let  $varpi$ be a representation of the homogeneous space $g/h$, where $g$ be a locally compact group and  $h$ be a compact subgroup of $g$. for  an admissible wavelet $zeta$ for $varpi$  and $psi in l^p(g/h), 1leq p

Let  $varpi$ be a representation of the homogeneous space $G/H$, where $G$ be a locally compact group and  $H$ be a compact subgroup of $G$. For  an admissible wavelet $zeta$ for $varpi$  and $psi in L^p(G/H), 1leq p <infty$, we determine a class of bounded  compact operators  which are related to continuous wavelet transforms on homogeneous spaces and they are called localization operators.

Consider the semidirect product group H ×? K, where H and K are two arbitrary locally compact groups and K is also abelian. We introduce the continuous wavelet transform associated to some square integrable representations H ×? K. Moreover, we try to obtain a concrete form for admissible vectors of these integrable representations.

It is well known that for irreducible, square-integrable representations of a locally compact group, there exist so-called admissible vectors which allow the construction of generalized continuous wavelet transforms. In this paper we discuss when the irreducibility requirement can be dropped, using a connection between generalized wavelet transforms and Plancherel theory. For unimodular groups ...

Density conditions for wavelet systems with arbitrary sampling points to be frames are studied. We show that for a wavelet system generated by admissible functions and irregular affine lattices to be a frame, the sampling points must have a positive lower Beurling density. The same is true for wavelet systems with arbitrary sampling points and nice generating functions.

let $g$ be a locally compact group, $h$ be a compact subgroup of $g$ and $varpi$ be a representation of the homogeneous space $g/h$ on a hilbert space $mathcal h$. for $psi in l^p(g/h), 1leq p leqinfty$, and an admissible wavelet $zeta$ for $varpi$, we define the localization operator $l_{psi,zeta} $ on $mathcal h$ and we show that it is a bounded operator. moreover, we prove that the localizat...

We propose a novel method for simultaneous speckle reduction and data compression based on shrinking, quantizing and coding the wavelet packet coeecients of the logarithmically transformed image. A fast algorithm is used to nd the best wavelet packet basis in the rate-distortion sense from the entire library of admissible wavelet packet bases. Soft-thresholding in wavelet domain can signiicantl...