A multiscale framework for probability measures in Wasserstein spaces is developed, including a refinement operator preserving geodesic structure and an optimality number for detecting non-geodesic dynamics across scales.
Application of opti- mal transport and the quadratic Wasserstein metric to full-waveform inversion.Geophysics, 83(1):R43–R62, 2018
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Multiscaling in Wasserstein Spaces
A multiscale framework for probability measures in Wasserstein spaces is developed, including a refinement operator preserving geodesic structure and an optimality number for detecting non-geodesic dynamics across scales.