmetric wavelets with less dissimilar lengths. This variation, no longer a spline function, is popular in image processing applications.