Book ChapterDOI
Signal processing and compression with wavelet packets
Ronald R. Coifman,Yves Meyer,Steven Quake,M. Victor Wickerhauser +3 more
- pp 363-379
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This work applies an algorithm to chose a best basis subset, tailored to fit a specific signal or class of signals, to two signal processing tasks: acoustic signal compression, and feature extraction in certain images.Abstract:
Wavelet packets are a versatile collection of functions generalizing the compactly supported wavelets of Daubechies. They are used to analyze and manipulate signals such as sound and images. We describe a library of such waveforms and demonstrate a few of their analytic properties. We also describe an algorithm to chose a best basis subset, tailored to fit a specific signal or class of signals. We apply this algorithm to two signal processing tasks: acoustic signal compression, and feature extraction in certain images.read more
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Wavelets and Subband Coding
Martin Vetterli,Jelena Kovacevic +1 more
TL;DR: Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding and developed the theory in both continuous and discrete time.
Journal ArticleDOI
Wavelet Transforms and their Applications to Turbulence
TL;DR: Wavelet transforms are recent mathematical techniques, based on group theory and square integrable representations, which allows one to unfold a signal, or a field, into both space and scale, and possibly directions.
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For most large underdetermined systems of linear equations the minimal 1-norm solution is also the sparsest solution
TL;DR: In this article, the authors consider linear equations y = Φx where y is a given vector in ℝn and Φ is a n × m matrix with n 0 so that for large n and for all Φ's except a negligible fraction, the solution x1of the 1-minimization problem is unique and equal to x0.
Journal ArticleDOI
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images
TL;DR: The aim of this paper is to introduce a few key notions and applications connected to sparsity, targeting newcomers interested in either the mathematical aspects of this area or its applications.
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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.
References
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Journal ArticleDOI
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.
Book
Wavelets: A Tutorial in Theory and Applications
TL;DR: A.G. Unser and A.Aldroubi as discussed by the authors constructed a block spin construction of wavelets with boundary conditions on the interval, P.A. Berger and Y.W. Wickerhauser constructed wavelet-like local bases wavelets and other bases for fast numerical linear algebra, B.C. Burrus second generation compact image coding with wavelets, J. Froment and S. Mallat acoustic signal compression with wavelet packets, M.
Book ChapterDOI
Acoustic signal compression with wavelet packets
TL;DR: In this article, the wavelet transform is generalized to produce a library of orthonormal bases of modulated wavelet packets, where each basis comes with a fast transform, and hence give rise to the notion of a "best basis" for a signal subject to a given cost function.