Wavelets

Wavelets: Theory, Algorithms, and Applications is the fifth volume in the highly respected series, WAVELET ANALYSIS AND ITS APPLICATIONS. This volume shows why wavelet analysis has become a tool of choice infields ranging from image compression, to signal detection and analysis in electrical engineering and geophysics, to analysis of turbulent or intermittent processes. The 28 papers comprising this volume are organized into seven subject areas: multiresolution analysis, wavelet transforms, tools for time-frequency analysis, wavelets and fractals, numerical methods and algorithms, and applications. More than 135 figures supplement the text. - Features theory, techniques, and applications - Presents alternative theoretical approaches including multiresolution analysis, splines, minimum entropy, and fractal aspects - Contributors cover a broad range of approaches and applications

Multiresolution and Multilevel Analyses: A. Cohen, Non-stationary Multiscale Analysis. P.N. Heller, and R.O. Wells, Jr., The Spectral Theory of Multiresolution Operators and Applications. S. Dahlke, Multiresolution Analysis, Haar Bases and Wavelets on Reimannian Manifolds. T.N.T. Goodman and C.A. Micchelli, Orthonormal Cardinal Functions. Wavelet Transforms: B. Torresani, Some Remarks on Wavelet Representations and Geometric Aspects. J. Kautsky and R. Turcajova, A Matrix Approach to Discrete Wavelets. G. Plonka and M. Tasche, A Unified Approach to Periodic Wavelets. Spline-Wavelets: G. Steidl, Spline Wavlets over R Z R/NZ and Z/NZ. S. Sakakibara, A Practice of Data Smoothing by B-Spline Wavelets. T. Lyche and L.L. Schumaker, L-Spline Wavelets. C.K. Chui, K. Jetter, and J. Stickler, Wavelets and Frames on the Four-Directional Mesh. Other Mathematical Tools for Time-Frequency Analysis: D.L. Donoho, On Minimum Entropy Segmentation. G. Davis, S. Mallat, and Z. Zhang, Adaptive Time-Frequency Approximations with Matching Pursuits. B.W. Suter and M.E. Oxley, Getting Around the Balian-Low Theorem Using Generalized Malvar Wavelets. G. Courbebaisse, B. Escudie, and T. Paul, Time Scale Energetic Distribution. Wavelets and Fractals: S. Jaffard, Some Mathematical Results about the Multifractal Formalism for Functions. M. Holschneider, Fractal Wavelet Dimensions and Time Evolution. Numerical Methods and Algorithms: W. Dahmen, S. Prissdorf, and R. Schneider Multiscale Methods for Pseudo-Differential Equations on Smooth Closed Manifolds. S. Bertoluzza, G. Naldi, and J.C. Ravel, Wavelet Methods for the Numerical Solution of Boundary Value Problems on the Interval. D. Karayannakis, On the Nodal Values of the Franklin Analyzing Wavelet. L.B. Montefusco, Parallel Numerical Algorithms with Orthonormal Wavelet Packet Bases. P. Fischer and M. Defranceschi, Representation of the Atomic Hartree-Fock Equations in a Wavelet Basis by Means of the BCR Algorithm. Applications: M.V. Wickerhauser, M. Farge, E. Goirand, E. Wesfreid, and E. Cubillo,Efficiency Comparison of Wavelet Packet and Adapted Local Cosine Bases for Compression of a Two-Dimensional Turbulent Flow. M.E. Mayer, L. Hudgins, and C.A. Friehe, Wavelet Spectra of Buoyant Atmospheric Turbulence. A. Druilhet, J.-L. Attiee, L.de Abreu Sa, P. Durand, and B. Benech, Experimental Study of Inhomogeneous Turbulence in the Lower Troposphere by Wavelet Analysis. G. Olmo and L.L. Presti, Applications of Wavelet Transform for Seismic Activity Monitoring. A. Denjean and F. Castanie, Mean Value Jump Detection: A Survey of Conventional and Wavelet Based Methods. M.V. Wickerhauser, Comparison of Picture Compression Methods: Wavelet, Wavelet Packet, and Local Cosine Transform Coding. Subject Index.