Image Processing and Data Analysis : The Multiscale Approach

Powerful techniques have been developed in recent years for the analysis of digital data, especially the manipulation of images. This book provides an in-depth introduction to a range of these innovative, avante-garde data-processing techniques. It develops the reader's understanding of each technique and then shows with practical examples how they can be applied to improve the skills of graduate students and researchers in astronomy, electrical engineering, physics, geophysics and medical imaging. What sets this book apart from others on the subject is the complementary blend of theory and practical application. Throughout, it is copiously illustrated with real-world examples from astronomy, electrical engineering, remote sensing and medicine. It also shows how many, more traditional, methods can be enhanced by incorporating the new wavelet and multiscale methods into the processing. For graduate students and researchers already experienced in image processing and data analysis, this book provides an indispensable guide to a wide range of exciting and original data-analysis techniques. 1. The wavelet transform; 1.1 Multiscale methods; 1.2 The continuous wavelet transform; 1.3 Examples of wavelet functions; 1.4 The discrete wavelet transform/ 1.5 Multiresolution based on the median transform/ 1.6 Multiresolution and mathematical morphology; 2. Multiresolution support and filtering; 2.1 Noise modeling; 2.2 Multiresolution support; 2.3 Filtering; 2.4 Image comparison using a multiresolution quality criterion; 3. Deconvolution; 3.1 Introduction to deconvolution; Regularization using the multiresolution support; 3.3 Multiscale entropy and image restoration; 3.4 Image restoration for aperture synthesis; 4. 1D signals and euclidean data analysis; 4.1 Analysis of 1D signals: spectral analysis; 4.2 Wedding the wavelet transform and multivariate data analysis; 4.3 The kohonean self-organizing map in wavelet space; 4.4 Multiresolution regression and forecastin; 5. Geometric registration; 5.1 Image distortions; 5.2 Geometrical image registration; 5.3 Ground control points; 5.4 Image registration using the wavelet transform; 5.5 Application; 5.6 Error analysis; 5.7 Conclusion on multscale goemetric registration; 6. Disparity analysis in remote sensing; 6.1 Definitions; 6.2 Disparity mapping; 6.3 Disparity mapping with the wavelet transform; 6.4 Image registration; 6.5 Application to real images; 6.6 Conclusion on disparity analysis. 7. Image compression; 7.1 Pyramidal median transform and image compression; 7.2 Examples and assessments; 7.3 Image transmission over networks; 7.4 Conclusion on image compression; 8. Object detection and point clustering; 8.1 The problem and the data; 8.2 Pyramidal median transform and minkowski operators; 8.3 Conclusion on astronomical object detection; 8.4 Object detection and clustering in point patterns; 8.5 Conclusion: cluster analysis in constant time; 9. Multiscale vision models; 9.1 Artificial vision and astronomical images; 9.2 Object definition in wavelet transform space; Partial reconstruction; Applications to a real image; 9.5 Vision models and image classes; Appendix A. Variance stabilization; A.1 Mean and variance expansions; A.2 Deterination of centered moments; A.3 Study of the expansions for the variance; A.4 Variance-stabilizing transformation; Appendix B. Software information; Appendix C. Acronys.; Bibliography; Index

Powerful techniques have been developed in recent years for the analysis of digital data, especially the manipulation of images. This book provides an in-depth introduction to a range of these innovative, avant-garde data-processing techniques. It develops the reader's understanding of each technique and then shows with practical examples how they can be applied to improve the skills of graduate students and researchers in astronomy, electrical engineering, physics, geophysics and medical imaging. What sets this book apart from others on the subject is the complementary blend of theory and practical application. Throughout, it is copiously illustrated with real-world examples from astronomy, electrical engineering, remote sensing and medicine. It also shows how many, more traditional, methods can be enhanced by incorporating the new wavelet and multiscale methods into the processing. For graduate students and researchers already experienced in image processing and data analysis, this book provides an indispensable guide to a wide range of exciting and original data-analysis techniques.

For graduate students and researchers already experienced in image processing and data analysis, a guide to a wide range of powerful and innovative data-analysis techniques J.-l. Starck, F. Murtagh, A. Bijaoui. Includes Bibliographical References (p. [271]-285) And Index.