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Discrete wavelet transform

About: Discrete wavelet transform is a(n) research topic. Over the lifetime, 27243 publication(s) have been published within this topic receiving 495741 citation(s). The topic is also known as: DWT. more


Open accessBook
01 Jan 1998-
Abstract: Introduction to a Transient World. Fourier Kingdom. Discrete Revolution. Time Meets Frequency. Frames. Wavelet Zoom. Wavelet Bases. Wavelet Packet and Local Cosine Bases. An Approximation Tour. Estimations are Approximations. Transform Coding. Appendix A: Mathematical Complements. Appendix B: Software Toolboxes. more

Topics: Wavelet packet decomposition (71%), Discrete wavelet transform (67%), Wavelet transform (67%) more

17,299 Citations

Open accessBook
Ingrid Daubechies1Institutions (1)
01 May 1992-
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. more

Topics: Spline wavelet (68%), Continuous wavelet (67%), Biorthogonal wavelet (64%) more

16,065 Citations

Abstract: A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmoller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of change... more

Topics: Wavelet (69%), Wavelet transform (68%), Morlet wavelet (67%) more

11,219 Citations

Journal ArticleDOI: 10.1109/18.57199
Ingrid Daubechies1Institutions (1)
Abstract: Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied. The first procedure is the short-time or windowed Fourier transform; the second is the wavelet transform, in which high-frequency components are studied with sharper time resolution than low-frequency components. The similarities and the differences between these two methods are discussed. For both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time-frequency density. Finally, the notion of time-frequency localization is made precise, within this framework, by two localization theorems. > more

5,889 Citations

Journal ArticleDOI: 10.1109/78.258085
J.M. Shapiro1Institutions (1)
Abstract: The embedded zerotree wavelet algorithm (EZW) is a simple, yet remarkably effective, image compression algorithm, having the property that the bits in the bit stream are generated in order of importance, yielding a fully embedded code The embedded code represents a sequence of binary decisions that distinguish an image from the "null" image Using an embedded coding algorithm, an encoder can terminate the encoding at any point thereby allowing a target rate or target distortion metric to be met exactly Also, given a bit stream, the decoder can cease decoding at any point in the bit stream and still produce exactly the same image that would have been encoded at the bit rate corresponding to the truncated bit stream In addition to producing a fully embedded bit stream, the EZW consistently produces compression results that are competitive with virtually all known compression algorithms on standard test images Yet this performance is achieved with a technique that requires absolutely no training, no pre-stored tables or codebooks, and requires no prior knowledge of the image source The EZW algorithm is based on four key concepts: (1) a discrete wavelet transform or hierarchical subband decomposition, (2) prediction of the absence of significant information across scales by exploiting the self-similarity inherent in images, (3) entropy-coded successive-approximation quantization, and (4) universal lossless data compression which is achieved via adaptive arithmetic coding > more

5,503 Citations

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Topic's top 5 most impactful authors

Michael Unser

75 papers, 4.2K citations

Yuan Yan Tang

24 papers, 601 citations

Hiroshi Toda

21 papers, 78 citations

Zhong Zhang

19 papers, 142 citations

Ivan Selesnick

18 papers, 5.7K citations

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