Compressive Imaging: Structure, Sampling, Learning

Erscheinungsjahr 2021
ISBN: 978-1-108-42161-4
Verlag: Cambridge University Press

Buch, Englisch, 614 Seiten, Format (B × H): 178 mm x 250 mm, Gewicht: 1332 g

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.

Autoren/Hrsg.

Hansen, Anders C.

Adcock, Ben

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Grafikprogrammierung
• Mathematik | Informatik EDV | Informatik Informatik Mathematik für Informatiker
• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen
• Mathematik | Informatik EDV | Informatik Informatik Bildsignalverarbeitung
• Technische Wissenschaften Sonstige Technologien | Angewandte Technik Signalverarbeitung, Bildverarbeitung, Scanning

Inhaltsverzeichnis

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.

Über Autor(innen)

Adcock, Ben
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.

Hansen, Anders C.
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.