Showing papers in "Applied and Computational Harmonic Analysis in 1996"
TL;DR: In this paper, a lifting scheme is proposed for constructing compactly supported wavelets with compactly support duals, which can also speed up the fast wavelet transform and is shown to be useful in the construction of wavelets using interpolating scaling functions.
2,322 citations
TL;DR: In this article, the wavelet-based synthesis technique for fractional Brownian motion proposed by Sellan in 1995 has been investigated and a fast and efficient pyramidal filter bank-based Mallat-type algorithm has been proposed.
211 citations
TL;DR: In this article, the authors studied nonorthogonal but in a certain sense stable and even local decompositions of nested spaces and developed tools which are not necessarily confined to the translation invariant setting.
157 citations
TL;DR: A family of invertible discrete-time signal transforms, referred to assymmetric extension transforms(SET's), for finite-length signals, is described and classifies and is shown to be complete in the sense that it contains all possible nonexpansive SET's.
149 citations
TL;DR: In this paper, a wavelet collocation method for the numerical solution of partial differential equations is described, which is based on the use of the autocorrelation functions of Daubechie's compactly supported wavelets.
134 citations
TL;DR: In this paper, the authors studied the minimax rates of convergence for wavelet estimators, which are based on the shrinkage of empirical coefficients βjkof wavelet decomposition of unknown function with thresholds λj.
133 citations
TL;DR: In this article, a subclass of Schoenberg's positive definite functions on the m-sphere is defined and decomposition, reconstruction, and localization for these wavelets are discussed.
120 citations
TL;DR: In this paper, the Gibbs effect was examined for wavelet expansions of functions at points with jump discontinuities and certain conditions on the size of the wavelet kernel were examined to determine if a Gibbs effect occurs and what magnitude it is.
77 citations
TL;DR: In this paper, the authors investigated a class of nonstationary, orthogonal periodic scaling functions and wavelets generated by continuously differentiable periodic functions with positive Fourier coefficients, termed periodic basis functions.
67 citations
TL;DR: The purpose of this note is to point out that results analogous to [2] hold under a model which measures bits encoded.
63 citations
TL;DR: In this article, the authors considered Bertrands' bilinear affine time-frequency distributions from the point of view of their geometry in the timefrequency plane and established general construction rules for interference terms, with further interpretations in terms of localization properties, generalized means and symmetries.
TL;DR: This paper generalizes Malvar–Coifman–Meyer wavelets by extending the choice of bell functions to produce a family of smooth local trigonometric bases that efficiently compress trig onometric functions.
TL;DR: In this paper, wavelets are used to provide an adaptive local smoothing of a short-time periodogram in the time-freqeuncy plane and a threshold choice is derived which is motivated by minimax properties w.r.t. the integrated mean squared error.
TL;DR: In this paper, it was shown that the wavelet expansion of any Lp function converges pointwise almost everywhere under hard sampling, soft sampling, and soft sampling summation methods, for 1
TL;DR: In this article, the authors consider orthonormal bases of open face RNconsisting of discretized rescaled Walsh functions, where the Walsh group is replaced by other finite abelian groups.
TL;DR: A result is proved that gives the support of the scaling vector under certain conditions on the coefficient matrices under which a given matrix refinement equation can be solved.
TL;DR: In this article, a Galerkin-type discretization in an adaptive basis of orthogonal wavelets was employed for numerical simulation of two-dimensional homogeneous decaying turbulence.
TL;DR: In this paper, the existence of a best approximation solution to the set of equations for irregular sampling in Gabor frames has been shown, where the solution changes if the Gabor frame is perturbed.
TL;DR: In this article, the connection between Besov spaces and certain approximation subspaces of the Hardy spaces H p (open face R d ), 0 p ≤ 1 was investigated and the wavelet coefficients of such decompositions were characterized under minimal decay and smoothness conditions on the Wavelet set Ψ.
TL;DR: In this paper, a semi-orthogonal cubic spline wavelet basis of homogeneous Sobolev space H 2 0 (I ) is constructed, which turns out to be a basis of the continuous space C 0 ( I ).
TL;DR: The Beyklin-Coifman-Rokhlin fast algorithm as discussed by the authors replaces almost diagonal matrices by banded ones, and compute the operator norm of the error term in this approximation.
TL;DR: The method of applying operators to functions may be used with any wavelet basis with a sufficient number of vanishing moments, and is particularly efficient for convolution operators.
TL;DR: In this paper, a simplified filtering procedure for the quasi-optimal approximation of functions in subspaces of L 2 generated from the translates of a function ϕ(x) is proposed.
TL;DR: In this article, two proofs are given for a variant of the standard Poisson summation formula, and two proofs for a Poisson version of this formula are shown to be correct.
TL;DR: In this paper, necessary and sufficient conditions for amulti-scaling function φ := (φ1,…, φr)T to have polynomial reproduction (p. r.) of ordermin terms of the eigenvalues and their corresponding eigenvectors of two finitematrices are established.
TL;DR: In this article, the authors provide a general framework for the construction of wavelets that are generated by translates of a given slowly growing function where the translates are defined by a sequence of arbitrarily spaced points.
TL;DR: The role of refinable PSI spaces in the construction of wavelets from multiresolution analysis, as well as in the study of subdivision algorithms is well-known, well-understood, and well-documented as discussed by the authors.
TL;DR: In this article, the multivariate Paley-Wiener bounds for Riesz bases of L2[−π, π] were derived, which improved a recent result of Favier and Zalik.
TL;DR: In this article, two-dimensional continuous smooth Malvar wavelets defined on a hexagon are constructed, which constitute an orthonormal basis of the wavelet construction, and can be generalized to many hexagons.
TL;DR: An extended family of almost orthogonal spline wavelets with compact support with snug basesL2( R ), preserving semiorthogonal properties is proposed, and several formulas in accord with these purposes are developed.