TY - GEN
T1 - An improved RIP-based performance guarantee for sparse signal reconstruction via subspace pursuit
AU - Chang, Ling Hua
AU - Wu, Jwo-Yuh
PY - 2014
Y1 - 2014
N2 - Subspace pursuit (SP) is a well-known greedy algorithm capable of reconstructing a sparse signal vector from a set of incomplete measurements. In this paper, by exploiting an approximate orthogonality condition characterized in terms of the achievable angles between two compressed orthogonal sparse vectors, we show that perfect signal recovery in the noiseless case, as well as stable signal recovery in the noisy case, is guaranteed if the sensing matrix satisfies RIP of order 3K with RIC δ3K ≤ 0.2412. Our work improves the best-known existing results, namely, δ3K < 0.165 for the noiseless case [3] and δ3K < 0.139 when noise is present [4]. In addition, for the noisy case we derive a reconstruction error upper bound, which is shown to be smaller as compared to the bound reported in [4].
AB - Subspace pursuit (SP) is a well-known greedy algorithm capable of reconstructing a sparse signal vector from a set of incomplete measurements. In this paper, by exploiting an approximate orthogonality condition characterized in terms of the achievable angles between two compressed orthogonal sparse vectors, we show that perfect signal recovery in the noiseless case, as well as stable signal recovery in the noisy case, is guaranteed if the sensing matrix satisfies RIP of order 3K with RIC δ3K ≤ 0.2412. Our work improves the best-known existing results, namely, δ3K < 0.165 for the noiseless case [3] and δ3K < 0.139 when noise is present [4]. In addition, for the noisy case we derive a reconstruction error upper bound, which is shown to be smaller as compared to the bound reported in [4].
KW - Compressive sensing
KW - restricted isometry constant (RIC)
KW - restricted isometry property (RIP)
KW - subspace pursuit
UR - http://www.scopus.com/inward/record.url?scp=84907386740&partnerID=8YFLogxK
U2 - 10.1109/SAM.2014.6882428
DO - 10.1109/SAM.2014.6882428
M3 - Conference contribution
AN - SCOPUS:84907386740
SN - 9781479914814
T3 - Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop
SP - 405
EP - 408
BT - 2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop, SAM 2014
PB - IEEE Computer Society
T2 - 2014 IEEE 8th Sensor Array and Multichannel Signal Processing Workshop, SAM 2014
Y2 - 22 June 2014 through 25 June 2014
ER -