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2024-04-04 08:36:39

This https://arxiv.org/abs/2403.02764 has been replaced.
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Unbalanced L1 optimal transport for vector valued measures and application to Full Waveform Inversion
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 positive (probability) measures and therefore strategies are needed for its applications in more general settings of interest. In this paper we introduce an unbalanced optimal transport problem for vector valued measures starting from the $L^1$ optimal transport. By lifting data in a self-dual cone of a higher dimensional v…