Abstract
As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple N indices are identified per iteration. Owing to the selection of multiple correct indices, the gOMP algorithm is finished with much smaller number of iterations when compared to the OMP. We show that the gOMP can perfectly reconstruct any K-sparse signals (K ≥ 1) , provided that the sensing matrix satisfies the RIP with δNK< √ N/√K+3√N. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to L1- minimization technique with fast processing speed and competitive computational complexity.
| Original language | English |
|---|---|
| Article number | 6302206 |
| Pages (from-to) | 6202-6216 |
| Number of pages | 15 |
| Journal | IEEE Transactions on Signal Processing |
| Volume | 60 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 2012 Dec 10 |
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Keywords
- Compressive sensing (CS)
- orthogonal matching pursuit
- restricted isometry property (RIP)
- sparse recovery
ASJC Scopus subject areas
- Electrical and Electronic Engineering
- Signal Processing
Cite this
Generalized orthogonal matching pursuit. / Wang, Jian; Kwon, Seokbeop; Shim, Byonghyo.
In: IEEE Transactions on Signal Processing, Vol. 60, No. 12, 6302206, 10.12.2012, p. 6202-6216.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Generalized orthogonal matching pursuit
AU - Wang, Jian
AU - Kwon, Seokbeop
AU - Shim, Byonghyo
PY - 2012/12/10
Y1 - 2012/12/10
N2 - As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple N indices are identified per iteration. Owing to the selection of multiple correct indices, the gOMP algorithm is finished with much smaller number of iterations when compared to the OMP. We show that the gOMP can perfectly reconstruct any K-sparse signals (K ≥ 1) , provided that the sensing matrix satisfies the RIP with δNK< √ N/√K+3√N. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to L1- minimization technique with fast processing speed and competitive computational complexity.
AB - As a greedy algorithm to recover sparse signals from compressed measurements, orthogonal matching pursuit (OMP) algorithm has received much attention in recent years. In this paper, we introduce an extension of the OMP for pursuing efficiency in reconstructing sparse signals. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple N indices are identified per iteration. Owing to the selection of multiple correct indices, the gOMP algorithm is finished with much smaller number of iterations when compared to the OMP. We show that the gOMP can perfectly reconstruct any K-sparse signals (K ≥ 1) , provided that the sensing matrix satisfies the RIP with δNK< √ N/√K+3√N. We also demonstrate by empirical simulations that the gOMP has excellent recovery performance comparable to L1- minimization technique with fast processing speed and competitive computational complexity.
KW - Compressive sensing (CS)
KW - orthogonal matching pursuit
KW - restricted isometry property (RIP)
KW - sparse recovery
UR - http://www.scopus.com/inward/record.url?scp=84870506486&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84870506486&partnerID=8YFLogxK
U2 - 10.1109/TSP.2012.2218810
DO - 10.1109/TSP.2012.2218810
M3 - Article
AN - SCOPUS:84870506486
VL - 60
SP - 6202
EP - 6216
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
SN - 1053-587X
IS - 12
M1 - 6302206
ER -