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About: Coiflet is a research topic. Over the lifetime, 473 publications have been published within this topic receiving 7196 citations.

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Journal ArticleDOI
TL;DR: In this article, a new method for remotely determining phenological stages of paddy rice was developed, which consists of three procedures: (i) prescription of multi-temporal MODIS/Terra data; (ii) filtering time-series Enhanced Vegetation Index (EVI) data by time-frequency analysis; and (iii) specifying the phenology stages by detecting the maximum point, minimal point and inflection point from the smoothed EVI time profile.

817 citations

31 Jan 1992
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.
Abstract: Orthogonal wavelets daubechies' scaling function on (0.3), D. Pollen wavelet matrices and the representation of discrete functions, P.N. Heller, et al wavelets and generalized functions, G.G. Walter semi-orthogonal and nonorthogonal wavelets cardinal spline interpolation and teh block spin construction of wavelets, G. Battle polynomial splines and wavelets - a signal processing perspective, M. Unser and A. Aldroubi biorthogonal wavelets, A. Cohen nonorthogonal multiresolution analysis using wavelets, J.C. Feauveau wavelet-like local bases wavelets and other bases for fast numerical linear algebra, B.K. Alpert wavelets with boundary conditions on the interval, P. Aushcer local sine and cosine bases of coifman and meyer and the construction of smooth wae-lets, P. Auscher, et al some elementary properties of multiresolution analysis of L2 (Rn), W.R. Madych multi-dimensional two-scale dilation equations, M.A. Berger and Y. Wang multivariate wavelets short-time fourier and window-radon transforms, J. Stockler gabor wavelets and the heisenberg group, H.G. Feichtinger and K. Grochenig gabor expansions and short time fourier transform from the group theoetical point of view windowed radon transforms, analytic signals and the wave equation theory of sampling and interpolation, G. Kaiser and R.F. Streater irregular sampling and frames, J.J. Benedetto families of wavelet tranforms in connections with Shannon's sampling theory and the gabor tranform, A.Aldroubi and M. Unser wavelets in H2(R), K. Seip sampling, interpolation and phase space density applications to numerical analysis and signal processing orthonormal wave-lets, analysis of operators and applications to numerical analysis, S. Jaffard and Ph. Laurencot wavelet transforms and filter banks, R.A. Gopinath and C.S. Burrus second generation compact image coding with wavelets, J. Froment and S. Mallat acoustic signal compression with wavelet packets, M.V. Wickerhauser.

752 citations

30 Apr 1998
TL;DR: In this paper, the Haar basis wavelet system is used for multiresolution analysis and wavelet thresholding, and a cascade algorithm is used to transform wavelets into a wavelet transform.
Abstract: 1 Wavelets.- 1.1 What can wavelets offer?.- 1.2 General remarks.- 1.3 Data compression.- 1.4 Local adaptivity.- 1.5 Nonlinear smoothing properties.- 1.6 Synopsis.- 2 The Haar basis wavelet system.- 3 The idea of multiresolution analysis.- 3.1 Multiresolution analysis.- 3.2 Wavelet system construction.- 3.3 An example.- 4 Some facts from Fourier analysis.- 5 Basic relations of wavelet theory.- 5.1 When do we have a wavelet expansion?.- 5.2 How to construct mothers from a father.- 5.3 Additional remarks.- 6 Construction of wavelet bases.- 6.1 Construction starting from Riesz bases.- 6.2 Construction starting from m0.- 7 Compactly supported wavelets.- 7.1 Daubechies' construction.- 7.2 Coiflets.- 7.3 Symmlets.- 8 Wavelets and Approximation.- 8.1 Introduction.- 8.2 Sobolev Spaces.- 8.3 Approximation kernels.- 8.4 Approximation theorem in Sobolev spaces.- 8.5 Periodic kernels and projection operators.- 8.6 Moment condition for projection kernels.- 8.7 Moment condition in the wavelet case.- 9 Wavelets and Besov Spaces.- 9.1 Introduction.- 9.2 Besov spaces.- 9.3 Littlewood-Paley decomposition.- 9.4 Approximation theorem in Besov spaces.- 9.5 Wavelets and approximation in Besov spaces.- 10 Statistical estimation using wavelets.- 10.1 Introduction.- 10.2 Linear wavelet density estimation.- 10.3 Soft and hard thresholding.- 10.4 Linear versus nonlinear wavelet density estimation.- 10.5 Asymptotic properties of wavelet thresholding estimates.- 10.6 Some real data examples.- 10.7 Comparison with kernel estimates.- 10.8 Regression estimation.- 10.9 Other statistical models.- 11 Wavelet thresholding and adaptation.- 11.1 Introduction.- 11.2 Different forms of wavelet thresholding.- 11.3 Adaptivity properties of wavelet estimates.- 11.4 Thresholding in sequence space.- 11.5 Adaptive thresholding and Stein's principle.- 11.6 Oracle inequalities.- 11.7 Bibliographic remarks.- 12 Computational aspects and software.- 12.1 Introduction.- 12.2 The cascade algorithm.- 12.3 Discrete wavelet transform.- 12.4 Statistical implementation of the DWT.- 12.5 Translation invariant wavelet estimation.- 12.6 Main wavelet commands in XploRe.- A Tables.- A.1 Wavelet Coefficients.- A.2.- B Software Availability.- C Bernstein and Rosenthal inequalities.- D A Lemma on the Riesz basis.- Author Index.

634 citations

12 Mar 2014
TL;DR: In this article, a 2D Transform based on Lifting is presented, where the Haar Transform is used for denoising and the Discrete Wavelet Transform via Lifting.
Abstract: 1. Introduction.- 1.1 Prerequisites.- 1.2 Guide to the Book.- 1.3 Background Information.- 2. A First Example.- 2.1 The Example.- 2.2 Generalizations.- Exercises.- 3. The Discrete Wavelet Transform via Lifting.- 3.1 The First Example Again.- 3.2 Definition of Lifting.- 3.3 A Second Example.- 3.4 Lifting in General.- 3.5 DWT in General.- 3.6 Further Examples.- Exercises.- 4. Analysis of Synthetic Signals.- 4.1 The Haar Transform.- 4.2 The CDF(2,2) Transform.- Exercises.- 5. Interpretation.- 5.1 The First Example.- 5.2 Further Results on the Haar Transform.- 5.3 Interpretation of General DWT.- Exercises.- 6. Two Dimensional Transforms.- 6.1 One Scale DWT in Two Dimensions.- 6.2 Interpretation and Examples.- 6.3 A 2D Transform Based on Lifting.- Exercises.- 7. Lifting and Filters I.- 7.1 Fourier Series and the z-Transform.- 7.2 Lifting in the z-Transform Representation.- 7.3 Two Channel Filter Banks.- 7.4 Orthonormal and Biorthogonal Bases.- 7.5 Two Channel Filter Banks in the Time Domain.- 7.6 Summary of Results on Lifting and Filters.- 7.7 Properties of Orthogonal Filters.- 7.8 Some Examples.- Exercises.- 8. Wavelet Packets.- 8.1 From Wavelets to Wavelet Packets.- 8.2 Choice of Basis.- 8.3 Cost Functions.- Exercises.- 9. The Time-Frequency Plane.- 9.1 Sampling and Frequency Contents.- 9.2 Definition of the Time-Frequency Plane.- 9.3 Wavelet Packets and Frequency Contents.- 9.4 More about Time-Frequency Planes.- 9.5 More Fourier Analysis. The Spectrogram.- Exercises.- 10. Finite Signals.- 10.1 The Extent of the Boundary Problem.- 10.2 DWT in Matrix Form.- 10.3 Gram-Schmidt Boundary Filters.- 10.4 Periodization.- 10.5 Moment Preserving Boundary Filters.- Exercises.- 11. Implementation.- 11.1 Introduction to Software.- 11.2 Implementing the Haar Transform Through Lifting.- 11.3 Implementing the DWT Through Lifting.- 11.4 The Real Time Method.- 11.5 Filter Bank Implementation.- 11.6 Construction of Boundary Filters.- 11.7 Wavelet Packet Decomposition.- 11.8 Wavelet Packet Bases.- 11.9 Cost Functions.- Exercises.- 12. Lifting and Filters II.- 12.1 The Three Basic Representations.- 12.2 From Matrix to Equation Form.- 12.3 From Equation to Filter Form.- 12.4 From Filters to Lifting Steps.- 12.5 Factoring Daubechies 4 into Lifting Steps.- 12.6 Factorizing Coiflet 12 into Lifting Steps.- Exercises.- 13. Wavelets in Matlab.- 13.1 Multiresolution Analysis.- 13.2 Frequency Properties of the Wavelet Transform.- 13.3 Wavelet Packets Used for Denoising.- 13.4 Best Basis Algorithm.- 13.5 Some Commands in Uvi_Wave.- Exercises.- 14. Applications and Outlook.- 14.1 Applications.- 14.2 Outlook.- 14.3 Some Web Sites.- References.

341 citations

Journal ArticleDOI
TL;DR: It was found that Coiflets 1 is the most suitable candidate among the wavelet families considered in this study for accurate classification of the EEG signals.

263 citations

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