Regularization parameter choice

A regularization parameter choice selects the amount of stabilization from the noise level, the measured data, or both. For Tikhonov regularization with deterministic error at most $\delta$, a sufficient a priori condition for convergence is $\alpha (\delta )\to 0$ and $\delta /\sqrt{\alpha (\delta )}\to 0$.

An a priori regularization parameter choice depends on a known noise bound and fixed problem information, but not on the observed values of the noisy data.