On the choice of the Tikhonov regularization parameter and the discretization level: A discrepancy-based strategy

Vinicius Albani, Adriano De Cezaro, Jorge P. Zubelli

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20 Scopus citations

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.

Original languageBritish English
Pages (from-to)1-25
Number of pages25
JournalInverse Problems and Imaging
Volume10
Issue number1
DOIs
StatePublished - Feb 2016

Keywords

  • Discrepancy principles
  • Discrete setting
  • Regularization convergence rates
  • Tikhonov regularization

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