Bounded Perturbation Regularization for Linear Least Squares Estimation

Tarig Ballal, Mohamed Abdalla Elhag Suliman, Tareq Y. Al-Naffouri

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.
Original languageEnglish (US)
Pages (from-to)27551-27562
Number of pages12
JournalIEEE Access
StatePublished - Oct 18 2017

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was supported by the KAUST-KFUPM joint research initiative and the KAUST CRG3 funding.


Dive into the research topics of 'Bounded Perturbation Regularization for Linear Least Squares Estimation'. Together they form a unique fingerprint.

Cite this