Continuous wavelet transforms on the space L2 (R, H; dx)

Irregular wavelet frames on L2(R)

If the wavelet system {aψ(a ·−bk)}j,k∈Z forms a frame onL(R) for some a > 1 and b > 0, then it is called a (regular) wavelet frame. In this case we can reconstruct any f from the sampled values (Wψf)(a , abk). In practice the sampling points may be irregular. We need to know for which wavelet ψ and parameters {(sj , bk)}j,k , the wavelet system {s j ψ(sj · −bk)}j,k∈Z forms a frame on L (R). In ...

Continuous and Discrete Wavelet Transforms

Rob A. Zuidwijk CWI E-mail: [email protected] Url: http://www.cwi.nl/cwi/projects/wavelets.html November 6, 1997 Abstract In this lecture, the continuous wavelet transform will be discussed and some attention will be given to the discrete wavelet transform. Finally, wavelet transforms on multidimensional data will be considered. The set-up of the lecture is as follows: 1. The continuous wavelet t...

Continuous and Discrete Wavelet Transforms

This paper is an expository survey of results on integral representations and discrete sum expansions of functions in L(R) in terms of coherent states. Two types of coherent states are considered: Weyl–Heisenberg coherent states, which arise from translations and modulations of a single function, and affine coherent states, called “wavelets,” which arise as translations and dilations of a singl...

Examples of Integral Transforms 351 Continuous Wavelet Transform on R 352 Windowed Fourier

Multiscaled Wavelet Transforms, Ridgelet Transforms, and Radon Transforms on the Space of Matrices

Let Mn,m be the space of real n × m matrices which can be identified with the Euclidean space R. We introduce continuous wavelet transforms on Mn,m with a multivalued scaling parameter represented by a positive definite symmetric matrix. These transforms agree with the polar decomposition on Mn,m and coincide with classical ones in the rank-one case m = 1. We prove an analog of Calderón’s repro...