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Compressed sensing is a growing field which is attracting considerable attention in signal processing and computing. This book provides the first applications in optical telecommunications and wireless. After extensive development of the basic theory, many techniques are presented, such as non-asymptotic analysis of random matrices, adaptive detection, greedy algorithms and the use of graphical models. It can be used as a comprehensive manual as well for teaching and for research in courses covering advanced signal processing, efficient data processing algorithms, and telecommunications. After a thorough review of the basic theory of compressed sensing, many mathematical techniques are presented, including advanced signal modeling, Nyquist sub-sampling of analog signals, the non-asymptotic analysis of random matrices, adaptive detection, greedy algorithms and the use of graphical models. We give applications of compressed sensing in optical telecommunications (LIFI) and wireless networks (WiFi). Broad coverage of Treat Compressed Sensing, including electromagnetism signalsProvides insights into the two key areas of telecommunications: WIFI and LIFIDeepening the application of compressed sensing in radar