Reconstructing discrete measures from projections. Consequences on the empirical Sliced Wasserstein Distance

Eloi Tanguy, Rémi Flamary, Julie Delon

This paper deals with the reconstruction of a discrete measure ${\hat{I}}_Z^3$ on ${\mathbb{R}}^d$ from the knowledge of its pushforward measures $P_i\#{\hat{I}}_Z^3$ by linear applications $P_i: \mat…