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A Parameter Choice Rule for Tikhonov Regularization Based on Predictive Risk

Benvenuto, F; Jin, B; (2020) A Parameter Choice Rule for Tikhonov Regularization Based on Predictive Risk. Inverse Problems , 36 (6) , Article 065004. 10.1088/1361-6420/ab6d58. Green open access

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Abstract

In this work, we propose a new criterion for choosing the regularization parameter in Tikhonov regularization when the noise is white Gaussian. The criterion minimizes a lower bound of the predictive risk, when both data norm and noise variance are known, and the parameter choice involves minimizing a function whose solution depends only on the signal-to-noise ratio. Moreover, when neither noise variance nor data norm is given, we propose an iterative algorithm which alternates between a minimization step of finding the regularization parameter and an estimation step of estimating signal-to-noise ratio. Simulation studies on both small- and large-scale datasets suggest that the approach can provide very accurate and stable regularized inverse solutions and, for small sized samples, it outperforms discrepancy principle, balancing principle, unbiased predictive risk estimator, L-curve method, generalized cross validation, and quasi-optimality criterion, and achieves excellent stability hitherto unavailable.

Type: Article
Title: A Parameter Choice Rule for Tikhonov Regularization Based on Predictive Risk
Open access status: An open access version is available from UCL Discovery
DOI: 10.1088/1361-6420/ab6d58
Publisher version: https://doi.org/10.1088/1361-6420/ab6d58
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/10090039
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