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Abstract: This paper introduces a simple and very general theory of compressivesensing. In this theory, the sensing mechanism simply selects sensing vectorsindependently at random from a probability distribution F; it includes allmodels - e.g. Gaussian, frequency measurements - discussed in the literature,but also provides a framework for new measurement strategies as well. We provethat if the probability distribution F obeys a simple incoherence property andan isotropy property, one can faithfully recover approximately sparse signalsfrom a minimal number of noisy measurements. The novelty is that our recoveryresults do not require the restricted isometry property RIP - they make useof a much weaker notion - or a random model for the signal. As an example, thepaper shows that a signal with s nonzero entries can be faithfully recoveredfrom about s log n Fourier coefficients that are contaminated with noise.



Author: Emmanuel J. Candes, Yaniv Plan

Source: https://arxiv.org/







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