Some Remarks on Wavelet Representations and Geometric Aspects

Abstract

We consider continuous wavelet decompositions, mainly from geometric and algebraic aspects. As examples we describe a scheme for construction of wavelet decompositions of functions on spaces that are homogeneous with respect to some group action. Restricting to discrete group actions we show how multiresolution structures can be directly derived from algebraic arguments. We finally describe approximate multiresolution structures adapted to cases in which no exact pyramidal algorithm can be associated with a given wavelet.