% % BIBLIOGRAPHY OF WAVELET AND WAVELET-RELATED DOCUMENTS % % Steven K. Baum % Dept. of Physical Oceanography % Texas A&M University % baum@astra.tamu.edu % Version 1.4 % 6/3/94 % % Kindly don't remove this header if you copy or transfer this file. % % %AAAA @techreport{andersson-hall-etal:1993, Author = "Andersson, L., N. Hall, B. Jawerth, and G. Peters", Title = "Wavelets on closed subsets of the real line", Year = "1993", Ftp = "maxwell.math.scaroline.edu:pub/imi_93/imi_93_2.ps", Size = "667,500 bytes", Pages = "60", Abstract = "Orthogonal and biorthogonal wavelets are constructed on a given closed subset of the real line. Wavelets satisfying certain types of boundary conditions are studied and the concept of 'wavelet probing' is introduced which allows a number of different numerical tasks associated with wavelets to be performed quickly. This paper is at the wavelet archive site." } @article{argoul-arneodo-etal:1988a, Author = "Argoul, F., A. Arneodo, J. ELezgaray, G. Grasseau, and R. Murenzi", Title = "Wavelet transform of two--dimensional fractal aggregates", Journal = "Phys. Rev. Lett. A", Volume = "135", Pages = "327--336" } @article{argoul-arneodo-etal:1988b, Author = "Argoul, F., A. Arneodo, J. ELezgaray, G. Grasseau, and R. Murenzi", Title = "Wavelet analysis of the self-similarity of diffusion--limited aggregates and electrodeposition clusters", Journal = "Phys. Rev. A", Volume = "41", Pages = "5537--5560" } @article{argoul-arneodo-etal:1989, Author = "Argoul, F., A. Arneodo, G. Grasseau, Y. Gagne, E. J. Hopfinger, and U. Frisch", Title = "Wavelet analysis of turbulence reveals the multifractal nature of the Richardson cascade", Journal = "Nature", Volume = "338", Year = "1989", Pages = "51--53" } @article{arneodo-grasseau-etal:1988, Author = "Arneodo, A., G. Grasseau, and M. Holschneider", Title = "Wavelet transform of multifractals", Journal = "Phys. Rev. Lett.", Volume = "61", Year = "1988", Pages = "2281--2284" } %BBBB @article{bacry-arneodo-etal:1990, Author = "Bacry, E., A. Arneodo, U. Frisch, Y. Gagne, and E. Hopfinger", Title = "Wavelet analysis of fully developed turbulence data and measurement of scaling exponent", Booktitle = "Turbulence and Coherent Structures", Editor = "M. Lesieur and O. Metais", Publisher = "Kluwer Academic Pub.", Year = "1990", Pages = "????" } @article{bacry-mallat-etal:1992, Author = "Bacry, Emmanual, St/'ephane Mallat, and George Papanicolaou", Title = "A wavelet based space--time adaptive numerical method for partial differential equations", Journal = "Mathematical Modelling and Numerical Analysis", Volume = "26", Date = "1992", Pages = "793--834", Abstract = "This describes a space and time adaptive numerical method based on wavelet orthonormal bases for solving partial differential equations. The multiresolution structure of wavelet orthonormal bases provides a simple way to adapt computational refinements to the local regularity of the solution." } @techreport{bacry-mallat-etal:1993, Author = "Bacry, Emmanual, St/'ephane Mallat, and George Papanicolaou", Title = "A wavelet based space--time adaptive numerical method for partial differential equations", Date = "1993", Institution = "Courant Inst. of Math. Sci., New York Univ., 251 Mercer St., New York, N.Y., 10012", Ftp = "cs.nyu.edu:/pub/wave/report/pde.ps.Z", Size = "218,233 bytes", Pages = "33", Abstract = "This describes a space and time adaptive numerical method based on wavelet orthonormal bases for solving partial differential equations. The multiresolution structure of wavelet orthonormal bases provides a simple way to adapt computational refinements to the local regularity of the solution." } @article{bacry-muzy-etal:1993, Author = "Bacry, E., J. Muzy, and A. Arneodo", Title = "Singularity spectrum of fractal signals from wavelet analysis: exact results", Journal = "Journ. of Statistical Physics", Volume = "70", Year = "1993", Pages = "????" } @article{bendjoya-slezak:1993, Author = "Bendjoya, Ph., and E. Slezak" Title = "Wavelet analysis and applications to some dynamical systems" Journal = "Celestial Mech. and Dyn. Astron." Volume = "56" Year = "1993" Pages = "231--262" Note = "The wavelet transform appears as a new time-frequency method which is particulary well-suited to detect and to localize discontinuities and scaling behaviours in signals. The main properties of the wavelet transform and its improvements over classical analyzing methods are summarized. Some results among the first applications to the dynamical systems are presented: solution of PDEs, fractal and turbulence characterization, and asteroid family determination from cluster analysis." } @article{bendjoya-slezak-etal:1991, Author = "Bendjoya, Ph., E. Slezak, Cl. Froeschl/'e", Title = "The wavelet transform: a new tool for asteroid family determination", Journal = "Astron. Astroph.", Volume = "251", Year = "1991", Pages = "312--330" } @techreport{beylkin:1992, Author = "Beylkin, G.", Title = "On the fast algorithm for multiplication of functions in the wavelet bases", Year = "June 1992", Institution = "Prog. in Appl. Math., Univ. of Colorado at Boulder, Boulder, CO 80309-0526", Ftp = "newton.colorado.edu:/pub/wavelets/papers/malgToulouse.ps.Z", Size = "62,005 bytes", Pages = "9", Abstract = "This paper develops a novel approach to the pointwise multiplication of functions in the wavelet bases based on uncoupling the interactions between scales. The complexity of the algorithm is automatically adaptable to the complexity of the wavelet representation of a function u and proportional to the number of significant cofficients in the representation of u." } @techreport{beylkin:1993a, Author = "Beylkin, G.", Title = "On factored FIR approximation of IIR filters", Year = "1993", Institution = "Prog. in Appl. Math., Univ. of Colorado at Boulder, Boulder, CO 80309-0526", Ftp = "newton.colorado.edu:/pub/wavelets/papers/iir2fir.ps.Z", Size = "135,648 bytes", Pages = "11", Abstract = "This paper describes a simple and accurate method of approximating infinite impulse response (IIR) filters by finite impulse filters (FIR)." } @inproceedings{beylkin:1993b, Author = "Beylkin, Gregory", Title = "Wavelets and fast numerical algorithms", Booktitle = "Different Perspectives on Wavelets", Editor = "Ingrid Daubechies", Publisher = "American Math. Soc., Providence, RI", Series = "Proceedings of Symposia in Applied Mathematics", Volume = "47", Year = "1993", Pages = "89--117", Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San Antonio, TX", Abstract = "Reviews the standard and non--standard representations of operators in wavelet bases and associated fast numerical algorithms. The non--standard representation uncouples the interaction among the scales. Examples of the non--standard forms of several basic operators are computed explicitly." } @techreport{beylkin-saito:1993, Author = "Beylkin, Gregory, and Naoki Saito", Year = "1993", Title = "Wavelets, their autocorrelation functions, and multiresolution representation of signals", Institution = "Prog. in Appl. Math., Univ. of Colorado at Boulder, Boulder, CO 80309-0526", Ftp = "newton.colorado.edu:/pub/wavelets/papers/spie.ps.Z", Size = "160,004 bytes", Pages = "12", Abstract = "The properties of the auto-correlation functions of compactly supported wavelets are summarized as well as their connection to iterative interpolation schemes and the use of these functions for multiresolution analysis of signals." } @article{beylkin-coifman-etal:1991, Author = "Beylkin, G., R. Coifman, and V. Rokhlin", Title = "Fast wavelet transforms and numerical algorithms", Journal = "Comm. in Pure and Applied Math.", Volume = "44", Year = "1991", Pages = "141--183" } @techreport{bhatia-karl-etal:1993, Author = "Bhatia, M., W. C. Karl, and A. S. Willsky", Email = "mbhatia@mit.edu", Title = "A wavelet-based method for multiscale tomographic reconstruction", Number = "MIT Tech. Rep. LIDS-P-2182", Year = "1993", Institution = "Stochastic Systems Group, Lab. for Information and Dec. Systems, MIT, Cambridge, MA 02139", Ftp = "lids.mit.edu:/pub/ssg/papers/LIDS-P-2182.PS.gz", Size = "595,196 bytes", Pages = "31", Abstract = "A wavelet-based representation of the standard ramp filter operator of the filtered back-projection (FBP) reconstruction enables the formulation of a multiscale tomographic reconstruction technique wherein the object is reconstructed at multiple scales or resolutions. A complete reconstruction is obtained by combining the reconstructions at different scales. The framework for multiscale reconstruction presented here can find application in object feature recognition directly from projection data, and regularization of imaging problems where the projection data are noisy." } @techreport{bond-vavasis:1994, Author = "Bond, Dave M. and Stephen A. Vavasis", Title = "Fast wavelet transforms for matrices arising from boundary element methods", Year = "1994", Month = "mar", Number = "174", Institution = "Center for Applied Mathematics, Eng. and Theory Center, Cornell Univ., Ithaca, N.Y. 14853", URL = "ftp://ftp.tc.cornell.edu/pub/tech.reports/tr174.ps", Size = "465,044", Pages = "45", Abstract = "Wavelet transforms are applied to express matrices obtained from discretizing the integral equations obtained from applying the boundary element method to Laplace's equation. This transforms dense matrices to sparse ones and thus allows faster inversion." } @article{bradshaw-mcintosh:1994, Author = "Bradshaw, G. A., and B. A. McIntosh", Title = "Determining climate--induced patterns using wavelet analysis", Journal = "Environmental Pollution", Volume = "83", Year = "1994", Pages = "133--142", Abstract = "A method using wavelet analysis is introduced for the purpose of identifying and isolating inferred climatic components of the hydrologic record. This method affords an informed procedure for choosing filter dimensions for the purpose of signal decomposition." } 9109.ps.Z CML TR91-09, Hubert Bray, Kent McCormick, Raymond O. Wells, Jr. and Xiaodong Zhou, "Wavelet Variations on the Shannon Sampling Theorem" @techreport{bray-mccormick-etal:1991, Author = "Bray, Hubert and Kent McCormick and Raymond O. Wells and Xiaodong Zhou", Title = "Wavelet variations on the Shannon sampling theorem", Year = "1991", Number = "TR91-09", Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892", URL = "ftp://cml.rice.edu/pub/reports/9109.ps.Z", Size = "76,567", Pages = "?", Abstract = "?" } %CCCC @techreport{cabrera-kreinovich-etal:1992, Author = "Cabrera, Sergio, Vladik Kreinovich, and Ongard Sirisaengtaksin", Email = "vladik@cs.ep.utexas.edu", Title = "Wavelets compress better than all other methods: A 1-D theorem", Year = "1992", Institution = "Dept. of Comp. Sci., Univ. of Texas at El Paso, El Paso, TX 79968", Ftp = "cs.ep.utexas.edu:/pub/reports/tr92-25.tex", Size = "82,806 bytes", Pages = "31", Abstract = "Wavelet compression is compared with all possible compressions and is found, for smooth 1-dimensional signals, to be better in the sense that it requires the smallest number of bytes to store the wavelet representation." } @article{cohen_a-daubechies:1993, Author = "Cohen, A., and Ingrid Daubechies", Title = "Orthonormal bases of compactly supported wavelets: III. Better frequency resolution", Journal = "SIAM J. Math. Anal.", Volume = "24", Year = "1993", Pages = "520--527", Abstract = "Standard orthonormal bases of wavelets with dilation factor 2 use wavelets with one octave bandwidth. Orthonormal bases with 1/2 octave or even smaller bandwidth wavelets are constructed." } @techreport{cohen_j:1993a, Author = "Cohen, Jack K.",, Email = "jkc@keller.mines.colorado.edu", Title = "The Stein wavelet", Year = "Nov. 2, 1993", Institution = "Colorado School of Mines", Ftp = "hilbert.mines.colorado.edu:pub/wavelets/Stein.400dpi.ps.z", Size = "83,275 bytes", Pages = "6", Abstract = "This is a Mathematica notebook converted to TeX using nb2tex from mathsource and then converted to postscript. The notebook gives details for the construction of the Littlewood-Paley-Stein wavelet." } @techreport{cohen_j:1993b, Author = "Cohen, Jack K.",, Email = "jkc@keller.mines.colorado.edu", Title = "The foot problem in wavelet packet splitting", Year = "Nov. 1, 1993", Institution = "Colorado School of Mines", Ftp = "hilbert.mines.colorado.edu:pub/wavelets/PacketFeet.400dpi.ps.z", Size = "441,923 bytes", Pages = "35", Abstract = "This is a Mathematica notebook converted to TeX using nb2tex from mathsource and then converted to postscript. The notebook discusses the problem of pieces of non-adjacent bands creeping in when constructing wavelet packets." } @techreport{cohen_j:1993c, Author = "Cohen, Jack K.",, Email = "jkc@keller.mines.colorado.edu", Title = "Schauder basis for C[0,1]", Year = "Nov. 11, 1993", Institution = "Colorado School of Mines", Ftp = "hilbert.mines.colorado.edu:pub/wavelets/Schauder.400dpi.ps.z", Size = "231,729 bytes", Pages = "19", Abstract = "This is a Mathematica notebook converted to TeX using nb2tex from mathsource and then converted to postscript. The notebook discusses the Schauder basis for C[0,1] in the context of wavelets." } @techreport{cohen_j:1993d, Author = "Cohen, Jack K.",, Email = "jkc@keller.mines.colorado.edu", Title = "Battle-Lemarie wavelets", Year = "Nov. 1, 1993", Institution = "Colorado School of Mines", Ftp = "hilbert.mines.colorado.edu:pub/wavelets/Spline.400dpi.ps.z", Size = "120,847 bytes", Pages = "11", Abstract = "This is a Mathematica notebook converted to TeX using nb2tex from mathsource and then converted to postscript. The notebook discusses the details about and construction of Battle-Lamarie wavelets." } @techreport{cohen_j:1993e, Author = "Cohen, Jack K.",, Email = "jkc@keller.mines.colorado.edu", Title = "Dauchechies minimum phase wavelets", Year = "Nov. 22, 1993", Institution = "Colorado School of Mines", Ftp = "hilbert.mines.colorado.edu:pub/wavelets/Daubechies.400dpi.ps.z", Size = "211,543 bytes", Pages = "15", Abstract = "This is a Mathematica notebook converted to TeX using nb2tex from mathsource and then converted to postscript. The notebook discusses Daubechies minimum phase wavelets." } @techreport{cohen_j:1993f, Author = "Cohen, Jack K.",, Email = "jkc@keller.mines.colorado.edu", Title = "Meyer wavelets", Year = "Nov. 1, 1993", Institution = "Colorado School of Mines", Ftp = "hilbert.mines.colorado.edu:pub/wavelets/Meyer.400dpi.ps.z", Size = "138,220 bytes", Pages = "25", Abstract = "This is a Mathematica notebook converted to TeX using nb2tex from mathsource and then converted to postscript. The notebook discusses Meyer wavelets." } @article{cohen_l:1989, Author = "Cohen, L.", Title = "Time--frequency distributions -- A review", Journal = "Proc. IEEE", Volume = "77", Year = "1989", Pages = "941--981", Abstract = "A review and tutorial of the fundamental ideas and methods of joint time--frequency distributions is presented. The objective of the field is to describe how the spectral content of a signal is changing in time, and to develop the mathematical and physical ideas needed to understand what a time--varying spectrum is. The basic goal is to devise a distribution that represents the energy or intensity of a signal simultaneously in time and frequency. This review especially reflects recent advances in the field such as the use of wavelets." } @techreport{coifman-meyer-etal:1990, Author = "Coifman, Ronald R., Yves Meyer, Steven Quake and M. Victor Wickerhauser", Title = "Signal processing and compression with wave packets", Year = "Apr. 5, 1990", Institution = "Numerical Algorithms Res. Group, Dept. of Math., Yale Univ., New Haven, CT 06520", Ftp = "math.yale.edu:/pub/wavelets/cmqw.tex", Size = "33,511 bytes", Pages = "15", Abstract = "Algorithms for signal processing and data compression based on a collection of orthogonal functions called fast wave packets are described. Fast wave packets generalize the compactly supported wavelets of Daubechies and Meyer. The algorithms described combine the projection of a sequence onto fast wave packet components, the selection of an optimal orthonormal basis subset, some linear or quasilinear processing of the coefficients, and then reconstruction of the transformed sequence." } @techreport{coifman-meyer-etal:1991, Author = "Coifman, Ronald R., Yves Meyer and M. Victor Wickerhauser", Title = "Wavelet analysis and signal processing", Year = "1991", Institution = "Numerical Algorithms Res. Group, Dept. of Math., Yale Univ., New Haven, CT 06520", Ftp = "wuarchive.wustl.edu:/doc/techreports/wustl.edu/math/wasp.ps.Z", Size = "313,751 bytes", Pages = "29", Abstract = "This describes the use of wavelet analysis for various tasks in signal processing." } @techreport{coifman-wickerhauser:1991, Author = "Coifman, Ronald R. and M. Victor Wickerhauser", Title = "Wavelets and adapted waveform analysis", Year = "1991", Institution = "Numerical Algorithms Res. Group, Dept. of Math., Yale Univ., New Haven, CT 06520", Ftp = "wuarchive.wustl.edu:/doc/techreports/wustl.edu/math/wawa.ps.Z", Size = "878,503 bytes", Pages = "33", Abstract = "This describes tools for adapting methods of analysis to various tasks occuring in harmonic and numerical analysis and signal processing. The main point is that by choosing an orthonormal basis in which space and frequency are suitably localized one can achieve understanding of both structure and efficiency in computation." } @inproceedings{coifman-wickerhauser:1993, Author = "Coifman, Ronald R., and M. Victor Wickerhauser", Title = "Wavelets and adapted waveform analysis: A toolkit for signal processing and numerical analysis", Booktitle = "Different Perspectives on Wavelets", Editor = "Ingrid Daubechies", Publisher = "American Math. Soc., Providence, RI", Series = "Proceedings of Symposia in Applied Mathematics", Volume = "47", Year = "1993", Pages = "119--153", Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San Antonio, TX", Abstract = "Wavelet analysis or, more generally, Adapted Waveform Analysis (AWA) consists of a versatile collection of tools for the analysis and manipulation of signals such as sound and images, as well as more general digital data sets (including linear and non--linear operators occurring in the simulations of physical processes). AWA provides us with the ability to represent a function or signal in a mode similar to a musical score, where each note corresponds to a waveform having a duration, pitch and amplitude. The goal is to transcribe as efficiently as possible, and to orchestrate into different structures." } %DDDD @article{dallard-browand:1993, Author = "Dallard, T., and F. K. Browand", Title = "The growth of large scales at defect sites in the plane mixing layer", Journal = "J. Fluid Mech.", Volume = "247", Year = "1993", Pages = "339--368" } @article{dallard-spedding:1993, Author = "Dallard, T., and G. R. Spedding", Title = "2-D wavelet transforms: generalisation of the Hardy space and application to experimental studies", Journal = "Eur. J. Mech., B/Fluids", Volume = "12", Year = "1993", Pages = "107--134" } @inproceedings{daubechies:1993a, Author = "Daubechies, Ingrid", Title = "Wavelet transforms and orthonormal wavelet bases", Booktitle = "Different Perspectives on Wavelets", Editor = "Ingrid Daubechies", Publisher = "American Math. Soc., Providence, RI", Series = "Proceedings of Symposia in Applied Mathematics", Volume = "47", Year = "1993", Pages = "1--33", Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San Antonio, TX", Abstract = "Introduces the wavelet transform and discusses its motivation as a time--frequency localization tool. Reviews the different types of wavelet transform, with special emphasis on orthonormal wavelet bases and their properties. Concludes with a short discussion of shortcomings." } @article{daubechies:1993b, Author = "Daubechies, Ingrid", Title = "Orthonormal bases of compactly supported wavelets: II. Variations on a theme", Journal = "SIAM J. Math. Anal.", Volume = "24", Year = "1993", Pages = "499--519", Abstract = "Several variations are given on the construction of orthonormal bases of wavelets with compact support. They have, respectively, more symmetry, more regularity, and more vanishing moments for the scaling function than the examples in daubechies:1988." } @article{daubechies-lagarias:1991, Author = "Daubechies, I[ngrid]., and J. Lagarias", Title = "Two-scale difference equations, I", Journal = "SIAM J. Math. Anal.", Volume = "22", Year = "1991", Pages = "1388--1410" } @article{daubechies-lagarias:1992, Author = "Daubechies, I., and J. Lagarias", Title = "Two-scale difference equations, II", Journal = "SIAM J. Math. Anal.", Volume = "23", Year = "1992", Pages = "1031--1079" } @techreport{deboor-devore-etal:1992, Author = "de Boor, Carl and Ronald A. DeVore and Amos Ron", Title = "On the construction of multivariate (pre)wavelets", Year = "1992", Month = "Feb", Number = "92-09", Institution = "Cent. for Math. Sci., Univ. of Wisconsin-Madison, 610 Walnut St., Madison, WI 53705", URL = "ftp://stolp.cs.wisc.edu/wavelet.ps.Z", Size = "154,254", Pages = "42", Keyword = "wavelets", Abstract = "A new approach to the construction of wavelets and prewavelets from multiresolution is presented. The method uses only properties of shift-invariant spaces and orthogonal projectors onto these spaces, and requires neither decay nor stability of the scaling function." } @article{devore-lucier:1991, Author = "DeVore, R., and B. J. Lucier", Title = "Wavelets", Journal = "Acta Numerica", Volume = "1", Year = "1991", Pages = "1--56" } @article{devore-jawerth-etal:1992, Author = "DeVore, R., B. Jawerth, and B. J. Lucier", Title = "Image compression through wavelet transform coding", Journal = "IEEE Trans. Inform. Theory", Volume = "38", Year = "1992", Pages = "719--746" } @techreport{donoho:1992, Author = "Donoho, David L.", Title = "Wavelet shrinkage and W.V.D - A ten-minute tour", Year = "1992", Institution = "Stanford Univ.", Ftp = "playfair.stanford.edu:pub/reports/toulouse.tex", Size = "27,718 bytes", Pages = "12", Abstract = "According to the List file at the same address, there is supposed to be a toulouseps.shar file containing the figures for this paper available. As of 7/11/93 it ain't." } @inproceedings{donoho:1993a, Author = "Donoho, David L.", Title = "Nonlinear wavelet methods for recovery of signals, densities, and spectra from indirect and noisy data", Booktitle = "Different Perspectives on Wavelets", Editor = "Ingrid Daubechies", Publisher = "American Math. Soc., Providence, RI", Series = "Proceedings of Symposia in Applied Mathematics", Volume = "47", Year = "1993", Pages = "173--205", Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San Antonio, TX", Abstract = "Wavelet methods for the recovery of objects from noisy and incomplete data are described. The common themes: (a) the new methods use nonlinear operations in the wavelet domain; (b) they accomplish tasks which are not possible by traditional linear/Fourier approaches to such problems. An attempt is made to indicate the heuristic principles, theoretical foundations and possible application areas for these methods, i.e. wavelet de-noising, wavelet approaches to linear inverse problems, wavelet packet de-noising, segmented multiresolutions, and nonlinear multi-resolutions. This can also be obtained via anonymous ftp (donoho:1993b)." } @techreport{donoho:1993b, Author = "Donoho, David L.", Title = "Nonlinear wavelet methods for recovery of signals, densities, and spectral from indirect and noisy data", Year = "1993", Institution = "Stanford Univ.", Ftp = "playfair.stanford.edu:pub/software/wavelets/ShortCourse.ps", Size = "????? bytes", Pages = "33", Keywords = "wavelets", Abstract = "Wavelet methods for the recovery of objects from noisy and incomplete data are described. The common themes: (a) the new methods use nonlinear operations in the wavelet domain; (b) they accomplish tasks which are not possible by traditional linear/Fourier approaches to such problems. An attempt is made to indicate the heuristic principles, theoretical foundations and possible application areas for these methods, i.e. wavelet de-noising, wavelet approaches to linear inverse problems, wavelet packet de-noising, segmented multiresolutions, and nonlinear multi-resolutions. The size indicated above is for the text only. The 28 figures are contained in the separate file ShortCourseFigs.epsf.shar.Z (812,771)." } @EEEE @techreport{edwards:1992, Author = "Edwards, Tim", Email = "tim@sinh.stanford.edu", Title = "Discrete wavelet transforms: Theory and application (Draft #2)", Year = "June 4, 1992", Institution = "Stanford University", Ftp = "isl.stanford.edu:/pub/godfrey/reports/wavelets/wave_paper/wave_paper.ps", Size = "438,782 bytes", Pages = "27", Keywords = "wavelets", Abstract = "This includes a brief introduction to wavelets in general and the discrete wavelet transform in particular, covering a number of implementation issues that are often missed in the literature. A hardware implementation on a commercially available DSP system is described along with a program listing to show how such an implementation can be simulated." } %FFFF @article{farge:1992, Author = "Farge, Marie", Title = "Wavelet transforms and their applications to turbulence", Journal = "Ann. Rev. Fluid. Mech.", Volume = "24", Year = "1992", Pages = "395--457", Abstract = "Gives a general representation of both the continuous and discrete wavelet transforms, in a manner as complete and detailed as possible, to provide the reader with the basic information with which to start using these transforms. Brief reference is made to papers dealing with applications, and several new diagnostics, all based on wavelet coefficients, which may be useful to analyze, model, or compute turbulent flows are presented." } @incollection{farge-holschneider-etal:1989, Author = "Farge, M[arie], M. Holschneider, and J. F. Colonna", Title = "Wavelet analysis of coherent structures in 2-D turbulent flows", Booktitle = "Topological Fluid Mechanics", Editor = "K. Moffatt", Publisher = "Cambridge Univ. Press", Year = "1989, Pages = "765--767" } @article{flandrin:1992, Author = "Flandrin, P.", Title = "Wavelet analysis and synthesis of fractional Brownian motion", Journal = "IEEE Trans. Inf. Theory", Volume = "38", Year = "1992", Pages = "????" } %GGGG @article{gamage-blumen:1993, Author = "Gamage, Nimal, and William Blumen", Title = "Comparative analysis of low--level cold fronts: Wavelet, Fourier, and empirical orthogonal function decompositions", Journal = "Monthly Weather Review", Volume = "121", Year = "1993", Pages = "2867--2878", Abstract = "The relative merits of using both global and local (with respect to the span of a basis element) transforms to depict cold--front features are explored. It is concluded that the wavelet or local transform provides a superior representation of frontal phenomena when compared with global transform methods." @Article{gao-li:1993, Author = "Gao, W., and B. L. Li", Title = "Wavelet analysis of coherent structures at the atmosphere--forest interface", Journal = "J. Appl. Meteorol.", Volume = "32", Year = "1993", Pages = "1717--1725", Keywords = "coherent structures, wavelets" } @techreport{gilbert:1992, Author = "Gilbert, John E.", Title = "Wavelets: Theory and applications", Year = "1992", Institution = "University of Texas", Ftp = "math.utexas.edu:/pub/papers/lakey/m391c/gilbertnotes.ps", Size = "473,166 bytes", Pages = "66", Keywords = "wavelets", Abstract = "These are lecture notes for a course on wavelet analysis. The first part covers Fourier analysis on Euclidean space and the second wavelet analysis including such topics as the continuous wavelet transform, pre-historic wavelets, image analysis and multi-resolution, splines as pre-wavelets, and Daubechies reconstruction." } @inproceedings{glowinski-lawton-etal:1990, Author = "Glowinski, Roland and Wayne Lawton and Michel Ravachol and Eric Tenenbaum", Title = "Wavelet solutions of linear and nonlinear elliptic, parabolic and hyperbolic problems in one space dimension", Booktitle = "Computing Methods in Applied Sciences and Engineering", Editor = "Roland Glowinski and Alain Lichnewsky", Publisher = "Society for Industrial and Applied Mathematics", Note = "Proceedings of the Ninth International Conference on Computing Methods in Applied Sciences and Engineering", Year = "1990", Pages = "55--120", Abstract = "This discusses the Daubechies wavelet solution of boundary value problems and initial boundary value problems for ordinary and partial differential equations in one space dimension. The theoretical and numerical results suggest that for the above class of problems wavelets provide a robust and accurate alternative to more traditional methods such as finite differences and finite elements." } @techreport{glowinski-pan-etal:1993, Author = "Glowinski, Roland and T. W. Pan and Raymond O. Wells, Jr. and Xiaodong Zhou", Title = "Wavelet and finite element solutions for the Neumann problem using fictitious domains", Number = "TR92-01", Year = "1993", Month = "aug", Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892", URL = "ftp://cml.rice.edu/pub/reports/9201.ps.Z", Size = "385,687", Pages = "36", Keyword = "wavelets, finite elements", Abstract = "The boundary value problem is formulated for an open domain with a rectifiable boundary of any shape which is embedded in a larger and simpler domain (usually rectilinear in shape). The elliptic boundary value problem in the original domain is reformulated in a weak form as an integral equation in the larger domain, which involves introducing a regularization (or penalty) parameter. Solutions depending on this parameter converge to solutions of the original equation as the parameter converges to zero. Both wavelet and finite element Galerkin methods are used for numerical approximations in the larger domain for fixed and small values of the parameter, in which fast periodic solvers can be implemented due to its rectinlinearity." } @techreport{glowinski-rieder-etal:1993, Author = "Glowinski, Roland and Andreas Rieder and Raymond O. Wells, Jr. and Xiaodong Zhou", Title = "A wavelet multilevel method for Dirichlet boundary value problems in general domains", Year = "1993", Month = "sep", Number = "9306", Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892", URL = "ftp://cml.rice.edu/pub/reports/9306.ps.Z", Size = "144,071", Pages = "37", Keyword = "wavelets", Abstract = "A multilevel method for the efficient solution of the linear system arising from a Wavelet-Galerkin discretization of a Dirichlet boundary value problem via a penalty/fictitious domain formulation is presented. The presence of the penalty term requires a modified coarse grid correction process to guarantee a convergence rate which is independent of the discretization step size. Numerical experiments confirm the result." } @phdthesis{goldburg:1993, Author = "Goldburg, Marc", Title = "Applications of wavelets to quantization and random process representations", Year = "1993", Institution = "Dept. of Elect. Eng., Stanford Univ.", Ftp = "rascals.stanford.edu:/pub/marcg/mgThesis2side.ps.Z", Size = "1,099,639 bytes", Pages = "164", Abstract = "This thesis examines the utility of the wavelet transform for three different signal processing applications: the representation of continuously indexed random processes; transform vector quantization systems; and partial representations and subband coding of discretely indexed random processes." } @manual{gollmer:1992, Author = "Gollmer, Steven", Title = "DAUBWAVE.DOC", Year = "1992", Month = "oct", Ftp = "freehep.scri.fsu.edu:/freehep/lattice_field_theory/daubwave/daubwave.tar", Psize = "71,680 bytes", File = "daubwave.doc", Size = "34,803", Pages = "15", Keywords = "wavelets", Abstract = "The purpose of this program is to perform wavelet based operations on a data set. It should be useful in learning orthogonal wavelet analysis as well as data analysis using orthogonal wavelets. This program uses orthogonal wavelet analysis based on Daubechies' derived coefficients. This manual details how to perform wavelet transforms and inverse transforms using the program as well as how to use band pass, low pass, high pass, and notch filters." } @phdthesis{gopinath:1993, Author = "Gopinath, Ramesh A.", Title = "Wavelets and filter banks - New results and applications", Year = "1993", Institution = "Dept. of Elec. and Comp. Eng., Rice Univ., Houston, TX 77251", Ftp = "cml.rice.edu:/pub/ramesh/papers/phd.ps.Z", Size = "1,340,089 bytes", Pages = "270", Abstract = "Wavelet transforms provide a new technique for time--scale analysis of non--stationary signals. Wavelet analysis uses orthonormal bases in which computations can be done efficiently with multirate systems known as filter banks. This thesis develops a comprehensive set of tools for multidimensional multirate signal analysis and uses them to investigate two multirate systems: filter banks and transmultiplexers. Also described are the design of optimal wavelets for signal representation and the wavelet sampling theorem. Application of wavelets in signal interpolation and in the approximation of linear-- translation invariant operators is investigated." } @techreport{gopinath-burrus:1991a, Author = "Gopinath, R. A. and C. S. Burrus", Title = "Wavelet-based lowpass/bandpass interpolation", Year = "1991", Number = "TR91-06", Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892", URL = "ftp://cml.rice.edu/pub/reports/9106.ps.Z", Size = "92,999", Pages = "?", Abstract = "?" } @techreport{gopinath-burrus:1991b, Author = "Gopinath, R. A. and C. S. Burrus", Title = "On the correlation structure of multiplicity M scaling functions and wavelets", Year = "1991", Number = "TR91-19", Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892", URL = "ftp://cml.rice.edu/pub/reports/9119.ps.Z", Size = "57,763", Pages = "?", Abstract = "?" } @techreport{gopinath-burrus:1993, Author = "Gopinath, Ramesh A., and C. S. Burrus", Title = "Wavelets and filter banks", Year = "1991", Number = "TR91-20", Institution = "Dept. of Elec. and Comp. Eng., Rice Univ., Houston, TX 77251", Ftp = "cml.rice.edu:/pub/reports/9120.ps.Z", Size = "210,708 bytes", Pages = "48", Abstract = "Wavelet and short-time Fourier analysis is introduced in the context of frequency decompositions. Wavelet type frequency decompositions are associated with filter banks, and using this fact, filter bank theory is used to construct multiplicity M wavelet frames and tight frames. Efficient computational structures for both filter banks and wavelets are discussed." } @article{goubet:1992, Author = "Goubet, Olivier", Title = "Construction of approximate inertial manifolds using wavelets", Journal = "SIAM J. Math. Anal.", Volume = "23", Year = "1992", Pages = "1455--1481", Abstract = "Approximate inertial manifolds are constructed for a class of dissipative evolution equations. The innovation is that these manifolds are defined as graphs on orthonormal wavelet bases." } %HHHH @unpublished{harrod-nagy-etal:1994, Author = "Harrod, William J. and James G. Nagy and Robert J. Plemmons", Title = "Image restoration using fast Fourier and wavelet transforms", Year = "1994", Institution = "Cray Res., Inc., Eagan, MN 55121", URL = "ftp://deacon.mathscs.wfu.edu/pub/plemmons/fftrest.ps.Z", Size = "359,959", Pages = "16", Keyword = "wavelets, image processing, FFT", Abstract = "Image restoration can be modeled as a discrte, ill-posed, 2D inverse problem which can be solved by a preconditioned conjugate gradient least squares algorithm. The preconditioning is usually accomplished via FFT techniques, but for some situations this is not viable. The possible use of wavelet transform based conjugate gradient iterative methods of solution are thus explored." } @article{healy-weaver:1992, Author = "Healy, D. M., and J. B. Weaver", Title = "Two applications of wavelet transforms in magnetic resonance imaging", Journal = "IEEE Trans. Inform. Theory", Volume = "38", Year = "1992", Pages = "840--862" } @techreport{hwang:1993, Author = "Hwang, Wen-Liang", Title = "Singularity detection, noise reduction and multifractal characterization using wavelets", Year = "1993", Institution = "Dept. of Comp. Sci., New York Univ.", Ftp = "cs.nyu.edu:/pub/wave/software/wave1.tar.Z", Psize = "3,462,116 bytes", File = "(see comments)", Size = "(see comments)", Pages = "109", Keywords = "wavelets, fractals, noise reduction", Abstract = "The document is contained in parts in 4 directories within the package and must be processed using LaTeX and dvips. The final PostScript source code file is huge." } %IIII %JJJJ @techreport{jawerth-sweldens:1993a, Author = "Jawerth, Bjorn, and Wim Sweldens", Title = "Wavelet multiresolution analyses adapted for the fast solution of boundary value ordinary differential equations", Year = "1993", Institution = "University of South Carolina", Ftp = "casper.cs.yale.edu:mgnet/copper93/jawerth-sweldens.ps", Size = "154,619 bytes", Pages = "15", Abstract = "Ideas on how to use wavelets in the solution of boundary value ODEs. Rather than using classical wavelets, they are adapted so that they become (bi)orthogonal with respect to the inner product defined by the operator. The stiffness matrix in a Galerkin method then becomes diagonal and can thus be trivially inverted. One can construct an O(N) algorithm for various constant and variable coefficient operators." } @techreport{jawerth-sweldens:1993b, Author = "Jawerth, Bjorn, and Wim Sweldens", Title = "An overview of wavelet based multiresolution analyses", Year = "Feb. 8, 1993", Institution = "University of South Carolina", Ftp = "maxwell.math.scarolina.edu:/pub/wavelet/papers/varia/sirev-36-3.tex", Size = "142,288 bytes", Pages = "39", Abstract = "An overview of some wavelet based multiresolution analyses is given. First, the continuous wavelet transform in its simplest form is discussed, then the definition of multiresolution analysis is given and it is shown how wavelets fit into it. Also discussed are the fast wavelet transform, wavelets on closed sets, multidimensional wavelets, and wavelet packets, and several examples of wavelet families are given and compared." } %KKKK @unpublished{kautsky:1994, Author = "Kautsky, Jaroslav", Title = "An algebraic construction of discrete wavelet transforms", Year = "1994", Institution = "School of Information Sci. and Tech., Flinders Univ., GPO Box 2100, Adelaide, SA 5001, Australia", URL = "ftp://ftp.cs.flinders.edu.au/pub/wavelets/jk1.ps", Size = "204,768", Pages = "18", Keyword = "wavelets", Abstract = "Discrete wavelets are viewed as linear algebraic transforms given by banded orthogonal matrices which can be built up from small matrix blocks satisfying certain conditions. A generalization of the finite support Daubechies wavelets is discussed and some special cases promising more rpaid signal reduction are derived." } @unpublished{kautsky-turcajova:1994a, Author = "Kautsky, Jaroslav and Radka Turcajov{\'a}", Title = "Discrete biorthogonal wavelet transforms as block circulant matrices", Year = "1994", Institution = "School of Information Sci. and Tech., Flinders Univ., GPO Box 2100, Adelaide, SA 5001, Australia", URL = "ftp://ftp.cs.flinders.edu.au/pub/wavelets/bio1.ps", Size = "158,125", Pages = "12", Keyword = "wavelets", Abstract = "A complete characterization of banded block circulant matrices with banded inverse is derived by factorizations similar to those used for orthogonal matrices of this kind. Matrices of this type appear in the description of the action of perfect reconstruction filter banks as well as biorthogonal higher multiplicity wavelet transforms." } @unpublished{kautsky-turcajova:1994b, Author = "Kautsky, Jaroslav and Radka Turcajov{\'a}", Title = "Pollen product factorization and construction of higher multiplicity wavelets", Year = "1994", Institution = "School of Information Sci. and Tech., Flinders Univ., GPO Box 2100, Adelaide, SA 5001, Australia", URL = "ftp://ftp.cs.flinders.edu.au/pub/wavelets/jkrt2.ps", Size = "164,210", Pages = "12", Keyword = "wavelets", Abstract = "This describes a simple, explicit and numerically reliable algorithm for construction of regular higher multiplicity wavelets. The existence and uniqueness of the factorization of wavelet matrices with respect to the Pollen product is also resolved." } @techreport{kreinovich-sirisaengtaksin-etal:1992, Author = "Kreinovich, Vladik, Ongard Sirisaengtaksin, and Sergio Cabrera", Email = "vladik@cs.ep.utexas.edu", Title = "Wavelet neural networks are optimal approximators for functions of one variable", Year = "1992", Institution = "Dept. of Comp. Sci., Univ. of Texas at El Paso, El Paso, TX 79968", Ftp = "cs.ep.utexas.edu:/pub/reports/tr92-29.tex", Size = "90,812 bytes", Pages = "33", Keywords = "neural networks, wavelets", Abstract = "It is shown that for some special neurons, neural networks are optimal approximators for functions of one variable in the sense that they require the smallest possible number of bits that must be stored to reconstruct a function with a given precision." } @article{kronland-martinet-morlet-etal:1987, Author = "Kronland-Martinet, R., J. Morlet, A. Grossmann", Title = "Analysis of sound patterns through wavelet transform", Journal = "Int. J. Pattern Recognition and Artif. Intell.", Volume = "?", Year = "1987", Pages = "273--302" } @article{kumar-foufoula-georgion:1993, Author = "Kumar, Praveau, and Efi Foufoula--Georgion", Title = "A new look at rainfall fluctuations and scaling properties of spatial rainfall using orthogonal wavelets", Journal = "J. Appl. Meteorol.", Volume = "32", Year = "1993", Pages = "209--222" } %LLLL @techreport{laine-schuler:1993, Author = "Laine, Andrew and Jian Fan", Title = "An adaptive approach for texture segmentation by multi-channel wavelet frames", Year = "1993", Number = "25", Institution = "Univ. of Florida", URL = "ftp://ftp.cis.ufl.edu/cis/tech-reports/tr93/tr93-025.ps.Z", Size = "1,310,748", Pages = "?", Keyword = "wavelets", Abstract = "This introduces an adaptive approach for texture feature extraction based on multi-channel wavelet frames and two-dimensional envelope detection. Representations obtained from both standard wavelets and wavelet packets are evaluated for reliable texture segmentation. Algorithms for envelope detection based on edge detection and the Hilbert transform are presented. Analytic filters are selected for each technique based on performance evaluation. A K-means clustering algorithm was used to test the performance of each representation feature set. Experimental results for both natural textures and synthetic textures are shown." } @unpublished{lakey:1993, Author = "LaKey, Joseph D.",, Title = "Lecture notes, Math 391 C, Fall 1993", Year = "1993", Institution = "University of Texas", Ftp = "math.utexas.edu:pub/papers/laKey/m391c/m391c.dvi", Size = "656,740 bytes", Pages = "178", Abstract = "These are notes for a course on wavelets given by Dr. Joseph LaKey at the University of Texas during Fall 1993. In addition to the dvi file, there are 19 additional postscript figure files at the same site. The dvi file is processed using the dvips utility to create a postscript file containing both text and figures." } @techreport{learned-willsky:1993, Author = "Learned, Rachel E., and Alan S. Willsky", Email = "learned@mit.edu", Title = "Wavelet packet approach to transient signal classification", Year = "1993", Institution = "Dept. of Elect. Eng. and Comp. Sci. and the Lab. for Information and Decision Systems, Room 35-439, 77 Massachusetts Ave., Cambridge, MA 02139", Ftp = "lids.mit.edu:/pub/ssg/papers/LIDS-P-2199.PS.gz", Size = "329,878 bytes", Pages = "55", Keywords = "wavelets", Abstract = "This describes an investigation to explore the feasibility of applying the wavelet packet transform to automatic detection and classification of a specific set of transient signals in background noise. In particular, a noncoherent wavelet-packet-based algorithm specific to the detection and classification of underwater acoustic signals generated by snapping shrimp and sperm whale clicks is proposed." } @inproceedings{lemarie-rieusset:1993, Author = "Lemarie-Rieusset, Pierre Gilles", Title = "Projection operators in multiresolution analysis", Booktitle = "Different Perspectives on Wavelets", Editor = "Ingrid Daubechies", Publisher = "American Math. Soc., Providence, RI", Series = "Proceedings of Symposia in Applied Mathematics", Volume = "47", Year = "1993", Pages = "59--76", Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San Antonio, TX", Abstract = "Describes various ways to deal with a bi--orthogonal multiresolution analysis." } @article{lewis-knowles:1990, Author = "Lewis, A. S., and G. Knowles", Title = "Video compression using 3d wavelet transforms", Journal = "Electron. Lett.", Volume = "26", Year = "1990", Pages = "396--398" } @article{liandrat-moret-bailly:1990, Author = "Liandrat, J., and F. Moret-Bailly", Title = "The wavelet transform: Some applications to fluid dynamics and turbulence", Journal = "Eur. J. Mech., B/Fluids", Vol = "9", Year = "1990", Pages = "1--19", Keywords = "wavelets, turbulence", Abstract = "In this paper the basic definitions and the most attractive properties of the wavelet transform are reviewed and explained using the classical language of turbulence. It is shown that the wavelet transform appears to be a natural alternative to the decompositions commonly used in fluid dynamics and turbulence (i.e. Fourier decomposition). Some especially interesting properties of the wavelet transform for interpretation or numerical approximation of turbulence are demonstrated on experimentally or numerically generated signal examples." } @phdthesis{luettgen:1993, Author = "Luettgen, Mark R.", Title = "Image processing with multiscale stochastic models", Year = "May 1993", Institution = "Dept. of Elect. Eng. and Comp. Sci. M.I.T.", Ftp = "lids.mit.edu:pub/ssg/papers/LIDS-TH-2178.PS.z", Size = "2,085,899 bytes", Pages = "217", Abstract = "Image processing algorithms and applications for a particular class of multiscale models are developed. These algorithms are shown to be related to wavelets and to be usable in the context of regularizing ill-posed inverse problems at a significant computational savings. It is concluded that the multiscale paradigm is a powerful paradigm for image processing because of the efficient algorithms it admits and the rich class of phenomena it can be used to describe." } %MMMM @article{mallat:1989, Author = "Mallat, S. G.", Title = "A theory for multiresolution signal decomposition: The wavelet representation", Journal = "IEEE Trans. Pattern Anal. Machine Intell.", Volume = "11", Year = "1989", Pages = "674--693" } @article{mallat-hwang:1992, Author = "Mallat, S., and W. L. Hwang", Title = "Singularity detection and processing with wavelets", Journal = "IEEE Trans. Info. Theory", Volume = "38", Year = "1992", Pages = "617--643" } @techreport{mann-haykin:1991, Author = "Mann, Steve, and Simon Haykin", Title = "The chirplet transform: A new signal analysis technique based on affine relationships in the time-frequency plane", Year = "1991", Institution = "M.I.T., 20 Ames St., Cambridge, MA 02139", Ftp = "media-lab.media.mit.edu:/pub/chirplet/chirplet_papers/assp.ps.Z", Size = "3,401,739 bytes", Pages = "46", Keywords = "chirplets, signal analysis", Abstract = "A multidimensional space is considered that includes both the time-frequency and time-scale planes, which encompasses both the short-time Fourier and wavelet transforms as slices along the time-frequency and time-scale axes, respectively. Chirplets are generalized wavelets, related to eachother by two-dimensional affine coordinate transformations (translations, dilations, rotations, and shears) in the time-frequency plane, as opposed to wavelets, related to each other by one-dimensional affine coordinate transformations in the time-domain only (translations and dilations). Practical applications of chirplets in such areas as machine vision, image processing, and radar are discussed." } @article{mann-haykin:1992, Author = "Mann, S., and S. Haykin", Title = "Adaptive ``chirplet'' transform: an adaptive generalization of the wavelet transform", Journal = "Optical Eng.", Volume = "31", Year = "1992", Pages = "1243--1256" } @techreport{mccormick-wells:1991, Author = "McCormick, Kent and Raymond O. Wells, Jr.", Title = "Wavelet calculus and finite difference operators", Year = "1991", Number = "TR91-02", Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892", URL = "ftp://cml.rice.edu/pub/reports/9102.ps.Z", Size = "85,285", Pages = "?", Abstract = "?" } @article{meneveau:1991, Author = "Meneveau, Charles", Title = "Analysis of turbulence in the orthonormal wavelet representation", Journal = "J. Fluid Mech.", Volume = "232", Year = "1991", Pages = "469--520", Abstract = "A decomposition of turbulent velocity fields into modes that exhibit both localization in wavenumber and physical space is performed. This reviews some basic properties of such a decomposition, the wavelet transform. The wavelet-transformed Navier-Stokes equations are derived and the kinetic energy and flux of kinetic energy are studied as functions of scale and position." } @inproceedings{meyer:1993, Author = "Meyer, Yves", Title = "Wavelets and operators", Booktitle = "Different Perspectives on Wavelets", Editor = "Ingrid Daubechies", Publisher = "American Math. Soc., Providence, RI", Series = "Proceedings of Symposia in Applied Mathematics", Volume = "47", Year = "1993", Pages = "35--58", Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San Antonio, TX", Abstract = "Addresses the possibility of using wavelet analysis for studying operators." } @article{mayers-obrien:1994, Author = "Meyers, Steven D. and James J. O'Brien", Title = "Spatial and temporal 26-day SST variations in the equatorial Indian Ocean using wavelet analysis", Journal = GRL, Volume = "21", Year = "1994", Pages = "777--780", Keyword = "wavelets, Indian Ocean, SST", Abstract = "Two-year sea-surface temperature time series of satellite data at two sites in the equatorial Indian Ocean are examined for oscillations with periods 2-70 days using wavelet transforms." } @article{meyers-kelly-etal:1993, Author = "Meyers, S. D., B. G. Kelly, and J. J. O'Brien", Title = "An introduction to wavelet analysis in oceanography and meteorology: With application to the dispersoion of Yanai waves", Journal = "Monthly Weather Review", Volume = "121", Year = "1993", Pages = "2858--2866", Abstract = "Wavelet analysis, an important addition to standard signal analysis methods, is unlike Fourier analysis in that while the latter yields an average amplitude and phase for each harmonic, the former produces an ``instantaneous'' estimate or local value for the amplitude and phase of each harmonic. This allows detailed study of nonstationary spatial or time--dependent signal characteristics. The wavelet transform is discussed, examples are given, and some methods for preprocessing data for wavelet analysis are compared. Yanai waves are studied using wavelet analysis." @article{morlet-arens-etal:1982, Author = "Morlet, J., G. Arens, I. FOurgeau, and D. Giard", Title = "Wave propagation and sampling theory", Journal = "Geophysics", Volume = "47", Year = "1982", Pages = "203--236" } @article{muzy-barcy-etal:1991, Author = "Muzy, J. F., E. Barcy, and A. Arneodo", Title = "Wavelets and multifractal formalism for singular signals: applications to turbulence data", Journal = "Phys. Rev. Lett.", Volume = "67", Year = "1991", Pages = "3515--3518" } %NNNN @techreport{nason:1994, Author = "Nason, G. P.", Title = "Wavelet regression by cross-validation", Year = "Mar. 24, 1994", Institution = "Dept. of Math., Univ. of Bristol, University Walk, Bristol, BS8 1TW, U.K.", Ftp = "playfair.stanford.edu:/pub/reports/wvcx.ps.gz", Size = "312,417 bytes", Pages = "45", Keywords = "wavelets", Abstract = "This paper is about using wavelets for regression. The main aim is to introduce and develop a cross-validation method for selecting a wavelet regression threshold that produces good estimates with respect to $L_2$ error. The selected threshold determines which coefficients to keep in an orthogonal wavelet expansion of noisy data and acts in a similar way to a smoothing parameter in non-parametric regression." } @article{newland:1993, Author = "Newland, David E.", Title = "Harmonic wavelet analysis", Journal = "Proc. R. Soc. Lond. A", Volume = "443", Year = "1993", Pages = "203--225", Abstract = "A new harmonic wavelet is suggested whose shape can be expressed in functional form. Its frequency spectrum is confined exactly to an octave band so that it is compact in the frequency (rather than in the x) domain. An efficient implementation of a discrete transform using this wavelet is based on the FFT. Fourier coefficients are processed in octave bands to generate wavelet coefficients by an orthogonal transformation which is implemented by the FFT. The same process works backwards for the inverse transform." @article{newland:1994a, Author = "Newland, David E.", Title = "Harmonic and musical wavelets", Journal = "Proc. R. Soc. Lond. A", Volume = "444", Year = "1994", Pages = "605--620" } @article{newland:1994b, Author = "Newland, David E.", Title = "Some properties of discrete wavelet maps", Journal = "Probabilisitic Eng. Mech.", Volume = "9", Year = "1994", Pages = "59--69" } %OOOO @techreport{odegard-gopinath-etal:1991, Author = "Odegard, J. E. and R. A. Gopinath and C. S. Burrus", Title = "Optimal wavelets for signal decomposition and the existence of scale limited signals", Year = "1991", Number = "TR91-07", Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892", URL = "ftp://cml.rice.edu/pub/reports/9107.ps.Z", Size = "55,674", Pages = "?", Abstract = "?" } @article{onsay-haddow:1994, Author = "{\"O}nsay, Taner and Alan G. Haddow", Title = "Wavelet transform analysis of transient wave propagation in a dispersive medium", Journal = JASA, Volume = "95", Pages = "1441--1449", Keyword = "wavelets", Abstract = "The wavelet transform is applied to the analysis of transient waves propagating in a dispersive medium. The wavelet transform of the acceleration process of the transient flexural vibrations of an impact excited uniform beam resulted in a time-scale representation which provided a clear exposition of the time evolution of the spectral components during the dispersion process. Based on the examples, the advantanges and shortcomings of the wavelet transform are discussed." } %PPPP %QQQQ @article{qian-weiss:1993, Author = "Qian, Sam, and John Weiss" Title = "Wavelets and the numerical solution of partial differential equations" Journal = "J. Comp. Phys." Volume = "106" Year = "1993" Pages = "155--175" Note = "A numerical method for the solution of PDEs in nonseparable domains usings a wavelet-Galerkin solver with a nontrivial adaptation of the standard capacitance method is presented. The numerical solutions exhibit spectral convergence at a rate that is independent of the geometry." } %RRRR @techreport{rieder:1993, Author = "Rieder, Andreas", Title = "Semi-algebraic multi-level methods based on wavelet decompositions I: Application to two-point boundary value problems", Year = "April 1993", Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892", Ftp = "cml.rice.edu:pub/reports/9304.ps.z", Size = "107,701 bytes", Pages = "31", Keywords = "wavelets, boundary value problems", Abstract = "The goal of this article is to clarify more precisely the vague but often indicated connection between wavelet and multi-grid theory. As such, a multi-level method based on a wavelet approximation of the successive error of a classical iterative solver is presented. The resulting iteration is a hybrid between a purely algebraic multi-level technique and the usual multi-grid technique related to a discretization of an elliptic differential operator. This new approach has the capacity to solve linear equations arising from the discretization of integral operators of the first kind by multi-level techniques." } @techreport{rieder-wells-etal:1993, Author = "Rieder, Andreas, Raymond O. Wells, Jr., and Xiaodong Zhou", Title = "A wavelet approach to robust multilevel solvers for anisotropic elliptic problems", Year = "Oct. 25, 1993", Institution = "Computational Math. Lab., Rice University, Houston, TX 77251-1892", Ftp = "cml.rice.edu:pub/reports/9307.ps.z", Size = "168,206 bytes", Pages = "42", Keywords = "wavelets, elliptic solvers", Abstract = "A wavelet variation of the frequency decomposition multigrid (FDMGM) method is presented that allows a deeper analysis of this method. The orthogonality and multiresolution structure of wavelets yield the robustness of the additive as well as of the multiplicative version of the FDMGM relative to any intermediate level. Aspects of the robustness of the multilevel scheme are discussed and numerical experiments used to confirm the theoretical results." } @article{rioul:1992, Author = "Rioul, Olivier", Title = "Simply regularity criteria for subdivision schemes", Journal = "SIAM J. Math. Anal.", Volume = "23", Year = "1992", Pages = "1544--1576", Abstract = "Convergent subdivision schemes arise in several fields of applied mathematics (computer-aided geometric design, fractals, compactly supported wavelets) and signal processing (multiresolution decomposition, filter banks). In this paper, a polynomial description is used to study the existence of H\"older regularity of limit functions of binary subdivision schemes." } @article{rioul-duhamel:1992, Author = "Rioul, O[livier], and P. Duhamel", Title = "Fast algorithms for the discrete and continuous wavelet transforms", Journal = "IEEE Trans. Info. Theory", Volume = "38", Year = "1992", Pages = "569--586" } @article{rioul-vetterli:1991, Author = "Rioul, O[livier]., and M. Vetterli", Title = "Wavelets and signal processing", Journal = "IEEE Signal Processing Magazine", Year = "1991", Month = "oct", Pages = "14--37" } %SSSS @techreport{saito-beylkin:1992, Author = "Saito, Naoki, and Gregory Beylkin", Title = "Multiresolution representations using the auto-correlation functions of compactly supported wavelets", Year = "Jan. 9, 1992", Institution = "Dept. of Math., Yale Univ., New Haven, CT 06520", Ftp = "newton.colorado.edu:/pub/wavelets/papers/minframe.ps.Z", Size = "493,997 bytes", Pages = "46", Keywords = "wavelets", Abstract = "This proposes a hybrid shift-invariant multiresolution representation which uses dilations and translations of the auto-correlation functions of compactly supported wavelets." } @techreport{shensa:1993, Author = "Shensa, M. J.", Email = "shensa@nosc.mil", Title = "An inverse DWT for nonorthogonal wavelets", Number = "1621", Year = "1993", Month = "jul", Institution = "NCCOSC RDTE DIV, code 782, San Diego, CA 92152-5702", URL = "ftp://ftp.nosc.mil/pub/Shensa/WTinverse_TR1621.ps.Z", Size = "200,705", Pages = "52", Keyword = "wavelets", Abstract = "Discrete nonorthogonal wavelet transforms play an important role in signal processing by offering finer resolution in time and scale than their orthogonal counterparts. This paper offers new algorithms for the DWT." } @article{slezak-bijaoui-etal:1990, Author = "Sl\'ezak, E., A. Bijaoui, and G. Mars", Title = "Identification of structures from galaxy count: use of the wavelet transform", Journal = "Astron. Astroph.", Volume = "227", Year = "1990", Pages = "301--316" } @article{spedding-browand-etal:1993, Author = "Spedding, G. R. and F. K. Browand and N. E. Huang and S. R. Long", Title = "A 2-D complex wavelet analysis of an unsteady wind-generated surface wave field", Journal = DAO, Volume = "20", Year = "1993", Pages = "55--77", Keyword = "wavelets, wind waves", Abstract = "2-D, complex wavelet functions are used to decompose a wave field to measure the energy of the wave field as a function of wavenumber as well as the spatial distribution of the wavenumbers." } @article{starck-bijaoui:1994, Author = "Starck, Jean-Luc and Albert Bijaoui", Title = "Filtering and deconvolution by the wavelet transform", Journal = "Signal Processing", Volume = "35", Year = "1994", Pages = "195--211", Keyword = "wavelets, filtering, deconvolution", Abstract = "A new approach to filtering based on the wavelet transform is presented and several algorithms are proposed. A criterion of quality, which takes into account the resolution, is used to compare these algorithms. It is shown that deconvolution can be done using filtered wavelet coefficients. By computing the wavelet from the point spread function, a new transform algorithm and a reconstruction method related to it are found." } @article{strang:1989, Author = "Strang, Gilbert", Title = "Wavelets and dilation equations: A brief introduction", Journal = "SIAM Review", Volume = "31", Year = "1989", Pages = "614--627", Abstract = "This is an introduction to the construction of wavelets from the solution to a dilation equation. It discusses the approximation and orthogonal properties of wavelets and describes the recursive algorithms that decompose and reconstruct a function. The object of wavelets is to localize as far as possible in both time and frequency, with efficient algorithms." } @article{strang:1993, Author = "Strang, Gilbert", Title = "Wavelet transforms versus Fourier transforms", Journal = "Bull. (New Series) AMS", Volume = "28", Year = "1993", Pages = "288--305", Abstract = "This is a very basic introduction to wavelets. Wavelets are constructed and studied in relation to the Fourier transform. The contest between these transforms is informally commented on in reference to signal processing, especially for video and image compression. It is stated that wavelets are already competitive with the Fourier transform for these applications, and head for the identification of fingerprints. Samples of the developing theory concerning these results are presented." } @article{strichartz:1993, Author = "Strichartz, Robert S.", Title = "How to make wavelets", Journal = "American Mathematical Monthly", Volume = "100", Year = "1993", Pages = "539--556", Abstract = "This is an elementary mathematical introduction to wavelets with sections on Haar wavelets, multiresolution analysis, their relationship to the Fourier transform, and the construction of wavelets." } @phdthesis{sweldens:1994, Author = "Sweldens, Wim", Title = "The construction and application of wavelets in numerical analysis", Year = "1994", Month = "mar", Institution = "Departement Computerwetenschappen, K.U. Leuven and Dept. of Math., Univ. of S. Carolina, Columbia, S.C. 29208", URL = "ftp://maxwell.math.scarolina.edu/pub/wavelet/papers/varia/thesis/thesis[1-6].ps", Size = "682,479; 811,088; 1,204,962; 1,588,071; 942,484; 609,104", Pages = "198", Keyword = "wavelets, numerical methods", Abstract = "This thesis investigates the use of wavelets in numerical analysis problems. In the first part two basic tools, quadrature formulae and asymptotic error expansions, are constructed. The former provides an easy way to calculate the wavelet coefficients, while the latter allows a simple comparison of different wavelet families. In the second part wavelets adapted to a weighted inner product are constructed and studied, and it is shown how these can be used for the rapid solution of ordinary differential equations. The final part studies smooth local trigonometric functions, which can be seen as the Fourier transform of wavelets. Their construction is generalized to the biorthogonal case and they are used in data compression algorithms, with examples concerning image compression shown." } %TTTT @inproceedings{tchamitchian:1993, Author = "Tchamitchian, Philippe", Title = "Wavelets and differential operators", Booktitle = "Different Perspectives on Wavelets", Editor = "Ingrid Daubechies", Publisher = "American Math. Soc., Providence, RI", Series = "Proceedings of Symposia in Applied Mathematics", Volume = "47", Year = "1993", Pages = "77--88", Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San Antonio, TX" } @unpublished{turcajova:1994, Author = "Turcajov{\'a}, Radka", Title = "Factorizations and construction of linear phase paraunitary filter banks and higher multiplicity wavelets", Year = "1994", Institution = "School of Information Sci. and Tech., Flinders Univ., GPO Box 2100, Adelaide, SA 5001, Australia", URL = "ftp://ftp.cs.flinders.edu.au/pub/wavelets/symm.ps", Size = "211,390", Pages = "20", Keyword = "wavelets", Abstract = "Paraunitary matrices can be factored into shift products of orthogonal matrices or linear factors. These factorizations also allow the derivation of lattice structures for linear phase paraunitary filter banks and also for the construction of symmetric higher multiplicity wavelets." } @unpublished{turcajova-kautsky:1994, Author = "Turcajov{\'a}, Radka and Jaroslav Kautsky", Title = "Shift products and factorizations of wavelet matrices", Year = "1994", Institution = "School of Information Sci. and Tech., Flinders Univ., GPO Box 2100, Adelaide, SA 5001, Australia", URL = "ftp://ftp.cs.flinders.edu.au/pub/wavelets/shift.ps", Size = "169,779", Pages = "14", Keyword = "wavelets", Abstract = "A class of so-called shift products of wavelet matrices is introduced. These products are based on circulations of columns of orthogonal banded block circulant matrices arising in applications of discrete orthogonal wavelet transforms." } @Article{turner-leclerc:1994, Author = "Turner, B. J., and M. Y. LeClerc", Title = "Conditional sampling of coherent structures in atmospheric turbulence using the wavelet transform", Journal = "J. Atmospheric and Oceanic Techn.", Volume = "11", Year = "1994", Pages = "205--209". Keywords = "coherent structures, atmospheric turbulence, wavelets" } %UUUU %VVVV @article{vergassola-frisch:1991, Author = "Vergassola, M., and U. Frisch", Title = "Wavelet transforms of self--similar processes", Journal = "Physica D", Volume = "54", Year = "1991", Pages = "58--64" } @unpublished{vidakovic-muller:1994, Author = "Vidakovi{\'c}, Brani and Peter M{\"u}ller", Title = "Wavelets for kids: A tutorial introduction", Year = "1994", Institution = "Duke University, Durham, NC 27708-0251", URL = "ftp://ftp.isds.duke.edu/pub/brani/papers/wav4kids[A-B].ps.Z", Size = "318,373; 70,903", Keyword = "wavelets", Abstract = "This paper is intended to serve as a very first introduction to wavelets for the statistical community. References for further reading are given as well as some Mathematica procedures." } @article{villemoes:1992, Author = "Villemoes, L. F.", Title = "Energy moments in time and frequency for two--scale difference equation solutions and wavelets", Journal = "SIAM J. Math. Anal.", Volume = "23", Year = "1992", Pages = "1519--1543" } @article{vishwanath:1994, Author = "Vishwanath, Mohan", Title = "The recursive pyramid algorithm for the discrete wavelet transform", Journal = "IEEE Trans. Signal Proc.", Volume = "42", Year = "1994", Pages = "673--676", Keywords = "wavelets, recursive pyramid algorithm", Abstract = "The recursive pyramid algorithm (RPA) is a reformulation of the classical pyramid algorithm (PA) for computing the discrete wavelet transform (DWT). The RPA computes the N-point DWT in real time (running DWT) using just L(log N-1) words of storage, as compared with O(N) words required by the PA where L is the length of the wavelet filter. The RPA is combined with the short-length FIR filter algorithms to reduce the number of multiplications and additions." } %WWWW @article{weiss:1994, Author = "Weiss, Lora G.", Title = "Wavelets and wideband correlation processing", Journal = "IEEE Signal Processing Magazine", Volume = "?", Year = "1994", Month = "jan", Pages = "13--32", Keyword = "wavelets, wideband correlation processing", Abstract = "Wavelets are introduced and discussed along with wideband correlation processing. The connections between the two tools are investigated." } @techreport{wells:1994a, Author = "Wells, Raymond O, Jr.", Title = "Adaptive wave propagation modeling", Year = "1994", Number = "TR94-10", Institution = "Dept. of Math., Rice Univ., Houston, TX 77251-1892", URL = "ftp://cml.rice.edu/pub/reports/9410.ps.Z", Size = "71,435", Pages = "12", Abstract = "This discusses current attempts to use acoustic and electromagnetic wave propagation to model physical phenomena and the role that wavelet analysis is playing in these efforts. The areas of application are (1) computational fluid dynamics, (2) the geophysical modeling of the ocean floor using acoustic waves, (3) the modeling of SAR radar images in the context of automatic target recognition efforts, and (4) global illumination in computer graphics, i.e. simulation of reflected and absorbed light in everyday environments." } @techreport{wells:1994b, Author = "Wells, Raymond O, Jr.", Title = "Recent advances in wavelet technology", Year = "1994", Month = "mar", Number = "9412", Institution = "Dept. of Math., Rice Univ., Houston, TX 77251-1892", URL = "ftp://cml.rice.edu/pub/reports/9412.ps.Z", Size = "38,567", Pages = "8", Abstract = "This reviews some recent developments in wavelet technology at the Computational Mathematics Laboratory at Rice, which has as its primary focus research in the theory and applications of wavelets and more generally multiscale phenomena in mathematics, science and engineering. Brief synopses are given of the advances in the areas of wavelet mathematics, wavelet multiscale representation of data, image compression and telecommunications technology, and wavelet-based numerical solutions of differential equations." } @techreport{wells-zhou:1992a, Author = "Wells, Raymond O, Jr. and Xiaodong Zhou", Title = "Adaptive wave propagation modeling", Year = "1992", Number = "TR92-02", Institution = "Dept. of Math., Rice Univ., Houston, TX 77251-1892", URL = "ftp://cml.rice.edu/pub/reports/9202.ps.Z", Size = "629,946", Pages = "?", Abstract = "?" } @techreport{wells-zhou:1992b, Author = "Wells, Raymond O, Jr. and Ziaodong Zhou", Title = "Wavelet interpolation and approximate solutions of elliptic partial differential equations", Year = "1992", Number = "TR92-03", Institution = "Dept. of Math., Rice Univ., Houston, TX 77251-1892", URL = "ftp://cml.rice.edu/pub/reports/9203.ps.Z", Size = "76,105", Pages = "?", Abstract = "?" } @unpublished{wickerhauser:1991, Author = "Wickerhauser, Mladen V.", Email = "victor@jezebel.wustl.edu", Title = "Lectures on wavelet packet algorithms", Year = "Nov. 18, 1991", Institution = "Dept. of Math., Washington Univ., St. Louis, MO 63130", Ftp = "wuarchive.wustl.edu:/doc/techreports/wustl.edu/math/inria300.ps.Z", Size = "2,026,711 bytes", Pages = "75", Keywords = "wavelets", Abstract = "A series of lecture notes which begin by defining continuous wavelet packets and then defines several discrete algorithms and explores their advantages and disadvantages. Linear and nonlinear compression methods are also explored." } @techreport{wickerhauser:1992, Author = "Wickerhauser, Mladen V.", Email = "victor@jezebel.wustl.edu", Title = "Fast approximate factor analysis", Year = "1992", Institution = "Dept. of Math., Washington Univ., St. Louis, MO 63130", Ftp = "wuarchive.wustl.edu:/doc/techreports/wustl.edu/math/fakle.ps.Z", Size = "353,603 bytes", Pages = "10", Keywords = "wavelets", Abstract = "The principal orthogonal factor analysis or Karhunen-Loeve algorithm may be sped up by a low-complexity preprocessing step. A fast transform is selected from a large library of wavelet-like orthonormal bases, so as to maximize transform coding gain for an ensemble of vectors. On the top few coefficients in the new basis, in order of variance across the ensemble, are then decorrelated by diagonalizing the autocovariance matrix." } @inproceedings{wickerhauser:1993, Author = "Wickerhauser, Mladen Victor", Title = "Best--adapted wavelet packet bases", Booktitle = "Different Perspectives on Wavelets", Editor = "Ingrid Daubechies", Publisher = "American Math. Soc., Providence, RI", Series = "Proceedings of Symposia in Applied Mathematics", Volume = "47", Year = "1993", Pages = "155--171", Note = "From an American Math. Soc. short course, Jan. 11--12, 1993, San Antonio, TX", Abstract = "A review of the construction of orthogonal wavelet packets, using the quadarature mirror filters algorithm slightly generalized to the case of p $\ge$ 2 wavelets and scaling functions." } @article{wornell:1990, Author = "Wornell, G. W.", Title = "A Karhunen--Loeve--like expansion for 1/f processes via wavelet", Journal = "IEEE Trans. Inform. Theory", Volume = "36", Year = "1990", Pages = "859--861" } %XXXX @techreport{xu-shann:1993, Author = "Xu, Jin-Chao, and Wei-Chang Shann", Email = "xu@math.psu.edu; t210001@sparc20.ncu.edu.tw", Title = "Galerkin-wavelet methods for two-point boundary value problems", Year = "1993", Institution = "Dept. of Math., Pennsylvania State Univ., University Park, PA 16802", Ftp = "maxwell.math.scarolina.edu:/pub/wavelet/papers/galerkin.ps.Z", Size = "179,186 bytes", Pages = "22", Keywords = "wavelets, Galerkin methods", Abstract = "Anti-derivatives of wavelets are used for the numerical solution of differential equations. Optimal error estimates are obtained in the applications to two-point boundary value problems of second order. The orthogonal property of the wavelets is used to construct efficient iterative methods for the solution of the resultant linear algebraic systems and numerical examples are given." } %YYYY @article{yen:1994, Author = "Yen, Nai-chyuan", Title = "Wave packet decomposition", Journal = JASA, Volume = "95", Year = "1994", Pages = "889--896", Keyword = "wave packets, wavelets", Abstract = "This discusses a signal processing approach conceived from the observations of wave packets in scattering phenomena where the natural representation of a signal is examined through the dynamic time and frequency properties of its energy distribution. For a time-varying signal from a physical system with finite energy content, the selected natural frame component functions, which may not be necessarily orthogonal, can form a complete set for the particular signal under analysis. The decomposition with these nonorthogonal frames then becomes optimal and unique. Algorithms for evaluting the composition of this type of frame are given and examples are presented." } %ZZZZ @phdthesis{zubair:1993, Author = "Zubair, Lareef M.", Email = "zubair@chaos.yale.edu", Title = "Studies in turbulence using wavelet transforms for data compression and scale separation," Year = "May 1993", Institution = "Yale University", Ftp = "(see comments)" Size = "(see comments)" Pages = "221", Abstract = "The ftp address where this can be obtained along with the necessary username and password can be obtained via an e-mail message to the author. The wavelet transform is used to study the structure of turbulent flows. The structure of scalar and vorticity fields are studied using the continuous wavelet transform, the wavelet-packet transform is assessed as a tool for data compression, and a power-spectra and filtering technique based on the transform is introduced." }