A probabilistic and RIPless theory of compressed sensing

8 years 7 months ago
A probabilistic and RIPless theory of compressed sensing
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 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) -- they make use of a much weaker notion -- or 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 slog n Fourier coefficients that are contaminated with noise. Keywords. Compressed sensing, 1 minimization, the LASSO, the Dantzig select...
Emmanuel J. Candès, Yaniv Plan
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Emmanuel J. Candès, Yaniv Plan
Comments (0)