On the Choice of the Tikhonov Regularization Parameter and the Discretization Level: A Discrepancy-Based Strategy

28 Pages Posted: 10 Jul 2017

See all articles by Vinicius Albani

Vinicius Albani

Federal University of Santa Catarina

Adriano De Cezaro

Federal University Foundation of Rio Grande (FURG)

Jorge P. Zubelli

Instituto de Matematica Pura e Aplicada (IMPA)

Date Written: October 20, 2014

Abstract

We address the classical issue of appropriate choice of the regularization and discretization level for the Tikhonov regularization of an inverse problem with imperfectly measured data. We focus on the fact that the proper choice of the discretization level in the domain together with the regularization parameter is a key feature in adequate regularization. We propose a discrepancy-based choice for these quantities by applying a relaxed version of Morozov's discrepancy principle. Indeed, we prove the existence of the discretization level and the regularization parameter satisfying such discrepancy. We also prove associated regularizing properties concerning the Tikhonov minimizers. We conclude by presenting some numerical examples of interest.

Keywords: Tikhonov Regularization, Discrete Setting, Regularization Convergence Rates, Discrepancy Principles.

JEL Classification: C00, C61

Suggested Citation

Albani, Vinicius and De Cezaro, Adriano and Zubelli, Jorge P., On the Choice of the Tikhonov Regularization Parameter and the Discretization Level: A Discrepancy-Based Strategy (October 20, 2014). Available at SSRN: https://ssrn.com/abstract=2512441 or http://dx.doi.org/10.2139/ssrn.2512441

Vinicius Albani (Contact Author)

Federal University of Santa Catarina ( email )

Campus Trindade
Florianopolis, Santa Catarina 88040-900
Brazil
+554837216560 (Phone)
+554837214612 (Fax)

HOME PAGE: http://mtm.ufsc.br/~v.albani/

Adriano De Cezaro

Federal University Foundation of Rio Grande (FURG) ( email )

Rio Grande, Rio Grande do Sul
Brazil

Jorge P. Zubelli

Instituto de Matematica Pura e Aplicada (IMPA) ( email )

Estrada Dona Castorina 110
Jardim Botanico
Rio de Janeiro, 22460
Brazil

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