1. Signal Recovery from Random Measurements Via Orthogonal Matching Pursuit: The Gaussian Case
- Author
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Tropp, Joel A. and Gilbert, Anna C.
- Subjects
Statistics::Machine Learning ,signal recovery ,Compressed Sensing ,Basis Pursuit ,Orthogonal Matching Pursuit ,sparse approximation ,2000 Mathematics Subject Classication. 41A46, 68Q25, 68W20, 90C27 ,Computer Science::Numerical Analysis ,approximation ,Algorithms ,group testing - Abstract
This report demonstrates theoretically and empirically that a greedy algorithm called Orthogonal Matching Pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(mln d) random linear measurements of that signal. This is a massive improvement over previous results, which require O(m2) measurements. The new results for OMP are comparable with recent results for another approach called Basis Pursuit (BP). In some settings, the OMP algorithm is faster and easier to implement, so it is an attractive alternative to BP for signal recovery problems., A 20111010-134929077
- Published
- 2007
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