Compressive imaging: structure, sampling, learning

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.

Cover -- Half-title -- Title page -- Copyright information -- Dedication -- Contents -- Preface -- 1 Introduction -- 1.1 Imaging and Inverse Problems -- 1.2 What is Compressive Imaging? -- 1.3 Terminology -- 1.4 Imaging Modalities -- 1.5 Conventional Compressed Sensing -- 1.6 Imaging with Compressed Sensing -- 1.7 Neural Networks and Deep Learning for Compressive Imaging -- 1.8 Overview and Highlights -- 1.9 Disclaimers -- 1.10 Reading this Book -- Part I The Essentials of Compressive Imaging -- Summary of Part I -- 2 Images, Transforms and Sampling -- 2.1 Images -- 2.2 Sampling with the Fourier Transform -- 2.3 Sampling with the Radon Transform -- 2.4 Binary Sampling with the Walsh Transform -- 3 A Short Guide to Compressive Imaging -- 3.1 The Six Stages of the Compressive Imaging Pipeline -- 3.2 First Example: MRI -- 3.3 Second Example: X-ray CT -- 3.4 Third Example: Optical Imaging -- 3.5 Recovery of Image Sequences -- 4 Techniques for Enhancing Performance -- 4.1 Sampling Strategies -- 4.2 How to Design a Sampling Strategy -- 4.3 Resolution Enhancement -- 4.4 Discretization, Model Mismatch and the Inverse Crime -- 4.5 Sparsifying Transforms -- 4.6 Iterative Reweighting -- 4.7 …