Penalized linear regression for discrete ill-posed problems: A hybrid least-squares and mean-squared error approach

Abstract
This paper proposes a new approach to find the regularization parameter for linear least-squares discrete ill-posed problems. In the proposed approach, an artificial perturbation matrix with a bounded norm is forced into the discrete ill-posed model matrix. This perturbation is introduced to enhance the singular-value (SV) structure of the matrix and hence to provide a better solution. The proposed approach is derived to select the regularization parameter in a way that minimizes the mean-squared error (MSE) of the estimator. Numerical results demonstrate that the proposed approach outperforms a set of benchmark methods in most cases when applied to different scenarios of discrete ill-posed problems. Jointly, the proposed approach enjoys the lowest run-time and offers the highest level of robustness amongst all the tested methods.

Citation
Suliman M, Ballal T, Kammoun A, Al-Naffouri TY (2016) Penalized linear regression for discrete ill-posed problems: A hybrid least-squares and mean-squared error approach. 2016 24th European Signal Processing Conference (EUSIPCO). Available: http://dx.doi.org/10.1109/EUSIPCO.2016.7760279.

Acknowledgements
This work was supported by the King Abdulaziz City of Science and Technology (KACST) under Grant AT-34-345.

Publisher
Institute of Electrical and Electronics Engineers (IEEE)

Journal
2016 24th European Signal Processing Conference (EUSIPCO)

Conference/Event Name
24th European Signal Processing Conference, EUSIPCO 2016

DOI
10.1109/EUSIPCO.2016.7760279

Additional Links
http://ieeexplore.ieee.org/document/7760279/

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