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

A Parameter Choice Rule for Tikhonov Regularization Based on Predictive Risk