Limits on Sparse Data Acquisition: RIC Analysis of Finite Gaussian Matrices
| Autor: | Marco Chiani, Andrea Giorgetti, Ahmed Elzanaty |
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| Přispěvatelé: | Elzanaty, Ahmed, Giorgetti, Andrea, Chiani, Marco |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Signal Processing (eess.SP)
FOS: Computer and information sciences Wishart distribution Computer science Wishart matrice Gaussian Computer Science - Information Theory Mathematics - Statistics Theory Statistics Theory (math.ST) Information System 02 engineering and technology Library and Information Sciences Linear matrix inequalitie Upper and lower bounds Restricted isometry property Matrix (mathematics) symbols.namesake FOS: Electrical engineering electronic engineering information engineering FOS: Mathematics Eigenvalues and eigenfunction Robustne 0202 electrical engineering electronic engineering information engineering Gaussian measurement matrice Electrical Engineering and Systems Science - Signal Processing Eigenvalues and eigenvectors Probability Sparse matrice Sparse matrix robust recovery Information Theory (cs.IT) Data acquisition Computer Science Applications1707 Computer Vision and Pattern Recognition 020206 networking & telecommunications restricted isometry property sparse reconstruction Computer Science Applications Compressed sensing symbols Isometry Compressibility Algorithm Information Systems |
| Popis: | One of the key issues in the acquisition of sparse data by means of compressed sensing (CS) is the design of the measurement matrix. Gaussian matrices have been proven to be information-theoretically optimal in terms of minimizing the required number of measurements for sparse recovery. In this paper we provide a new approach for the analysis of the restricted isometry constant (RIC) of finite dimensional Gaussian measurement matrices. The proposed method relies on the exact distributions of the extreme eigenvalues for Wishart matrices. First, we derive the probability that the restricted isometry property is satisfied for a given sufficient recovery condition on the RIC, and propose a probabilistic framework to study both the symmetric and asymmetric RICs. Then, we analyze the recovery of compressible signals in noise through the statistical characterization of stability and robustness. The presented framework determines limits on various sparse recovery algorithms for finite size problems. In particular, it provides a tight lower bound on the maximum sparsity order of the acquired data allowing signal recovery with a given target probability. Also, we derive simple approximations for the RICs based on the Tracy-Widom distribution. 11 pages, 6 figures, accepted for publication in IEEE transactions on information theory |
| Databáze: | OpenAIRE |
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