Perturbation-Based Regularization for Signal Estimation in Linear Discrete Ill-posed Problems

Handle URI:
http://hdl.handle.net/10754/626536
Title:
Perturbation-Based Regularization for Signal Estimation in Linear Discrete Ill-posed Problems
Authors:
Suliman, Mohamed Abdalla Elhag ( 0000-0002-3447-1770 ) ; Ballal, Tarig; Al-Naffouri, Tareq Y. ( 0000-0003-2843-5084 )
Abstract:
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work, we propose a new regularization approach and a new regularization parameter selection approach for linear least-squares discrete ill-posed problems. The proposed approach is based on enhancing the singular-value structure of the ill-posed model matrix to acquire a better solution. Unlike many other regularization algorithms that seek to minimize the estimated data error, the proposed approach is developed to minimize the mean-squared error of the estimator which is the objective in many typical estimation scenarios. The performance of the proposed approach is demonstrated by applying it to a large set of real-world discrete ill-posed problems. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods in most cases. In addition, the approach also enjoys the lowest runtime and offers the highest level of robustness amongst all the tested benchmark regularization methods.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
arXiv
Issue Date:
29-Nov-2016
ARXIV:
arXiv:1611.09742
Type:
Preprint
Additional Links:
http://arxiv.org/abs/1611.09742v2; http://arxiv.org/pdf/1611.09742v2
Appears in Collections:
Other/General Submission; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSuliman, Mohamed Abdalla Elhagen
dc.contributor.authorBallal, Tarigen
dc.contributor.authorAl-Naffouri, Tareq Y.en
dc.date.accessioned2017-12-28T07:32:15Z-
dc.date.available2017-12-28T07:32:15Z-
dc.date.issued2016-11-29en
dc.identifier.urihttp://hdl.handle.net/10754/626536-
dc.description.abstractEstimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work, we propose a new regularization approach and a new regularization parameter selection approach for linear least-squares discrete ill-posed problems. The proposed approach is based on enhancing the singular-value structure of the ill-posed model matrix to acquire a better solution. Unlike many other regularization algorithms that seek to minimize the estimated data error, the proposed approach is developed to minimize the mean-squared error of the estimator which is the objective in many typical estimation scenarios. The performance of the proposed approach is demonstrated by applying it to a large set of real-world discrete ill-posed problems. Simulation results demonstrate that the proposed approach outperforms a set of benchmark regularization methods in most cases. In addition, the approach also enjoys the lowest runtime and offers the highest level of robustness amongst all the tested benchmark regularization methods.en
dc.publisherarXiven
dc.relation.urlhttp://arxiv.org/abs/1611.09742v2en
dc.relation.urlhttp://arxiv.org/pdf/1611.09742v2en
dc.rightsArchived with thanks to arXiven
dc.titlePerturbation-Based Regularization for Signal Estimation in Linear Discrete Ill-posed Problemsen
dc.typePreprinten
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.eprint.versionPre-printen
dc.identifier.arxividarXiv:1611.09742en
kaust.authorSuliman, Mohamed Abdalla Elhagen
kaust.authorBallal, Tarigen
kaust.authorAl-Naffouri, Tareq Y.en
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