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2016

Recovery of Sparse Signals via Generalized Orthogonal Matching Pursuit: A New Analysis

3 years 3 months ago
Recovery of Sparse Signals via Generalized Orthogonal Matching Pursuit: A New Analysis
As an extension of orthogonal matching pursuit (OMP) for improving the recovery performance of sparse signals, generalized OMP (gOMP) has recently been studied in the literature. In this paper, we present a new analysis of the gOMP algorithm using the restricted isometry property (RIP). We show that if a measurement matrix Φ ∈ Rm×n satisfies the RIP with isometry constant δmax{9,S+1}K ≤ 1 8 , then gOMP performs stable reconstruction of all K-sparse signals x ∈ Rn from the noisy measurements y = Φx + v, within max K, 8K S iterations, where v is the noise vector and S is the number of indices chosen in each iteration of the gOMP algorithm. For Gaussian random measurements, our result indicates that the number of required measurements is essentially m = O(K log n K ), which is a significant improvement over the existing result m = O(K2 log n K ), especially for large K.
Jian Wang, Suhyuk Kwon, Ping Li, Byonghyo Shim
Added 11 Apr 2016
Updated 11 Apr 2016
Type Journal
Year 2016
Where TSP
Authors Jian Wang, Suhyuk Kwon, Ping Li, Byonghyo Shim
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