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A mixed finite element discretization of dynamical optimal transport

Natale, Andrea; Todeschi, Gabriele (2020), A mixed finite element discretization of dynamical optimal transport. https://basepub.dauphine.fr/handle/123456789/20681

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02501634
Date
2020
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
25
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Author(s)
Natale, Andrea
Laboratoire de Mathématiques d'Orsay [LMO]
Todeschi, Gabriele
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
In this paper we introduce a new class of finite element discretizations of the quadratic optimal transport problem based on its dynamical formulation. These generalize to the finite element setting the finite difference scheme proposed by Papadakis et al. [SIAM J Imaging Sci, 7(1):212–238,2014]. We solve the discrete problem using a proximal-splitting approach and we show how to modify this in the presence of regularization terms which are relevant for imaging applications.
Subjects / Keywords
dynamical optimal transport