30 research outputs found
The continuous shearlet transform in arbitrary dimensions
This paper is concerned with the generalization of the continuous shearlet transform to higher dimensions. Similar to the two-dimensional case, our approach is based on translations, anisotropic dilations and specific shear matrices. We show that the associated integral transform again originates from a square-integrable representation of a specific group, the full n-variate shearlet group. Moreover, we verify that by applying the coorbit theory, canonical scales of smoothness spaces and associated Banach frames can be derived. We also indicate how our transform can be used to characterize singularities in signals
The fast Fourier Transform and fast Wavelet Transform for Patterns on the Torus
We introduce a fast Fourier transform on regular d-dimensional lattices. We
investigate properties of congruence class representants, i.e. their ordering,
to classify directions and derive a Cooley-Tukey-Algorithm. Despite the fast
Fourier techniques itself, there is also the advantage of this transform to be
parallelized efficiently, yielding faster versions than the one-dimensional
Fourier transform. These properties of the lattice can further be used to
perform a fast multivariate wavelet decomposition, where the wavelets are given
as trigonometric polynomials. Furthermore the preferred directions of the
decomposition itself can be characterised.Comment: 23 pages, 10 figures, revised versio