Shift-Invariant Adaptive Wavelet Decompositions And Applications

1 List of Symbols and Abbreviations 4

[1]  Olivier Rioul,et al.  Fast algorithms for discrete and continuous wavelet transforms , 1992, IEEE Trans. Inf. Theory.

[2]  Amara Lynn Graps,et al.  An introduction to wavelets , 1995 .

[3]  Israel Cohen,et al.  Orthonormal shift-invariant adaptive local trigonometric decomposition , 1997, Signal Process..

[4]  Stephen P. Del Marco,et al.  M-band wavepacket-based transient signal detector using a translation-invariant wavelet transform , 1994 .

[5]  G. Weiss,et al.  Local sine and cosine bases of Coifman and Meyer and the construction of smooth wavelets , 1993 .

[6]  M. Victor Wickerhauser,et al.  Adapted local trigonometric transforms and speech processing , 1993, IEEE Trans. Signal Process..

[7]  G. Walter.  Wavelets and other orthogonal systems with applications , 1994 .

[8]  Henrique S. Malvar.  Fast computation of discrete cosine transform through fast Hartley transform , 1986 .

[9]  Douglas L. Jones,et al.  A simple scheme for adapting time-frequency representations , 1994, IEEE Trans. Signal Process..

[10]  Richard S. Orr,et al.  Cross term deleted Wigner representation (CDWR) based signal detection methodologies , 1996, 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings.

[11]  Yi Liu,et al.  Signal compression with smooth local trigonometric bases , 1994 .

[12]  W. Madych.  Some elementary properties of multiresolution analyses of L 2 (R n ) , 1993 .

[13]  Vladimir Pavlovic,et al.  Transform image coding based on joint adaptation of filter banks and tree structures , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[14]  L. Cohen.  Generalized Phase-Space Distribution Functions , 1966 .

[15]  Maxim J. Goldberg,et al.  Removing noise from music using local trigonometric bases and wavelet packets , 1994 .

[16]  D Marr,et al.  Theory of edge detection , 1979, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[17]  M. Wickerhauser,et al.  Wavelets and time-frequency analysis , 1996, Proc. IEEE.

[18]  Ronald R. Coifman,et al.  Signal processing and compression with wavelet packets , 1994 .

[19]  Gilbert Strang,et al.  Wavelets and Dilation Equations: A Brief Introduction , 1989, SIAM Rev..

[20]  Thomas W. Parks,et al.  A two-dimensional translation invariant wavelet representation and its applications , 1994, Proceedings of 1st International Conference on Image Processing.

[21]  M. Wickerhauser.  Acoustic signal compression with wavelet packets , 1993 .

[22]  C.-C. Jay Kuo,et al.  Texture analysis and classification with tree-structured wavelet transform , 1993, IEEE Trans. Image Process..

[23]  J. Pesquet,et al.  On the Statistics of Best Bases Criteria , 1995 .

[24]  Y. Meyer,et al.  Remarques sur l'analyse de Fourier à fenêtre , 1991 .

[25]  Thomas W. Parks,et al.  A translation-invariant wavelet representation algorithm with applications , 1996, IEEE Trans. Signal Process..

[26]  Israel Cohen,et al.  Translation-invariant denoising using the minimum description length criterion , 1999, Signal Process..

[27]  R. S. Orr,et al.  Use of the Gabor representation for Wigner distribution crossterm suppression , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[28]  Israel Cohen,et al.  Shift invariant wavelet packet bases , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[29]  I. Cohen,et al.  Adaptive time-frequency distributions via the shift-invariant wavelet packet decomposition , 1998, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (Cat. No.98TH8380).

[30]  T Lu,et al.  Optical wavelet matched filters for shift-invariant pattern recognition. , 1993, Optics letters.

[31]  José M. F. Moura,et al.  Nearly shiftable scaling functions , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[32]  John S. Baras,et al.  Properties of the multiscale maxima and zero-crossings representations , 1993, IEEE Trans. Signal Process..

[33]  Robert Hummel,et al.  Reconstructions from zero crossings in scale space , 1989, IEEE Trans. Acoust. Speech Signal Process..

[34]  T. Claasen,et al.  THE WIGNER DISTRIBUTION - A TOOL FOR TIME-FREQUENCY SIGNAL ANALYSIS , 1980 .

[35]  I. Cohen,et al.  MDL-based translation-invariant denoising and robust time-frequency representations , 1998, Proceedings of the IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis (Cat. No.98TH8380).

[36]  A. Enis Çetin,et al.  Signal recovery from wavelet transform maxima , 1994, IEEE Trans. Signal Process..

[37]  X. Fang,et al.  Adapted Multiple Folding Local Trigonometric Transforms and Wavelet Packets , 1994 .

[38]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[39]  Israel Cohen,et al.  Eliminating interference terms in the Wigner distribution using extended libraries of bases , 1997, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[40]  Hervé Carfantan,et al.  Estimation of noisy signals using time-invariant wavelet packets , 1993, Proceedings of 27th Asilomar Conference on Signals, Systems and Computers.

[41]  Robert J. Marks,et al.  The use of cone-shaped kernels for generalized time-frequency representations of nonstationary signals , 1990, IEEE Trans. Acoust. Speech Signal Process..

[42]  Israel Cohen,et al.  Evolution of spectral power density in grounded-cathode relativistic magnetron , 1996, Optics & Photonics.

[43]  Stéphane Mallat,et al.  Matching pursuits with time-frequency dictionaries , 1993, IEEE Trans. Signal Process..

[44]  N. Hess-Nielsen.  Control of Frequency Spreading of Wavelet Packets , 1994 .

[45]  O. Rioul,et al.  Wavelets and signal processing , 1991, IEEE Signal Processing Magazine.

[46]  Jian Fan,et al.  Texture Classification by Wavelet Packet Signatures , 1993, MVA.

[47]  Naoki Saito,et al.  Multiresolution representations using the auto-correlation functions of compactly supported wavelets , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[48]  M. Vetterli,et al.  Wavelets, subband coding, and best bases , 1996, Proc. IEEE.

[49]  Naoki Saito,et al.  Simultaneous noise suppression and signal compression using a library of orthonormal bases and the minimum-description-length criterion , 1994, Defense, Security, and Sensing.

[50]  Douglas L. Jones,et al.  Adaptive cone-kernel time-frequency analysis , 1995, IEEE Trans. Signal Process..

[51]  Peter N. Heller,et al.  An M-band, 2-dimensional translation-invariant wavelet transform and applications , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[52]  David L. Donoho,et al.  De-noising by soft-thresholding , 1995, IEEE Trans. Inf. Theory.

[53]  Ronald R. Coifman,et al.  Wavelet analysis and signal processing , 1990 .

[54]  Ali N. Akansu,et al.  Time-frequency localization in transforms, subbands, and wavelets: a critical review , 1993 .

[55]  I. Johnstone,et al.  Ideal denoising in an orthonormal basis chosen from a library of bases , 1994 .

[56]  Henrique S. Malvar.  Lapped transforms for efficient transform/subband coding , 1990, IEEE Trans. Acoust. Speech Signal Process..

[57]  Albert Cohen,et al.  Time-Frequency Localization with Non-Stationary Wavelet Packets , 1996 .

[58]  S. Raz,et al.  Synthesis of signals from wigner distributions: representation on biorthogonal bases , 1990 .

[59]  Stéphane Mallat,et al.  Characterization of Signals from Multiscale Edges , 2011, IEEE Trans. Pattern Anal. Mach. Intell..

[60]  Jonathan Cohen,et al.  Reduction of autoregressive noise with shift-invariant wavelet-packets , 1996, Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96).

[61]  B. Silverman,et al.  The Stationary Wavelet Transform and some Statistical Applications , 1995 .

[62]  G. Beylkin,et al.  On the representation of operators in bases of compactly supported wavelets , 1992 .

[63]  Carl Taswell,et al.  WavBox 4: A Software Toolbox for Wavelet Transforms and Adaptive Wavelet Packet Decompositions , 1995 .

[64]  Ronald R. Coifman,et al.  Local discriminant bases , 1994, Optics & Photonics.

[65]  Edward H. Adelson,et al.  Shiftable multiscale transforms , 1992, IEEE Trans. Inf. Theory.

[66]  Nurgun Erdol,et al.  The optimal wavelet transform and translation invariance , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[67]  Pierre Moulin.  A new look at signal-adapted QMF bank design , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[68]  P. J. Burt,et al.  Fast Filter Transforms for Image Processing , 1981 .

[69]  Philip M. Woodward,et al.  Probability and Information Theory with Applications to Radar , 1954 .

[70]  M. Mugur-Schächter.  Study of Wigner's theorem on joint probabilities , 1979 .

[71]  Yves Meyer,et al.  Size properties of wavelet packets , 1992 .

[72]  Israel Cohen,et al.  Adaptive suppression of Wigner interference-terms using shift-invariant wavelet packet decompositions , 1999, Signal Process..

[73]  Martin Vetterli,et al.  Wavelets and filter banks: theory and design , 1992, IEEE Trans. Signal Process..

[74]  Michael T. Orchard,et al.  An efficient algorithm to find a jointly optimal time-frequency segmentation using time-varying filter banks , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[75]  Douglas L. Jones,et al.  A high resolution data-adaptive time-frequency representation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[76]  Hamid Krim,et al.  Robust multiscale representation of processes and optimal signal reconstruction , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[77]  I. Daubechies.  Orthonormal bases of compactly supported wavelets II: variations on a theme , 1993 .

[78]  D. Donoho,et al.  Translation-Invariant De-Noising , 1995 .

[79]  Stéphane Mallat,et al.  Singularity detection and processing with wavelets , 1992, IEEE Trans. Inf. Theory.

[80]  Ronald R. Coifman,et al.  On local orthonormal bases for classification and regression , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[81]  Stéphane Mallat,et al.  Zero-crossings of a wavelet transform , 1991, IEEE Trans. Inf. Theory.

[82]  Leon Cohen,et al.  Positive time-frequency distribution functions , 1985, IEEE Trans. Acoust. Speech Signal Process..

[83]  Richard Kronland-Martinet,et al.  Analysis of Sound Patterns through Wavelet transforms , 1987, Int. J. Pattern Recognit. Artif. Intell..

[84]  A. Cohen,et al.  Wavelets: the mathematical background , 1996, Proc. IEEE.

[85]  Carl Taswell.  Near-best basis selection algorithms with non-additive information cost functions , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[86]  Henrique S. Malvar,et al.  Signal processing with lapped transforms , 1992 .

[87]  M. Victor Wickerhauser,et al.  Adapted wavelet analysis from theory to software , 1994 .

[88]  W. J. Williams,et al.  Reduced interference distributions: biological applications and interpretations , 1996, Proc. IEEE.

[89]  Jorma Rissanen,et al.  Stochastic Complexity in Statistical Inquiry , 1989, World Scientific Series in Computer Science.

[90]  Theo A. C. M. Claasen,et al.  On positivity of time-frequency distributions , 1985, IEEE Trans. Acoust. Speech Signal Process..

[91]  Stephen P. Del Marco,et al.  Wavepacket-based transient signal detector using a translation-invariant wavelet transform , 1994, Defense, Security, and Sensing.

[92]  I. Daubechies.  Orthonormal bases of compactly supported wavelets , 1988 .

[93]  R. S. Orr,et al.  Instantaneous frequency estimation using the crossterm deleted Wigner representation (CDWR) , 1996, Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96).

[94]  Ronald R. Coifman,et al.  Adapted waveform analysis as a tool for modeling, feature extraction, and denoising , 1994 .

[95]  Pierre Moulin.  Signal estimation using adapted tree-structured bases and the MDL principle , 1996, Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96).

[96]  Ronald R. Coifman,et al.  Entropy-based algorithms for best basis selection , 1992, IEEE Trans. Inf. Theory.

[97]  Kannan Ramchandran,et al.  Tilings of the time-frequency plane: construction of arbitrary orthogonal bases and fast tiling algorithms , 1993, IEEE Trans. Signal Process..

[98]  I. Cohen,et al.  Best basis algorithm for orthonormal shift-invariant trigonometric decomposition , 1996, 1996 IEEE Digital Signal Processing Workshop Proceedings.

[99]  C. K. Chui,et al.  Wigner-Ville distribution decomposition via wavelet packet transform , 1996, Proceedings of Third International Symposium on Time-Frequency and Time-Scale Analysis (TFTS-96).

[100]  Ingrid Daubechies,et al.  Time-frequency localization operators: A geometric phase space approach , 1988, IEEE Trans. Inf. Theory.

[101]  Françoise Peyrin,et al.  A unified definition for the discrete-time, discrete-frequency, and discrete-time/Frequency Wigner distributions , 1986, IEEE Trans. Acoust. Speech Signal Process..

[102]  Israel Cohen,et al.  Time-frequency analysis and noise suppression with shift-invariant wavelet packets , 1998 .

[103]  F. Hlawatsch,et al.  Linear and quadratic time-frequency signal representations , 1992, IEEE Signal Processing Magazine.

[104]  Jorma Rissanen,et al.  Universal coding, information, prediction, and estimation , 1984, IEEE Trans. Inf. Theory.

[105]  William J. Williams,et al.  Improved time-frequency representation of multicomponent signals using exponential kernels , 1989, IEEE Trans. Acoust. Speech Signal Process..

[106]  R. Coifman,et al.  Local feature extraction and its applications using a library of bases , 1994 .

[107]  Hervé Carfantan,et al.  Time-invariant orthonormal wavelet representations , 1996, IEEE Trans. Signal Process..

[108]  Björn Jawerth,et al.  Biorthogonal Smooth Local Trigonometric Bases , 1995 .

[109]  Shie Qian,et al.  Decomposition of the Wigner-Ville distribution and time-frequency distribution series , 1994, IEEE Trans. Signal Process..

[110]  Israel Cohen,et al.  Orthonormal shift-invariant wavelet packet decomposition and representation , 1997, Signal Process..

[111]  Shie Qian,et al.  Wigner Distribution decomposition and cross-terms deleted representation , 1992, Signal Process..

[112]  Michael A. Saunders,et al.  Atomic Decomposition by Basis Pursuit , 1998, SIAM J. Sci. Comput..

[113]  J. Mayer,et al.  On the Quantum Correction for Thermodynamic Equilibrium , 1947 .

[114]  D. Donoho.  Unconditional Bases Are Optimal Bases for Data Compression and for Statistical Estimation , 1993 .

[115]  D. L. Donoho,et al.  Ideal spacial adaptation via wavelet shrinkage , 1994 .

[116]  Carl Taswell,et al.  Top-Down and Bottom-Up Tree Search Algorithms for Selecting Bases in Wavelet Packet Transforms , 1995 .

[117]  Wen-Hsiung Chen,et al.  A Fast Computational Algorithm for the Discrete Cosine Transform , 1977, IEEE Trans. Commun..

[118]  L. Cohen,et al.  Time-frequency distributions-a review , 1989, Proc. IEEE.

[119]  Zhifeng Zhang,et al.  Adaptive time-frequency decompositions , 1994 .

[120]  G. MallatS..  A Theory for Multiresolution Signal Decomposition , 1989 .

[121]  K Ramchandran,et al.  Best wavelet packet bases in a rate-distortion sense , 1993, IEEE Trans. Image Process..

[122]  Stéphane Mallat,et al.  Best basis algorithm for signal enhancement , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[123]  Jechang Jeong,et al.  Kernel design for reduced interference distributions , 1992, IEEE Trans. Signal Process..

[124]  Israel Cohen,et al.  Shift-invariant adaptive local trigonometric decomposition , 1995, EUROSPEECH.

[125]  Douglas L. Jones,et al.  A signal-dependent time-frequency representation: fast algorithm for optimal kernel design , 1994, IEEE Trans. Signal Process..

[126]  N.A. Whitmal,et al.  Wavelet-based noise reduction , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[127]  G. Walter,et al.  Wavelets and Other Orthogonal Systems , 2018 .

[128]  M. Wickerhauser.  Best-Adapted Wavelet Packet Bases , 1990 .

[129]  A. Nuttall.  Wigner Distribution Function: Relation to Short-Term Spectral Estimation, Smoothing, and Performance in Noise. , 1988 .

[130]  Henrique S. Malvar,et al.  The LOT: transform coding without blocking effects , 1989, IEEE Trans. Acoust. Speech Signal Process..

[131]  Benoit M. Macq,et al.  Signal-adapted multiresolution transform for image coding , 1992, IEEE Trans. Inf. Theory.

[132]  Richard G. Baraniuk,et al.  Hybrid linear/bilinear time-scale analysis , 1999, IEEE Trans. Signal Process..