Near-Optimal Parameters for Tikhonov and Other Regularization Methods
Near-Optimal Parameters for Tikhonov and Other Regularization Methods
Loading...
Files
Publication or External Link
Date
1999-04-06
Authors
O'Leary, Dianne P.
Advisor
Citation
DRUM DOI
Abstract
Choosing the regularization parameter for an ill-posed problem is an art
based on good heuristics and prior knowledge of the noise in the
observations. In this work we propose choosing the parameter, without a
priori information, by approximately minimizing the distance between the
true solution to the discrete problem and the family of regularized
solutions. We demonstrate the usefulness of this approach for Tikhonov
regularization and for an alternate family of solutions. Further, we prove
convergence of the regularization parameter to zero as the standard
deviation of the noise goes to zero. We also prove that the alternate
family produces solutions closer to the true solution than the Tikhonov
family when the noise is small enough.
Also cross-referenced as UMIACS-TR-99-17