Compressive Imaging: Structure, Sampling, Learning

This is a practical, rigorous guide to the compressive imaging revolution that has fundamentally changed modern image reconstruction.

Ben Adcock (Author), Anders C. Hansen (Author)

9781108421614, Cambridge University Press

Hardback, published 16 September 2021

614 pages
24.8 x 17.4 x 3.1 cm, 1.34 kg

Accurate, robust and fast image reconstruction is a critical task in many scientific, industrial and medical applications. Over the last decade, image reconstruction has been revolutionized by the rise of compressive imaging. It has fundamentally changed the way modern image reconstruction is performed. This in-depth treatment of the subject commences with a practical introduction to compressive imaging, supplemented with examples and downloadable code, intended for readers without extensive background in the subject. Next, it introduces core topics in compressive imaging – including compressed sensing, wavelets and optimization – in a concise yet rigorous way, before providing a detailed treatment of the mathematics of compressive imaging. The final part is devoted to recent trends in compressive imaging: deep learning and neural networks. With an eye to the next decade of imaging research, and using both empirical and mathematical insights, it examines the potential benefits and the pitfalls of these latest approaches.

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.

Subject Areas: Image processing [UYT], Signal processing [UYS], Machine learning [UYQM], Mathematical theory of computation [UYA], Graphics programming [UML], Imaging systems & technology [TTBM], Calculus & mathematical analysis [PBK]