期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 57, 期 11, 页码 7235-7254出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2011.2161794
关键词
Compressed sensing; Dantzig selector; l(1) minimization; Gross' golfing scheme; LASSO; operator Bernstein inequalities; random matrices; sparse regression; (weak) restricted isometries
资金
- Office of Naval Research (ONR) [N00014-09-1-0469, N00014-08-1-0749]
- National Science Foundation (NSF)
This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F; it includes all standard models-e. g., Gaussian, frequency measurements-discussed in the literature, but also provides a framework for new measurement strategies as well. We prove that if the probability distribution F obeys a simple incoherence property and an isotropy property, one can faithfully recover approximately sparse signals from a minimal number of noisy measurements. The novelty is that our recovery results do not require the restricted isometry property (RIP) to hold near the sparsity level in question, nor a random model for the signal. As an example, the paper shows that a signal with s nonzero entries can be faithfully recovered from about s log n Fourier coefficients that are contaminated with noise.
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