An Inverse Problem: Recovery of a Distribution Using Wasserstein Barycenter

Eustasio DEL Barrio, Jean-Michel Loubes and Bruno Pelletier

Annals of Economics and Statistics, 2017, issue 128, 229-259

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.

Keywords: Wasserstein Distance; Inverse Problem; Registration. (search for similar items in EconPapers)
JEL-codes: C18 C44 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:adr:anecst:y:2017:i:128:p:229-259

DOI: 10.15609/annaeconstat2009.128.0229

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