Bounded Perturbation Regularization for Linear Least Squares Estimation

Handle URI:
http://hdl.handle.net/10754/626111
Title:
Bounded Perturbation Regularization for Linear Least Squares Estimation
Authors:
Ballal, Tarig; Suliman, Mohamed Abdalla Elhag ( 0000-0002-3447-1770 ) ; Al-Naffouri, Tareq Y. ( 0000-0003-2843-5084 )
Abstract:
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.
KAUST Department:
Electrical Engineering Program
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.
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
IEEE Access
Issue Date:
18-Oct-2017
DOI:
10.1109/ACCESS.2017.2759201
Type:
Article
ISSN:
2169-3536
Sponsors:
This work was supported by the KAUST-KFUPM joint research initiative and the KAUST CRG3 funding.
Additional Links:
http://ieeexplore.ieee.org/document/8070950/
Appears in Collections:
Articles; Electrical Engineering Program

Full metadata record

DC FieldValue Language
dc.contributor.authorBallal, Tarigen
dc.contributor.authorSuliman, Mohamed Abdalla Elhagen
dc.contributor.authorAl-Naffouri, Tareq Y.en
dc.date.accessioned2017-11-06T07:09:04Z-
dc.date.available2017-11-06T07:09:04Z-
dc.date.issued2017-10-18en
dc.identifier.citationBallal 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.en
dc.identifier.issn2169-3536en
dc.identifier.doi10.1109/ACCESS.2017.2759201en
dc.identifier.urihttp://hdl.handle.net/10754/626111-
dc.description.abstractThis 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.en
dc.description.sponsorshipThis work was supported by the KAUST-KFUPM joint research initiative and the KAUST CRG3 funding.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.relation.urlhttp://ieeexplore.ieee.org/document/8070950/en
dc.rights(c) 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.en
dc.subjectBusiness process re-engineeringen
dc.subjectCovariance matricesen
dc.subjectEstimationen
dc.subjectleast squaresen
dc.subjectLinear estimationen
dc.subjectMatrix convertersen
dc.subjectmean squared erroren
dc.subjectMinimizationen
dc.subjectOptimizationen
dc.subjectPeriodic structuresen
dc.subjectTikhonov regularizationen
dc.titleBounded Perturbation Regularization for Linear Least Squares Estimationen
dc.typeArticleen
dc.contributor.departmentElectrical Engineering Programen
dc.identifier.journalIEEE Accessen
dc.eprint.versionPost-printen
kaust.authorBallal, Tarigen
kaust.authorSuliman, Mohamed Abdalla Elhagen
kaust.authorAl-Naffouri, Tareq Y.en
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