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

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

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.
Original languageEnglish (US)
Title of host publication2016 24th European Signal Processing Conference (EUSIPCO)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages403-407
Number of pages5
ISBN (Print)9780992862657
DOIs
StatePublished - Dec 19 2016

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