Wavelets on the Interval and Fast Wavelet Transforms
TLDR
In this paper, the authors discuss several constructions of orthonormal wavelet bases on the interval, and introduce a new construction that avoids some of the disadvantages of earlier constructions.About:
This article is published in Applied and Computational Harmonic Analysis.The article was published on 1993-12-01 and is currently open access. It has received 1065 citations till now. The article focuses on the topics: Wavelet transform & Discrete wavelet transform.read more
Citations
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Wavelet Methods for Time Series Analysis
TL;DR: Wavelet analysis of finite energy signals and random variables and stochastic processes, analysis and synthesis of long memory processes, and the wavelet variance.
Book
Introduction to Wavelets and Wavelet Transforms: A Primer
TL;DR: This work describes the development of the Basic Multiresolution Wavelet System and some of its components, as well as some of the techniques used to design and implement these systems.
Book
Concentration Inequalities and Model Selection
TL;DR: In this article, Gaussian Processes and Gaussian Model Selection are used to estimate density estimation via model selection via statistical learning.Exponential and Information Inequalities, Gaussian processes and model selection.
Journal ArticleDOI
Wavelet analysis of long-range-dependent traffic
Patrice Abry,Darryl Veitch +1 more
TL;DR: A wavelet-based tool for the analysis of long-range dependence and a related semi-parametric estimator of the Hurst parameter is introduced and is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions.
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Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage
TL;DR: Extensive computations are presented that support the hypothesis that near-optimal shrinkage parameters can be derived if one knows (or can estimate) only two parameters about an image F: the largest alpha for which FinEpsilon(q)(alpha )(L( q)(I)),1/q=alpha/2+1/2, and the norm |F|B(q) alpha)(L(Q)(I)).
References
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Orthonormal bases of compactly supported wavelets
TL;DR: This work construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity, by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction.
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Biorthogonal bases of compactly supported wavelets
TL;DR: In this paper, it was shown that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual Riesz bases of compactly supported wavelets.
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Orthonormal bases of compactly supported wavelets II: variations on a theme
TL;DR: Several variations on the construction of orthonormal bases of wavelets with compact support are given in this article, which have, respectively, more symmetry, more regularity, or more vanishing moments for the scaling function than the examples constructed in Daubechies.
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Two-scale difference equations I: existence and global regularity of solutions
TL;DR: It is shown that if a lattice two-scale difference equation has a compactly supported solution in $C^m (\mathbb{R})$, then $m < {{(\beta _n - \beta _0 )} / {(\alpha - 1)}} - 1$.