In this short note we discuss the interplay between finite Coxeter groups and construction of wavelet sets, generalized multiresolution analysis and sampling.

This paper proposes Principal Component Analysis (PCA) to find adaptive bases for multiresolution. An input image is decomposed into components (compressed images) which are uncorrelated and have maximum l2 energy. With only minor modification, a single layer linear network using the Generalized Hebbian Algorithm (GHA) is used for multiresolution PCA. The decomposition has been successfully app...

Homogeneous wavelets and framelets have been extensively investigated in the classical theory of wavelets and they are often constructed from refinable functions via the multiresolution analysis. On the other hand, nonhomogeneous wavelets and framelets enjoy many desirable theoretical properties and are often intrinsically linked to the refinable structure and multiresolution analysis. In this ...

We present some applications of general harmonic/wavelet analysis approach (generalized coherent states, wavelet packets) to numerical/analytical calculations in (nonlinear) quasiclassical/quantum beam dynamics problems. (Naive) deformation quantization, multiresolution representations and Wigner transform are the key points.

These operators are very important inmathematics and physics. They allow the development of generalized wavelets from generalized continuous classical wavelet analysis. Moreover, we have proved in [2] that the generalized two-scale equation associated with the Dunkl operator has a solution and then we can define continuous multiresolution analysis. Dunkl has proved in [1] that there exists a un...