Compressive Imaging

Structure, Sampling, Learning


Compressive Imaging: Structure, Sampling, Learning
Ben Adcock & Anders C. Hansen
Cambridge University Press (in press)


This book presents an in-depth treatment of compressive imaging, a topic which has developed over the last decade and has fundamentally changed the way modern image reconstruction is performed. It commences with a practical introduction to the subject, supported with examples and downloadable code. Next, it introduces core mathematical techniques in a concise yet rigorous way, before providing a detailed treatment of the mathematics of compressive imaging. The final part is devoted to the most recent trends in compressive imaging, deep learning and neural networks. This highly timely component of the book provides the first readable overview of this nascent topic. Looking toward the next 10-20 years of imaging research, and using both empirical and mathematical insights, this book examines both the potential benefits and the pitfalls of these latest approaches.


This book will be published by Cambridge University Press in 2021. In the meantime, selected materials are available for viewing.

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Code to generate many of the figures in the book is available here:

CIlib - A software library for compressive imaging

This library has been created by Vegard Antun.


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 accuracy neural networks for compressive imaging
22. Epilogue