Compressive Imaging

Structure, Sampling, Learning


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

The book is available for purchase on the publisher's website or Amazon.


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.


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.


List of Errata

If you find any additional errors, please contact the authors at or


Selected draft materials are available for viewing below. For updated versions of these materials, please see the final book.


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