Showing papers in "Applied and Computational Harmonic Analysis in 2003"

TL;DR: The application of Grassmannian frames to wireless communication and to multiple description coding is discussed and their connection to unit norm tight frames for frames which are generated by group-like unitary systems is discussed.

TL;DR: Wavelet frames constructed via multiresolution analysis (MRA), with emphasis on tight wavelet frames, are discussed and it is shown how they can be used for systematic constructions of spline, pseudo-spline tight frames, and symmetric bi-frames with short supports and high approximation orders.

TL;DR: This work analyzes the convergence and smoothness of certain class of nonlinear subdivision schemes based on ENO and weighted-ENO interpolation techniques, motivated by their application to signal and image processing.

TL;DR: The 3D discrete definition of the Radon transform is shown to be geometrically faithful as the planes used for summation exhibit no wraparound effects and there exists a special set of planes in the 3D case for which the transform is rapidly computable and invertible.

TL;DR: In this article, the authors investigated compactly supported wavelet bases for Sobolev spaces, starting with a pair of compactly supportable refinable functions φ and ˜ φ.

TL;DR: It is shown that an arbitrary function f, analytic within a rectangle around the real interval x ∈[ −1, 1], can be approximated by a bandlimited function of bandwidth c with an accuracy on x ∢1 which decreases exponentially fast with the bandwidth c.

TL;DR: In this article, the affine Beurling density of time-scale parameters of irregular wavelet systems is defined and sufficient conditions including necessary and sufficient ones for irregular wavelets to be frames are studied.

TL;DR: The innovation is to directly construct refinable bivariate spline function vectors with minimum supports and highest approximation orders on the six-directional mesh, and to compute their refinement masks which give rise to the matrix-valued coefficient stencils for the surface subdivision schemes.

TL;DR: In this paper, the authors studied the smoothness of quasi-uniform bivariate subdivision and derived a sufficient condition for C m continuity of the limit function, which is simple enough to be used in practice.

TL;DR: A new approach to invertible integer D CT-II and integer DCT-IV is presented, based on a factorization of the cosine matrices of types II and IV into products of sparse, orthogonal matrices.

TL;DR: In this article, a wavelet approach on a regular surface is presented, and the properties of a multiresolution analysis are verified, and a tree algorithm for fast computation is developed based on numerical integration.

TL;DR: In this paper, it was shown that an overcomplete Gabor frame has infinite excess, and in fact there exists an infinite subset of points that can be removed yet leave a frame.

TL;DR: In this article, the authors investigate Riesz wavelets in the context of generalized multiresolution analysis (GMRA), and they show that Zalik's class of wavelets obtained by an MRA is the same as the class of biorthogonal wavelets associated with a generalized MRA.

TL;DR: A family of coarse quantization algorithms for heavily oversampled Gabor expansions of certain classes of functions in L2(R), inspired by sigma–delta modulation, which produce weak type approximations where modulation spaces M1,1m with suitable weight functions m are the appropriate test function spaces.

TL;DR: Weierstrass-Mandelbrot functions are given a time-frequency interpretation which puts emphasis on their possible decomposition on chirps as an alternative to their standard, Fourier-based representation.

TL;DR: In this article, a detailed analysis of all pseudo-differential operators of orders up to 2 encountered in classical potential theory in two dimensions is presented, which leads to an extremely simple analysis of spectra of such operators, and simplifies the design of procedures for their numerical evaluation.

TL;DR: This is a very basic property of the Fourier transform on the real line proved by H Weyl and W Pauli by using the two most basic tools of analysis: integration by parts and Schwarz's inequality as discussed by the authors.

TL;DR: In this paper, a finite family of foveal wavelets, which are not translated, are used to construct orthogonal bases with compact support and high regularity, and an algorithm to detect singularities and choose the points to pointwise characterize nonoscillatory singularities is derived.

TL;DR: Integrated wavelets are presented as a method for discretizing the continuous wavelet transform using the language of group theory and tight wavelet frames are obtained for wavelet transforms over semidirect product groups.

TL;DR: In this article, lower bounds of the Hausdorff dimension of random wavelet series (RWS) have been obtained essentially under the hypothesis that the wavelet coefficients have a bounded probability density function (p.d.f.) with respect to the Lebesgue measure.

TL;DR: A fast implementation based on the discrete dyadic wavelet decomposition that allows the analysis with fewer operations than the method originally proposed by Siegmund and Worlsey to detect a sharp but continuous signal in a background noise is introduced.

TL;DR: In this paper, the smoothness of symmetric orthonormal wavelets arising from Hermite Distributed Approximating Functionals (HDAFs) was studied and their corresponding associated low pass filters are symmetric with respect to the origin.