An Introduction to Sparse Stochastic Processes

Informationen zum Autor Michael Unser is Professor and Director of EPFL's Biomedical Imaging Group, Switzerland. He is a member of the Swiss Academy of Engineering Sciences, a Fellow of EURASIP, and a Fellow of the IEEE. Klappentext A detailed guide to sparsity, providing a description of their transform-domain statistics and applying the models to practical algorithms. Zusammenfassung Providing a novel approach to sparsity! this comprehensive book presents the theory of stochastic processes that are ruled by linear stochastic differential equations! and sets out a general stochastic framework for developing efficient and practical nonlinear algorithms. Inhaltsverzeichnis 1. Introduction; 2. Roadmap to the book; 3. Mathematical context and background; 4. Continuous-domain innovation models; 5. Operators and their inverses; 6. Splines and wavelets; 7. Sparse stochastic processes; 8. Sparse representations; 9. Infinite divisibility and transform-domain statistics; 10. Recovery of sparse signals; 11. Wavelet-domain methods; 12. Conclusion; Appendix A. Singular integrals; Appendix B. Positive definiteness; Appendix C. Special functions.

Texte du rabat

A detailed guide to sparsity, providing a description of their transform-domain statistics and applying the models to practical algorithms.

Résumé
Providing a novel approach to sparsity, this comprehensive book presents the theory of stochastic processes that are ruled by linear stochastic differential equations, and sets out a general stochastic framework for developing efficient and practical nonlinear algorithms.

Contenu

1. Introduction; 2. Roadmap to the book; 3. Mathematical context and background; 4. Continuous-domain innovation models; 5. Operators and their inverses; 6. Splines and wavelets; 7. Sparse stochastic processes; 8. Sparse representations; 9. Infinite divisibility and transform-domain statistics; 10. Recovery of sparse signals; 11. Wavelet-domain methods; 12. Conclusion; Appendix A. Singular integrals; Appendix B. Positive definiteness; Appendix C. Special functions.