Signal Recovery from Partial Information via Orthogonal Matching Pursuit
نویسنده
چکیده
This article 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(m ln d) random linear measurements of that signal. This is a massive improvement over previous results for OMP, which require O(m) measurements. The new results for OMP are comparable with recent results for another algorithm called Basis Pursuit (BP). The OMP algorithm is much faster and much easier to implement, which makes it an attractive alternative to BP for signal recovery problems.
منابع مشابه
Sparse Matrix Recovery from Random Samples via 2D Orthogonal Matching Pursuit
Since its emergence, compressive sensing (CS) has attracted many researchers’ attention. In the CS, recovery algorithms play an important role. Basis pursuit (BP) and matching pursuit (MP) are two major classes of CS recovery algorithms. However, both BP and MP are originally designed for one-dimensional (1D) sparse signal recovery, while many practical signals are two-dimensional (2D), e.g. im...
متن کاملSignal Recovery from Random Measurements via Orthogonal Matching Pursuit: the Gaussian Case
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(m ln d) random linear measurements of that signal. This is a massive improvement over previous results, which require O(m) measurements. The new results for OMP are comparable with recent results for a...
متن کاملA sharp recovery condition for sparse signals with partial support information via orthogonal matching pursuit
This paper considers the exact recovery of k-sparse signals in the noiseless setting and support recovery in the noisy case when some prior information on the support of the signals is available. This prior support consists of two parts. One part is a subset of the true support and another part is outside of the true support. For k-sparse signals x with the prior support which is composed of g ...
متن کامل8 Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-mi...
متن کاملUniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit
This paper seeks to bridge the two major algorithmic approaches to sparse signal recovery from an incomplete set of linear measurements – L1-minimization methods and iterative methods (Matching Pursuits). We find a simple regularized version of Orthogonal Matching Pursuit (ROMP) which has advantages of both approaches: the speed and transparency of OMP and the strong uniform guarantees of L1-mi...
متن کامل