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."--Back cover.

Introduction -- The essentials of compressive imaging. Images, transforms, and sampling -- A short guide to compressive imaging -- Techniques for enhancing performance -- Compressed sensing, optimization and wavelets. An introduction to conventional compressed sensing -- The LASSO and its cousins -- Optimization for compresed sensing --Analysis of optimazation algorithms -- Wavelets -- A taste of wavelet approximation theory -- Compressed sensing with local structure. From global to local -- Local structure and nonuniform recovery -- Local structure and uniform recovery -- Infinite-dimensional compressed sensing -- Compressed sensing for imaging. Sampling strategies for compressive imaging -- Recovery guarantees for wavelet-based compressed imaging -- Total variation minimization -- From compressed sensing to deep learniing. Neural networks and deep learning -- Deep learning for compressive imaging -- Accuracy and stability of deep learning for compressive imaging -- Stable and accurate neural networks for compressive imaging -- Epilogue -- Appendices. Linear algebra -- Functional analysis -- Probability -- Convex analysis and convex optimization -- Fourier transforms and series -…