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.
- A practical guide to the basics of compressive imaging, including the key considerations, common pitfalls and techniques to boost performance
- Provides an in-depth and comprehensive theoretical treatment of the mathematics of compressive imaging
- Includes many examples, plus downloadable code to generate them
- Contains an extensive bibliography with over 500 references
- Provides a novel treatment of the latest advances in the field based on neural networks and deep learning
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Awards
- Finalist, 2022 PROSE Award for Computing and Information Sciences
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Product details
- Date Published: September 2021
- format: Hardback
- isbn: 9781108421614
- length: 614 pages
- dimensions: 248 x 174 x 31 mm
- weight: 1.34kg
- availability: In stock
Table of Contents
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.
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Authors
Ben Adcock, Simon Fraser University, British Columbia
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, University of Cambridge
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.
Awards
- Finalist, 2022 PROSE Award for Computing and Information Sciences