A parameter choice rule for Tikhonov regularization based on predictive risk
A parameter choice rule for Tikhonov regularization based on predictive risk
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DOI：
10.1088/1361-6420/ab6d58
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发表时间：
2020-06-01
期刊：
影响因子：
2.1
通讯作者：
Jin, Bangti
中科院分区：
文献类型：
--
作者：
Benvenuto, Federico;Jin, Bangti
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.
