Table of Contents

Foreword; Preface; Acknowledgements; 1. Introduction; Part I. Principles of Low-Dimensional Models: 2. Sparse Signal Models; 3. Convex Methods for Sparse Signal Recovery; 4. Convex Methods for Low-Rank Matrix Recovery; 5. Decomposing Low-Rank and Sparse Matrices; 6. Recovering General Low-Dimensional Models; 7. Nonconvex Methods for Low-Dimensional Models; Part II. Computation for Large-Scale Problems: 8. Convex Optimization for Structured Signal Recovery; 9. Nonconvex Optimization for High-Dimensional Problems; Part III. Applications to Real-World Problems: 10. Magnetic Resonance Imaging; 11. Wideband Spectrum Sensing; 12. Scientific Imaging Problems; 13. Robust Face Recognition; 14. Robust Photometric Stereo; 15. Structured Texture Recovery; 16. Deep Networks for Classification; Appendices: Appendix A. Facts from Linear Algebra and Matrix Analysis; Appendix B. Convex Sets and Functions; Appendix C. Optimization Problems and Optimality Conditions; Appendix D. Methods for Optimization; Appendix E. Facts from High-Dimensional Statistics; Bibliography; List of Symbols; Index.

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Connects fundamental mathematical theory with real-world problems, through efficient and scalable optimization algorithms.

About the Author

John Wright is an Associate Professor in the Electrical Engineering Department and the Data Science Institute at Columbia University. Yi Ma is a Professor in the Department of Electrical Engineering and Computer Sciences at the University of California, Berkeley. He is a Fellow of the IEEE, ACM, and SIAM.

Reviews

'Students will learn a lot from reading this book … They will learn about mathematical reasoning, they will learn about data models and about connecting those to reality, and they will learn about algorithms. The book also contains computer scripts so that we can see ideas in action, and carefully crafted exercises making it perfect for upper-level undergraduate or graduate-level instruction. The breadth and depth make this a reference for anyone interested in the mathematical foundations of data science.' Emmanuel Candès, Stanford University (from the foreword)

'At the very core of our ability to process data stands the fact that sources of information are structured. Modeling data, explicitly or implicitly, is our way of exposing this structure and exploiting it, being the essence of the fields of signal and image processing and machine learning. The past two decades have brought a revolution to our understanding of these facts, and this 'must-read' book provides the foundations of these recent developments, covering theoretical, numerical, and applicative aspects of this field in a thorough and clear manner.' Michael Elad, Technion – Israel Institute of Technology