4 papers
Debiasing optimal transport: classical and entropic
Pierre-Cyril Aubin-Frankowski, Virginie Ehrlacher, Gabriele Todeschi
We study the notion of debiasability for cost functions arising in optimal transport. We call a symmetric cost function …
Nonnegative cross-curvature in infinite dimensions: synthetic definition and spaces of measures
Flavien Léger, Gabriele Todeschi, François-Xavier Vialard
Nonnegative cross-curvature (NNCC) is a geometric property of a cost function defined on a product space that originates in optimal transportation and the Ma-Trudinger-Wang theory.…
Metric extrapolation in the Wasserstein space
Thomas O. Gallouët, Andrea Natale, Gabriele Todeschi
In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. Thi…
Unbalanced L1 optimal transport for vector valued measures and application to Full Waveform Inversion
Gabriele Todeschi, Ludovic Métivier, Jean-Marie Mirebeau
Optimal transport has recently started to be successfully employed to define misfit or loss functions in inverse problems. However, it is a problem intrinsically defined for positi…