Subdivision derives its name from a splitting of the domain. A spline x on the initial domain S
is mapped to a finer domain S̃ where it is represented by more, smaller pieces. This chapter …

Second Generation Wavelets and Applications introduces" second generation wavelets"
and the lifting transform that can be used to apply the traditional benefits of wavelets into a …

In this article we review techniques for building and analysing wavelets on irregular point
sets in one and two dimensions. We discuss current results both on the practical and …

For regularly spaced one-dimensional data, wavelet shrinkage has proven to be a
compelling method for non-parametric function estimation. We create three new multiscale …

Developed in this book are several deep connections between time-frequency
(Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful …

We study the smoothness of the limit function for one-dimensional unequally spaced
interpolating subdivision schemes. The new grid points introduced at every level can lie in …

The notion of tight (wavelet) frames could be viewed as a generalization of orthonormal
wavelets. By allowing redundancy, we gain the necessary flexibility to achieve such …

We propose a general study of the convergence of a Hermite subdivision scheme ℋ of
degree d> 0 in dimension 1. This is done by linking Hermite subdivision schemes and Taylor …

It is well known that ω-circulant matrices with ω≠ 0 can be simultaneously diagonalized by a
transform matrix, which can be factored as the product of a diagonal matrix, depending on ω …

These notes introduce the central concepts surrounding wavelets and their applications. By
focusing on the essential ideas and arguments, the authors enable readers to get to the …