  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.
