TY - GEN
T1 - 1-Bit compressed sensing of positive semi-definite matrices via rank-1 measurement matrices
AU - Wang, Xiyuan
AU - Wang, Kun
AU - Zhang, Zhongshan
AU - Long, Keping
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/5/18
Y1 - 2016/5/18
N2 - In this paper, we investigate the problem of recovering positive semi-definite (PSD) matrix from 1-bit sensing. The measurement matrix is rank-1 and constructed by the outer product of a pair of vectors, whose entries are independent and identically distributed (i.i.d.) Gaussian variables. The recovery problem is solved in closed form through a convex programming. Our analysis reveals that the solution is biased in general. However, in case of error-free measurement, we find that for rank-r PSD matrix with bounded condition number, the bias decreases with an order of O(1/r). Therefore, an approximate recovery is still possible. Numerical experiments are conducted to verify our analysis.
AB - In this paper, we investigate the problem of recovering positive semi-definite (PSD) matrix from 1-bit sensing. The measurement matrix is rank-1 and constructed by the outer product of a pair of vectors, whose entries are independent and identically distributed (i.i.d.) Gaussian variables. The recovery problem is solved in closed form through a convex programming. Our analysis reveals that the solution is biased in general. However, in case of error-free measurement, we find that for rank-r PSD matrix with bounded condition number, the bias decreases with an order of O(1/r). Therefore, an approximate recovery is still possible. Numerical experiments are conducted to verify our analysis.
KW - 1-bit compressed sensing
KW - positive semi-definite matrix recovery
KW - rank-1 measurement matrix
KW - signal quantization
UR - http://www.scopus.com/inward/record.url?scp=84973326498&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2016.7472551
DO - 10.1109/ICASSP.2016.7472551
M3 - Conference contribution
AN - SCOPUS:84973326498
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 4613
EP - 4617
BT - 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
Y2 - 20 March 2016 through 25 March 2016
ER -