%0 Journal Article
%T Wavelets centered on a knot sequence: theory, construction, and applications
%A Bruce W. Atkinson
%A Derek O. Bruff
%A Jeffrey S. Geronimo
%A Douglas P. Hardin
%J Mathematics
%D 2011
%I arXiv
%X We develop a general notion of orthogonal wavelets `centered' on an irregular knot sequence. We present two families of orthogonal wavelets that are continuous and piecewise polynomial. We develop efficient algorithms to implement these schemes and apply them to a data set extracted from an ocelot image. As another application, we construct continuous, piecewise quadratic, orthogonal wavelet bases on the quasi-crystal lattice consisting of the $\tau$-integers where $\tau$ is the golden ratio. The resulting spaces then generate a multiresolution analysis of $L^2(\mathbf{R})$ with scaling factor $\tau$.
%U http://arxiv.org/abs/1102.4246v2