TY - JOUR

T1 - Sparsity-cognizant total least-squares for perturbed compressive sampling

AU - Zhu, Hao

AU - Leus, Geert

AU - Giannakis, Georgios B

PY - 2011/5/1

Y1 - 2011/5/1

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. However, existing TLS approaches do not account for sparsity possibly present in the unknown vector of regression coefficients. On the other hand, sparsity is the key attribute exploited by modern compressive sampling and variable selection approaches to linear regression, which include noise in the data, but do not account for perturbations in the regression matrix. The present paper fills this gap by formulating and solving (regularized) TLS optimization problems under sparsity constraints. Near-optimum and reduced-complexity suboptimum sparse (S-) TLS algorithms are developed to address the perturbed compressive sampling (and the related dictionary learning) challenge, when there is a mismatch between the true and adopted bases over which the unknown vector is sparse. The novel S-TLS schemes also allow for perturbations in the regression matrix of the least-absolute selection and shrinkage selection operator (Lasso), and endow TLS approaches with ability to cope with sparse, under-determined errors-in-variables models. Interesting generalizations can further exploit prior knowledge on the perturbations to obtain novel weighted and structured S-TLS solvers. Analysis and simulations demonstrate the practical impact of S-TLS in calibrating the mismatch effects of contemporary grid-based approaches to cognitive radio sensing, and robust direction-of-arrival estimation using antenna arrays.

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. However, existing TLS approaches do not account for sparsity possibly present in the unknown vector of regression coefficients. On the other hand, sparsity is the key attribute exploited by modern compressive sampling and variable selection approaches to linear regression, which include noise in the data, but do not account for perturbations in the regression matrix. The present paper fills this gap by formulating and solving (regularized) TLS optimization problems under sparsity constraints. Near-optimum and reduced-complexity suboptimum sparse (S-) TLS algorithms are developed to address the perturbed compressive sampling (and the related dictionary learning) challenge, when there is a mismatch between the true and adopted bases over which the unknown vector is sparse. The novel S-TLS schemes also allow for perturbations in the regression matrix of the least-absolute selection and shrinkage selection operator (Lasso), and endow TLS approaches with ability to cope with sparse, under-determined errors-in-variables models. Interesting generalizations can further exploit prior knowledge on the perturbations to obtain novel weighted and structured S-TLS solvers. Analysis and simulations demonstrate the practical impact of S-TLS in calibrating the mismatch effects of contemporary grid-based approaches to cognitive radio sensing, and robust direction-of-arrival estimation using antenna arrays.

KW - Direction-of-arrival estimation

KW - errors-in-variables models

KW - sparsity

KW - spectrum sensing

KW - total least-squares

UR - http://www.scopus.com/inward/record.url?scp=79954496453&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79954496453&partnerID=8YFLogxK

U2 - 10.1109/TSP.2011.2109956

DO - 10.1109/TSP.2011.2109956

M3 - Article

AN - SCOPUS:79954496453

VL - 59

SP - 2002

EP - 2016

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 5

M1 - 5706373

ER -