Sparse Recovery With Orthogonal Matching Pursuit Under RIP

• Published in: IEEE transactions on information theory Vol. 57; no. 9; pp. 6215 - 6221
• Main Author: Zhang, Tong
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.2011; Institute of Electrical and Electronics Engineers
• Subjects: Access methods and protocols, osi model; Algorithm design and analysis; Applied sciences; Approximation algorithms; Compressed sensing; Detection, estimation, filtering, equalization, prediction; Estimation theory; Exact sciences and technology; feature selection; greedy algorithms; Information theory; Information, signal and communications theory; Matching pursuit algorithms; Noise; Optimization; Sampling, quantization; Signal and communications theory; Signal processing algorithms; Signal, noise; sparse recovery; statistical learning; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Isometry; statistical learning; greedy algorithms; Transmission protocol; Estimation theory; Iterative method; sparse recovery; Research and development; Learning; Matching pursuit; Greedy algorithm; Signal processing; Feature extraction; Routing protocols; Compressed sensing; feature selection
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2011.2162263

This paper presents a new analysis for the orthogonal matching pursuit (OMP) algorithm. It is shown that if the restricted isometry property (RIP) is satisfied at sparsity level O (k̅), then OMP can stably recover a k̅ -sparse signal in 2-norm under measurement noise. For compressed sensing applications, this result implies that in order to uniformly recover a k̅ -sparse signal in R d , only O ( k̅ ln d ) random projections are needed. This analysis improves some earlier results on OMP depending on stronger conditions that can only be satisfied with Ω( k̅ 2 ln d ) or Ω( k̅ 1.6 ln d ) random projections.