Wavelets: Time-frequency Methods And Phase Space Proceedings Of The International Conference, Marseille, France, December 14?18, 1987 (inverse Problems And Theoretical Imaging)

The last two subjects mentioned in the title "Wavelets, Time Frequency Methods and Phase Space" are so well established that they do not need any explanations. The first is related to them, but a short introduction is appropriate since the concept of wavelets emerged fairly recently. Roughly speaking, a wavelet decomposition is an expansion of an arbitrary function into smooth localized contributions labeled by a scale and a position pa­ rameter. Many of the ideas and techniques related to such expansions have existed for a long time and are widely used in mathematical analysis, theoretical physics and engineering. However, the rate of progress increased significantly when it was realized that these ideas could give rise to straightforward calculational methods applicable to different fields. The interdisciplinary structure (R.C.P. "Ondelettes") of the C.N.R.S. and help from the Societe Nationale Elf-Aquitaine greatly fostered these developments. The conference, the proceedings of which are contained in this volume, was held at the Centre National de Rencontres Mathematiques (C.N.R.M) in Marseille from December 14-18, 1987 and bought together an interdisciplinary mix of par­ ticipants. We hope that these proceedings will convey to the reader some of the excitement and flavor of the meeting. Front Matter....Pages I-IX Front Matter....Pages 1-1 Reading and Understanding Continuous Wavelet Transforms....Pages 2-20 Orthonormal Wavelets....Pages 21-37 Orthonormal Bases of Wavelets with Finite Support — Connection with Discrete Filters....Pages 38-66 Front Matter....Pages 67-67 Some Aspects of Non-Stationary Signal Processing with Emphasis on Time-Frequency and Time-Scale Methods....Pages 68-98 Detection of Abrupt Changes in Signal Processing....Pages 99-101 The Computer, Music, and Sound Models....Pages 102-123 Front Matter....Pages 125-125 Wavelets and Seismic Interpretation....Pages 126-131 Wavelet Transformations in Signal Detection....Pages 132-138 Use of Wavelet Transforms in the Study of Propagation of Transient Acoustic Signals Across a Plane Interface Between Two Homogeneous Media....Pages 139-146 Time-Frequency Analysis of Signals Related to Scattering Problems in Acoustics Part I: Wigner-Ville Analysis of Echoes Scattered by a Spherical Shell....Pages 147-153 Coherence and Projectors in Acoustics....Pages 154-157 Wavelets and Granular Analysis of Speech....Pages 158-163 Time-Frequency Representations of Broad-Band Signals....Pages 164-171 Operator Groups and Ambiguity Functions in Signal Processing....Pages 172-180 Front Matter....Pages 181-181 Wavelet Transform Analysis of Invariant Measures of Some Dynamical Systems....Pages 182-196 Holomorphic Integral Representations for the Solutions of the Helmholtz Equation....Pages 197-203 Wavelets and Path Integrals....Pages 204-208 Mean Value Theorems and Concentration Operators in Bargmann and Bergman Space....Pages 209-215 Besov-Sobolev Algebras of Symbols....Pages 216-220 Poincaré Coherent States and Relativistic Phase Space Analysis....Pages 221-231 Front Matter....Pages 181-181 A Relativistic Wigner Function Affiliated with the Weyl-Poincaré Group....Pages 232-238 Wavelet Transforms Associated to the n-Dimensional Euclidean Group with Dilations: Signal in More Than One Dimension....Pages 239-246 Construction of Wavelets on Open Sets....Pages 247-252 Wavelets on Chord-Arc Curves....Pages 253-258 Multiresolution Analysis in Non-Homogeneous Media....Pages 259-262 About Wavelets and Elliptic Operators....Pages 263-268 Towards a Method for Solving Partial Differential Equations Using Wavelet Bases....Pages 269-283 Front Matter....Pages 285-285 A Real-Time Algorithm for Signal Analysis with the Help of the Wavelet Transform....Pages 286-297 An Implementation of the “algorithme à trous” to Compute the Wavelet Transform....Pages 298-304 An Algorithm for Fast Imaging of Wavelet Transforms....Pages 305-312 Multiresolution Approach to Wavelets in Computer Vision....Pages 313-327 Back Matter....Pages 329-331 Time-frequency methods and phase space are well known to most physicists, engineers and mathematicians as is the traditional Fourier analysis. Recently the latter found for quite a few applications a competitor in the concept of wavelets. Crudely speaking a wavelet decomposition is an expansion of an arbitrary function into smooth localized contributions labeled by a scale and a position parameter. This meeting brought together people exploring and applying these concepts in an interdisciplinary framework. The topics discussed range from purely mathematical aspects over signal analysis, seismic and acoustic applications via animal sonar systems to wavelets in computer vision. Time-frequency methods and phase space are as well known to most physicists, engineers and mathematicians as traditional Fourier analysis, which has recently found for many applications a competitor in the concept of wavelets. Crudely speaking a wavelet decomposition is an expansion of an arbitrary function into smooth localized contributions labeled by a scale and a position parameter. The meeting recorded in this volume brought together people exploring and applying these concepts in an interdisciplinary framework. Topics discussed range from purely mathematical aspects to signal and speech analysis, seismic and acoustic applications, and wavelets in computer vision.