Compressed Sensing: Theory and ApplicationsYonina C. Eldar, Gitta Kutyniok Compressed sensing is an exciting, rapidly growing field, attracting considerable attention in electrical engineering, applied mathematics, statistics and computer science. This book provides the first detailed introduction to the subject, highlighting theoretical advances and a range of applications, as well as outlining numerous remaining research challenges. After a thorough review of the basic theory, many cutting-edge techniques are presented, including advanced signal modeling, sub-Nyquist sampling of analog signals, non-asymptotic analysis of random matrices, adaptive sensing, greedy algorithms and use of graphical models. All chapters are written by leading researchers in the field, and consistent style and notation are utilized throughout. Key background information and clear definitions make this an ideal resource for researchers, graduate students and practitioners wanting to join this exciting research area. It can also serve as a supplementary textbook for courses on computer vision, coding theory, signal processing, image processing and algorithms for efficient data processing. |
Contents
structured | 65 |
compressed sensing of analog signals | 88 |
theory and applications | 148 |
Introduction to the nonasymptotic analysis of random matrices | 210 |
Adaptive sensing for sparse recovery | 269 |
Greedy algorithms for compressed sensing | 348 |
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Common terms and phrases
algorithm amplitudes analog signals analysis applications approach approximation bound chapter coefficients columns components compressed sensing Comput convex cross-polytope data domain defined denote distribution Donoho Eldar entries error estimation example face recognition Figure filter finite Fourier FRI signals function Gaussian greedy algorithms guarantees IEEE Trans Inform independent inequality Inform Theory input isometry iteration k-sparse l₁ minimization LASSO Lemma linear Matching Pursuit measurement domain methods multiband noise nonzero norm null space Nyquist rate obtain optimization parameters performance probability problem Proof pulse random matrices random variables random vectors rate of innovation reconstruction recover restricted isometry robustness sampling kernels sampling rate satisfies the RIP Section sensing matrix signal reconstruction sparse models sparse recovery sparse representation sparse signals sparsity SVM's classifier Theorem threshold Trans Inform Theory Trans Sig Proc union of subspaces UoS models wavelet Y. C. Eldar