Related papers: Higher Rank Wavelets
We construct directional wavelet systems that will enable building efficient signal representation schemes with good direction selectivity. In particular, we focus on wavelet bases with dyadic quincunx subsampling. In our previous work, We…
Partitions of unity in ${\mathbf R}^d$ formed by (matrix) scales of a fixed function appear in many parts of harmonic analysis, e.g., wavelet analysis and the analysis of Triebel-Lizorkin spaces. We give a simple characterization of the…
We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…
Modeling of multidimensional signal using tensor is more convincing than representing it as a collection of matrices. The tensor based approaches can explore the abundant spatial and temporal structures of the mutlidimensional signal. The…
We develop a class of multivariate ordered discrete response models featuring general rectangular structures, which allow for functionally interdependent thresholds across dimensions, extending beyond traditional (lattice) models that…
We present applications of variational -- wavelet approach to nonlinear (rational) rms envelope dynamics. We have the solution as a multiresolution (multiscales) expansion in the base of compactly supported wavelet basis.
We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0…
Multiresolution analyses based upon interpolets, interpolating scaling functions introduced by Deslauriers and Dubuc, are particularly well-suited to physical applications because they allow exact recovery of the multiresolution…
In a previous paper we have introduced a new class of radial basis functions that are powerful means to approximate functions by quasi-interpolation. In this article we extend the results to create new ways of approximating functions by…
We study many properties of level-dependent Hermite subdivision, focusing on schemes preserving polynomial and exponential data. We specifically consider interpolatory schemes, which give rise to level-dependent multiresolution analyses…
We verify a conjecture on the structure of higher-rank numerical ranges for a wide class of unitary and normal matrices. Using analytic and geometric techniques, we show precisely how the higher-rank numerical ranges for a generic unitary…
In this paper it is shown, that B-splines are scaling functions for any natural N. For any natural N construction of Haar wavelets, Kotelnikov-Shannon wavelets, nonorthogonal wavelets based on B-splines is given. Examples of construction of…
We give an equivariant version of Packer and Rieffel's theorem on sufficient conditions for the existence of orthonormal wavelets in projective multiresolution analyses. The scaling functions that generate a projective multiresolution…
Wavelets have been shown to be effective bases for many classes of natural signals and images. Standard wavelet bases have the entire vector space $\mathbb R^n$ as their natural domain. It is fairly straightforward to adapt these to…
We define the notion of "projective" multiresolution analyses, for which, by definition, the initial space corresponds to a finitely generated projective module over the algebra $C(\btn)$ of continuous complex-valued functions on an…
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…
An algebra is introduced which can be considered as a rank 2 extension of the Askey-Wilson algebra. Relations in this algebra are motivated by relations between coproducts of twisted primitive elements in the two-fold tensor product of the…
We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…
(Bi)orthogonal (multi)wavelets on the real line have been extensively studied and employed in applications with success. A lot of problems in applications are defined on bounded intervals or domains. Therefore, it is important in both…
A classical theorem attributed to Naimark states that, given a Parseval frame $\mathcal{B}$ in a Hilbert space $\mathcal{H}$, one can embed $\mathcal{H}$ in a larger Hilbert space $\mathcal{K}$ so that the image of $\mathcal{B}$ is the…