Analysis and regularization of problems in diffuse optical tomography

Herbert Egger*, Matthias Schlottbom

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

13 Citations (Scopus)
9 Downloads (Pure)

Abstract

In this paper we consider the regularization of the inverse problem of diffuse optical tomography by standard regularization methods with quadratic penalty terms. We therefore investigate in detail the properties of the associated forward operators and derive continuity and differentiability results, which are based on derivation of W1,pregularity of solutions for the governing elliptic boundary value problems. We then show that Tikhonov regularization can be applied for a stable solution and that the standard convergence and convergence rates results hold. Our analysis also allows us to ensure convergence of iterative regularization methods, which are important from a practical point of view.

Original languageEnglish
Pages (from-to)1934-1948
Number of pages15
JournalSIAM journal on mathematical analysis
Volume42
Issue number5
DOIs
Publication statusPublished - 26 Oct 2010
Externally publishedYes

Keywords

  • Diffuse optical tomography
  • Elliptic partial differential equations
  • Inverse problems
  • Parameter identification
  • Regularity
  • Regularization

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