Multiresolution representations using the autocorrelation functions of compactly supported wavelets

Wavelets, their autocorrelation functions, and multiresolution representation of signals

We summarize the properties of the auto-correlation functions of compactly supported wavelets, their connection to iterative interpolation schemes, and the use of these functions for multiresolution analysis of signals. We briefly describe properties of representations using dilations and translations of these autocorrelation functions (the auto-correlation shell) which permit multiresolution a...

Compactly supported wavelets and representations of the Cuntz relations , II

We show that compactly supported wavelets in L (R) of scale N may be effectively parameterized with a finite set of spin vectors in C , and conversely that every set of spin vectors corresponds to a wavelet. The characterization is given in terms of irreducible representations of orthogonality relations defined from multiresolution wavelet filters.

Time-frequency localization of compactly supported wavelets

Two items will be presented in the talk. The rst one is modiication of classic Daubechies compactly supported wavelets preserving localization in time with the growth of smoothness. The second one is nonstation-ary wavelets with the use of scaling lters that vary from one scale to the next ner one. Wavelets are a tool for decomposing functions in various applications. It is closely connected wi...

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Wavelet Multiresolution Representation of Curves and Surfaces

We develop wavelet methods for the multiresolution representation of parametric curves and surfaces. To support the representation, we construct a new family of compactly supported symmetric biorthogonal wavelets with interpolating scaling functions. The wavelets in these biorthogonal pairs have properties better suited for curves and surfaces than many commonly used lters. We also give example...