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Ten lectures on wavelets
TLDR
This paper presents a meta-analyses of the wavelet transforms of Coxeter’s inequality and its applications to multiresolutional analysis and orthonormal bases.Abstract:
Introduction Preliminaries and notation The what, why, and how of wavelets The continuous wavelet transform Discrete wavelet transforms: Frames Time-frequency density and orthonormal bases Orthonormal bases of wavelets and multiresolutional analysis Orthonormal bases of compactly supported wavelets More about the regularity of compactly supported wavelets Symmetry for compactly supported wavelet bases Characterization of functional spaces by means of wavelets Generalizations and tricks for orthonormal wavelet bases References Indexes.read more
Citations
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Journal ArticleDOI
A Practical Guide to Wavelet Analysis.
TL;DR: In this article, a step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino-Southern Oscillation (ENSO).
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Atomic Decomposition by Basis Pursuit
TL;DR: Basis Pursuit (BP) is a principle for decomposing a signal into an "optimal" superposition of dictionary elements, where optimal means having the smallest l1 norm of coefficients among all such decompositions.
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Matching pursuits with time-frequency dictionaries
Stéphane Mallat,Zhifeng Zhang +1 more
TL;DR: The authors introduce an algorithm, called matching pursuit, that decomposes any signal into a linear expansion of waveforms that are selected from a redundant dictionary of functions, chosen in order to best match the signal structures.
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Ideal spatial adaptation by wavelet shrinkage
TL;DR: In this article, the authors developed a spatially adaptive method, RiskShrink, which works by shrinkage of empirical wavelet coefficients, and achieved a performance within a factor log 2 n of the ideal performance of piecewise polynomial and variable-knot spline methods.
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Content-based image retrieval at the end of the early years
TL;DR: The working conditions of content-based retrieval: patterns of use, types of pictures, the role of semantics, and the sensory gap are discussed, as well as aspects of system engineering: databases, system architecture, and evaluation.