Showing papers in "Applied and Computational Harmonic Analysis in 2001"

TL;DR: In this article, a dual tree of wavelet filters is proposed to obtain real and imaginary parts of the wavelet transform. And the dual tree can be extended for image and other multi-dimensional signals.

TL;DR: This paper places frames in a new setting, where some of the elements are deleted, and shows that a normalized frame minimizes mean-squared error if and only if it is tight.

TL;DR: This work develops an efficient technique for estimation, and demonstrates in a denoising application that it preserves natural image structure (e.g., edges) and generates global yet structured image models, thereby providing a unified basis for a variety of applications in signal and image processing.

TL;DR: In this article, a three-dimensional embedded subband coding with optimized truncation (3-D ESCOT) algorithm is proposed, in which coefficients in different subbands are independently coded using fractional bit-plane coding and candidate truncation points are formed at the end of each fractional bits-plane.

TL;DR: It is shown that the restrictions of tree approximation cost little in terms of rates of approximation, and encoders for compression are designed that provide upper estimates for the Kolmogorov entropy of Besov balls.

TL;DR: The design of systems that are analogous to Daubechies orthonormal wavelets—that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case, are taken up.

TL;DR: In this paper, the authors studied tight wavelet frames associated with given refinable functions which are obtained with the unitary extension principles and proved that the problem of the extension may be always solved with two framelets.

TL;DR: A method to approximate the dual Gabor frame, that is much simpler than previously proposed techniques, is derived and provides a theoretical foundation for a recently proposed method for the design of time-frequency well-localized pulse shapes for orthogonal frequency division multiplexing systems.

TL;DR: In this article, the authors consider the problem of finding the maximal space over which a given loss function can be estimated at a prescribed rate, and propose an estimation method to find such a space.

TL;DR: It is shown that if a dimension function of a wavelet not associated with a multiresolution analysis (MRA) attains the value K, then it attains all integer values from 0 to K and it is proved that every expansive matrix which preserves Z N admits an MRA structure with an analytic (multi)wavelet.

TL;DR: In this article, it was shown that there are duals { x * n } to a given (nonexact) frame { x n } that are not usual frames.

TL;DR: The numerical results reveal that these ENO-type nonlinear multiresolution transformations strongly outperform the more classical wavelet decompositions in the case of piecewise smooth geometric images.

TL;DR: In this paper, the authors studied nonlinear n-term approximation in L p (R 2 ) (0 R 2 ) which allow arbitrarily sharp angles and developed three families of smoothness spaces generated by multilevel nested triangulations.

TL;DR: In this article, a discrete wavelet basis analysis is used to estimate the visual displacement of a flow map from an optic flow equation projected onto analytic wavelets, which gives small local linear systems (3-5 equations) that are solved to find the visual displacements.

TL;DR: It is established that some of the filter banks obtained by combining monodimensional filter banks lead to arbitrarily smooth, nonseparable, orthonormal, compactly supported wavelet bases.

TL;DR: In this article, a Kronecker-product approach is introduced to build compactly supported tight frames associated with φi, using the two-scale symbols of the univariate tight frame generators associated with the φI's.

TL;DR: In this article, a generalized wavelet transform of Lipschitz/Holder regularity of nonoscillating singularities is proposed to provide local estimates from information, essentially residing at only one single scale.

TL;DR: In this article, the authors present necessary and sufficient conditions for a frame multiresolution analysis to admit a frame wavelet whose dyadic dilations and integer translates generate a frame for L2(R ) and propose a construction of a wavelet, if it exists.

TL;DR: In this paper, the authors characterize all totally interpolating biorthogonal finite impulse response (FIR) multifilter banks of multiplicity two and provide a design framework for corresponding compactly supported multi-wavelet systems with high approximation order.

TL;DR: In this paper, the windowed Fourier transform and wavelet transform are used for analyzing persistent signals, such as bounded power signals and almost periodic functions, and the analogous Parseval-type identities are established.

TL;DR: In this paper, the Riesz wavelet associated with multiresolution analyses (MRAs) was characterized and the dual of the wavelet was shown to have a dual Riestz wavelet.

TL;DR: This paper focuses on the construction of a multiresolution analysis leading to C1-functions on S2, and employs a factorization of the refinement matrices which leads to refinementMatrices characterizing complement spaces characterizes complement spaces in a wavelet construction.

TL;DR: In this article, a multiscale generalization of traditional techniques, such as unsharp masking, while using the smoothness parameter α in the Besov space Bαq(Lp) to provide a unifying framework for the two operations sharpening and smoothing.

TL;DR: In this paper, the authors give a formula for the asymptotic behavior of the Lp-norms of the combinations of the shifts of f with the subdivision sequence coefficients: ∑α∈Zsan(α)f(x−α)

TL;DR: It is shown how wavelet-based scaling analysis methods may be used to monitor and infer network properties (in conjunction with on-line algorithms and careful network experimentation) and what types of networking questions the authors can and cannot investigate with such tools.

TL;DR: In this paper, it was shown that the discrete Calderon condition characterizes completeness of orthonormal wavelet systems, for arbitrary real dilations, if a>1,b>0, and the system Ψ={aj/2ψ(ajx−bk):j,k∈ Z } is orthonorm in L 2( R ), then Ψ is a basis for L 2 ( R ) if and only if ∑j ∈ Z |ψ (ajξ)|2=b for almost every ξ∈ R.

TL;DR: A review of the older classical methods to place the ideas in the right perspective and a review of recent results on principal component filter banks, which shows that the PCFB minimizes transmitted power for a given probability of error and bit rate.

TL;DR: In this paper, it was shown that the singularities of the Schauder function can disturb the Holder exponents of the associated selfsimilar function, modify the shape of the spectrum of singularities, and finally affect the validity of the multifractal formalism.

TL;DR: A best basis algorithm for orthonormal bases of local cosines which satisfy a uniform bound on their time-frequency concentration is developed and analyzed.

TL;DR: In this paper, the construction of biorthogonal wavelets that possess the largest possible regularities and required vanishing moments was discussed, and a general Daubechies' iteration method was given for constructing wavelets by using bior-thogon splines.