TY - GEN
T1 - Weighted and structured sparse total least-squares for perturbed compressive sampling
AU - Zhu, Hao
AU - Giannakis, Georgios B.
AU - Leus, Geert
PY - 2011
Y1 - 2011
N2 - Solving linear regression problems based on the total least-squares (TLS) criterion has well-documented merits in various applications, where perturbations appear both in the data vector as well as in the regression matrix. Weighted and structured generalizations of the TLS approach are further motivated in several signal processing and system identification related problems. On the other hand, modern compressive sampling and variable selection algorithms account for perturbations of the data vector, but not those affecting the regression matrix. The present paper addresses also the latter by introducing a weighted and structured sparse (S-) TLS formulation to exploit a priori knowledge on both types of perturbations, and on the sparsity of the unknown vector. The resultant novel approach is further able to cope with sparse, under-determined errors-in-variables models with structured and correlated perturbations, while allowing for efficient sub-optimum solvers. Simulated tests demonstrate the approach, and especially its ability to reliably recover the support of unknown sparse vectors.
AB - Solving linear regression problems based on the total least-squares (TLS) criterion has well-documented merits in various applications, where perturbations appear both in the data vector as well as in the regression matrix. Weighted and structured generalizations of the TLS approach are further motivated in several signal processing and system identification related problems. On the other hand, modern compressive sampling and variable selection algorithms account for perturbations of the data vector, but not those affecting the regression matrix. The present paper addresses also the latter by introducing a weighted and structured sparse (S-) TLS formulation to exploit a priori knowledge on both types of perturbations, and on the sparsity of the unknown vector. The resultant novel approach is further able to cope with sparse, under-determined errors-in-variables models with structured and correlated perturbations, while allowing for efficient sub-optimum solvers. Simulated tests demonstrate the approach, and especially its ability to reliably recover the support of unknown sparse vectors.
KW - Total least-squares
KW - coordinate descent
KW - errors-in-variables models
KW - sparsity
UR - http://www.scopus.com/inward/record.url?scp=80051606046&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80051606046&partnerID=8YFLogxK
U2 - 10.1109/ICASSP.2011.5947177
DO - 10.1109/ICASSP.2011.5947177
M3 - Conference contribution
AN - SCOPUS:80051606046
SN - 9781457705397
T3 - ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
SP - 3792
EP - 3795
BT - 2011 IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011 - Proceedings
T2 - 36th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2011
Y2 - 22 May 2011 through 27 May 2011
ER -