Bounded Perturbation Regularization for Linear Least Squares Estimation
Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionElectrical Engineering Program
Date
2017-10-18Online Publication Date
2017-10-18Print Publication Date
2017Permanent link to this record
http://hdl.handle.net/10754/626111
Metadata
Show full item recordAbstract
This paper addresses the problem of selecting the regularization parameter for linear least-squares estimation. We propose a new technique called bounded perturbation regularization (BPR). In the proposed BPR method, a perturbation with a bounded norm is allowed into the linear transformation matrix to improve the singular-value structure. Following this, the problem is formulated as a min-max optimization problem. Next, the min-max problem is converted to an equivalent minimization problem to estimate the unknown vector quantity. The solution of the minimization problem is shown to converge to that of the ℓ2 -regularized least squares problem, with the unknown regularizer related to the norm bound of the introduced perturbation through a nonlinear constraint. A procedure is proposed that combines the constraint equation with the mean squared error (MSE) criterion to develop an approximately optimal regularization parameter selection algorithm. Both direct and indirect applications of the proposed method are considered. Comparisons with different Tikhonov regularization parameter selection methods, as well as with other relevant methods, are carried out. Numerical results demonstrate that the proposed method provides significant improvement over state-of-the-art methods.Citation
Ballal T, Suliman MA, Al-Naffouri TY (2017) Bounded Perturbation Regularization for Linear Least Squares Estimation. IEEE Access: 1–1. Available: http://dx.doi.org/10.1109/ACCESS.2017.2759201.Sponsors
This work was supported by the KAUST-KFUPM joint research initiative and the KAUST CRG3 funding.Journal
IEEE AccessAdditional Links
http://ieeexplore.ieee.org/document/8070950/ae974a485f413a2113503eed53cd6c53
10.1109/ACCESS.2017.2759201