Compressive Imaging: Structure, Sampling, Learning

Ben Adcock is Associate Professor of Mathematics at Simon Fraser University. He received the CAIMS/PIMS Early Career Award (2017), an Alfred P. Sloan Research Fellowship (2015) and a Leslie Fox Prize in Numerical Analysis (2011). He has published fifteen conference proceedings, two book chapters and over fifty peer-reviewed journal articles. His work has been published in outlets such as SIAM Review and Proceedings of the National Academy of Sciences, and featured on the cover of SIAM News. Anders C. Hansen is Reader in Mathematics at University of Cambridge and Professor of Mathematics at the University of Oslo. He received the Leverhulme Prize in Mathematics and Statistics (2017), the 2018 IMA Prize in Mathematics and Applications and the Whitehead Prize (2019). He has had papers published in outlets such as the Journal of the American Mathematical Society and Proceedings of the National Academy of Sciences, and featured on the cover of Physical Review Letters and SIAM News.

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• 1. Introduction; Part I. The Essentials of Compressive Imaging: 2. Images, transforms and sampling; 3. A short guide to compressive imaging; 4. Techniques for enhancing performance; Part II. Compressed Sensing, Optimization and Wavelets: 5. An introduction to conventional compressed sensing; 6. The LASSO and its cousins; 7. Optimization for compressed sensing; 8. Analysis of optimization algorithms; 9. Wavelets; 10. A taste of wavelet approximation theory; Part III. Compressed Sensing with Local Structure: 11. From global to local; 12. Local structure and nonuniform recovery; 13. Local structure and uniform recovery; 14. Infinite-dimensional compressed sensing; Part IV. Compressed Sensing for Imaging: 15. Sampling strategies for compressive imaging; 16. Recovery guarantees for wavelet-based compressive imaging; 17. Total variation minimization; Part V. From Compressed Sensing to Deep Learning: 18. Neural networks and deep learning; 19. Deep learning for compressive imaging; 20. Accuracy and stability of deep learning for compressive imaging; 21. Stable and accurate neural networks for compressive imaging; 22. Epilogue; Appendices: A. Linear Algebra; B. Functional analysis; C. Probability; D. Convex analysis and convex optimization; E. Fourier transforms and series; F. Properties of Walsh functions and the Walsh transform; Notation; Abbreviations; References; Index.