TY - GEN
T1 - Exact reconstruction of sparse signals via generalized orthogonal matching pursuit
AU - Wang, Jian
AU - Shim, Byonghyo
PY - 2011
Y1 - 2011
N2 - As a greedy algorithm recovering sparse signal from compressed measurements, orthogonal matching pursuit (OMP) algorithm have received much attention in recent years. The OMP selects at each step one index corresponding to the column that is most correlated with the current residual. In this paper, we present an extension of OMP for pursuing efficiency of the index selection. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple (N ∈ ℕ) columns are identified per step. We derive rigorous condition demonstrating that exact reconstruction of K-sparse (K > 1) signals is guaranteed for the gOMP algorithm if the sensing matrix satisfies the restricted isometric property (RIP) of order NK with isometric constant δ NK < √N/√K + 2 √N. In addition, empirical results demonstrate that the gOMP algorithm has very competitive reconstruction performance that is comparable to the ℓ 1-minimization technique.
AB - As a greedy algorithm recovering sparse signal from compressed measurements, orthogonal matching pursuit (OMP) algorithm have received much attention in recent years. The OMP selects at each step one index corresponding to the column that is most correlated with the current residual. In this paper, we present an extension of OMP for pursuing efficiency of the index selection. Our approach, henceforth referred to as generalized OMP (gOMP), is literally a generalization of the OMP in the sense that multiple (N ∈ ℕ) columns are identified per step. We derive rigorous condition demonstrating that exact reconstruction of K-sparse (K > 1) signals is guaranteed for the gOMP algorithm if the sensing matrix satisfies the restricted isometric property (RIP) of order NK with isometric constant δ NK < √N/√K + 2 √N. In addition, empirical results demonstrate that the gOMP algorithm has very competitive reconstruction performance that is comparable to the ℓ 1-minimization technique.
KW - Compressed sensing (CS)
KW - generalized orthogonal matching pursuit (gOMP)
KW - restricted isometric property (RIP)
UR - http://www.scopus.com/inward/record.url?scp=84861321961&partnerID=8YFLogxK
U2 - 10.1109/ACSSC.2011.6190192
DO - 10.1109/ACSSC.2011.6190192
M3 - Conference contribution
AN - SCOPUS:84861321961
SN - 9781467303231
T3 - Conference Record - Asilomar Conference on Signals, Systems and Computers
SP - 1139
EP - 1142
BT - Conference Record of the 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011
T2 - 45th Asilomar Conference on Signals, Systems and Computers, ASILOMAR 2011
Y2 - 6 November 2011 through 9 November 2011
ER -