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Context: in astronomy, observing large fractions of the sky within areasonable amount of time implies using large field-of-view (fov) opticalinstruments that typically have a spatially varying Point Spread Function(PSF). Depending on the scientific goals, galaxies images need to be correctedfor the PSF whereas no direct measurement of the PSF is available. Aims: givena set of PSFs observed at random locations, we want to estimate the PSFs atgalaxies locations for shapes measurements correction. Contributions: wepropose an interpolation framework based on Sliced Optimal Transport. Anon-linear dimension reduction is first performed based on local pairwiseapproximated Wasserstein distances. A low dimensional representation of theunknown PSFs is then estimated, which in turn is used to derive representationsof those PSFs in the Wasserstein metric. Finally, the interpolated PSFs arecalculated as approximated Wasserstein barycenters. Results: the proposedmethod was tested on simulated monochromatic PSFs of the Euclid space missiontelescope (to be launched in 2020). It achieves a remarkable accuracy in termsof pixels values and shape compared to standard methods such as InverseDistance Weighting or Radial Basis Function based interpolation methods.

PSF field learning based on Optimal Transport Distances