An Introduction to Sparse Stochastic Processes

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. Pouya D. Tafti is a data scientist currently residing in Germany, and a former member of the Biomedical Imaging Group at EPFL, where he conducted research on the theory and applications of probabilistic models for data.

• 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.

'Over the last twenty years, sparse representation of images and signals became a very important topic in many applications, ranging from data compression, to biological vision, to medical imaging. The book An Introduction to Sparse Stochastic Processes by Unser and Tafti is the first work to systematically build a coherent framework for non-Gaussian processes with sparse representations by wavelets. Traditional concepts such as Karhunen-Loève analysis of Gaussian processes are nicely complemented by the wavelet analysis of Levy Processes which is constructed here. The framework presented here has a classical feel while accommodating the innovative impulses driving research in sparsity. The book is extremely systematic and at the same time clear and accessible, and can be recommended both to engineers interested in foundations and to mathematicians interested in applications.' David Donoho, Stanford University