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An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter

Author

Listed:
  • Eustasio DEL BARRIO
  • Jean-Michel LOUBES
  • Bruno PELLETIER

Abstract

We propose to study the inverse problem of estimating a distribution observed through an image by a parametric operator. We construct first estimators for the individual parameters of the operators and study their behaviour, then we invert the approximated operator to obtain and estimator of the distribution. The estimation procedure is given by the minimization of a criterion that compares the alignment of the operator to the Wasserstein barycenter of these warped distributions.

Suggested Citation

  • Eustasio DEL BARRIO & Jean-Michel LOUBES & Bruno PELLETIER, 2017. "An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter," Annals of Economics and Statistics, GENES, issue 128, pages 229-259.
  • Handle: RePEc:adr:anecst:y:2017:i:128:p:229-259
    DOI: 10.15609/annaeconstat2009.128.0229
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    File URL: http://www.jstor.org/stable/10.15609/annaeconstat2009.128.0229
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    Keywords

    Wasserstein Distance; Inverse Problem; Registration.;

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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