A detailed presentation of compressed sensing by leading researchers, covering the most significant theoretical and application-oriented advances.

1. Introduction to compressed sensing Mark A. Davenport, Marco F. Duarte, Yonina C. Eldar and Gitta Kutyniok; 2. Second generation sparse modeling: structured and collaborative signal analysis Alexey Castrodad, Ignacio Ramirez, Guillermo Sapiro, Pablo Sprechmann and Guoshen Yu; 3. Xampling: compressed sensing of analog signals Moshe Mishali and Yonina C. Eldar; 4. Sampling at the rate of innovation: theory and applications Jose Antonia Uriguen, Yonina C. Eldar, Pier Luigi Dragotta and Zvika Ben-Haim; 5. Introduction to the non-asymptotic analysis of random matrices Roman Vershynin; 6. Adaptive sensing for sparse recovery Jarvis Haupt and Robert Nowak; 7. Fundamental thresholds in compressed sensing: a high-dimensional geometry approach Weiyu Xu and Babak Hassibi; 8. Greedy algorithms for compressed sensing Thomas Blumensath, Michael E. Davies and Gabriel Rilling; 9. Graphical models concepts in compressed sensing Andrea Montanari; 10. Finding needles in compressed haystacks Robert Calderbank, Sina Jafarpour and Jeremy Kent; 11. Data separation by sparse representations Gitta Kutyniok; 12. Face recognition by sparse representation Arvind Ganesh, Andrew Wagner, Zihan Zhou, Allen Y. Yang, Yi Ma and John Wright.