The Lifting Scheme: A Custom-Design Construction of Biorthogonal Wavelets
TLDR
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.About:
This article is published in Applied and Computational Harmonic Analysis.The article was published on 1996-04-01 and is currently open access. It has received 2322 citations till now. The article focuses on the topics: Lifting scheme & Biorthogonal wavelet.read more
Citations
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Book
A wavelet tour of signal processing
TL;DR: An introduction to a Transient World and an Approximation Tour of Wavelet Packet and Local Cosine Bases.
Book
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 ChapterDOI
Factoring wavelet transforms into lifting steps
Ingrid Daubechies,Wim Sweldens +1 more
TL;DR: In this paper, a self-contained derivation from basic principles such as the Euclidean algorithm, with a focus on applying it to wavelet filtering, is presented, which asymptotically reduces the computational complexity of the transform by a factor two.
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.
The lifting scheme: A construction of second generation wavelets
TL;DR: The lifting scheme is presented, a simple construction of second generation wavelets; these are wavelets that are not necessarily translates and dilates of one fixed function, and can be adapted to intervals, domains, surfaces, weights, and irregular samples.
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.
Journal ArticleDOI
Decomposition of Hardy functions into square integrable wavelets of constant shape
A. Grossmann,J. Morlet +1 more
TL;DR: In this article, the authors studied square integrable coefficients of an irreducible representation of the non-unimodular $ax + b$-group and obtained explicit expressions in the case of a particular analyzing family that plays a role analogous to coherent states (Gabor wavelets) in the usual $L_2 $ -theory.
Journal ArticleDOI
Wavelets and signal processing
Olivier Rioul,Martin Vetterli +1 more
TL;DR: A simple, nonrigorous, synthetic view of wavelet theory is presented for both review and tutorial purposes, which includes nonstationary signal analysis, scale versus frequency,Wavelet analysis and synthesis, scalograms, wavelet frames and orthonormal bases, the discrete-time case, and applications of wavelets in signal processing.
Journal ArticleDOI
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.
Book
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.