Identification of discontinuous coefficients in elliptic problems using total variation regularization

Tony Chan*, Xue Cheng Tai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

85 Scopus citations

Abstract

We propose several formulations for recovering discontinuous coefficients in elliptic problems by using total variation (TV) regularization. The motivation for using TV is its well-established ability to recover sharp discontinuities. We employ an augmented Lagrangian variational formulation for solving the output-least-squares inverse problem. In addition to the basic output-least-squares formulation, we introduce two new techniques for handling large observation errors. First, we use a filtering step to remove as much of the observation error as possible. Second, we introduce two extensions of the output-least-squares model; one model employs observations of the gradient of the state variable while the other uses the flux. Numerical experiments indicate that the combination of these two techniques enables us to successfully recover discontinuous coefficients even under large observation errors.

Original languageEnglish (US)
Pages (from-to)881-904
Number of pages24
JournalSIAM Journal on Scientific Computing
Volume25
Issue number3
DOIs
StatePublished - Nov 1 2003

Keywords

  • Elliptic
  • Inverse problems
  • Noise removal
  • Parameter estimation
  • Regularization
  • Total variational norm

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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