Near-Optimal Parameter for Tikhonov and Other Regularization Methods

Published

December 1, 2001

Author(s)

Dianne M. O'Leary

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 Tokhonov family when the noise is small enough.

Citation

- 6317

Report Number

6317

Volume

23

Issue

4

Pub Type

NIST Pubs

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Keywords

ill-posed problems, regularization, Tokhonov

Citation

O'Leary, D. (2001), Near-Optimal Parameter for Tikhonov and Other Regularization Methods, - 6317, National Institute of Standards and Technology, Gaithersburg, MD, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150761 (Accessed October 15, 2025)