Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 55, Issue 5, Pages 2230-2249Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2009.2016006
Keywords
Compressive sensing; orthogonal matching pursuit; reconstruction algorithms; restricted isometry property; sparse signal reconstruction
Funding
- National Science Foundation (NSF) [CCF 0644427, 0729216]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [0821910, 0729216] Funding Source: National Science Foundation
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We propose a new method for reconstruction of sparse signals with and without noisy perturbations, termed the subspace pursuit algorithm. The algorithm has two important characteristics: low computational complexity, comparable to that of orthogonal matching pursuit techniques when applied to very sparse signals, and reconstruction accuracy of the same order as that of linear programming (LP) optimization methods. The presented analysis shows that in the noiseless setting, the proposed algorithm can exactly reconstruct arbitrary sparse signals provided that the sensing matrix satisfies the restricted isometry property with a constant parameter. In the noisy setting and in the case that the signal is not exactly sparse, it can be shown that the mean-squared error of the reconstruction is upper-bounded by constant multiples of the measurement and signal perturbation energies.
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