On the total variation Wasserstein gradient flow and the TV-JKO scheme

Abstract : We study the JKO scheme for the total variation, characterize the optimizers, prove some of their qualitative properties (in particular a sort of maximum principle and the regularity of level sets). We study in detail the case of step functions. Finally, in dimension one, we establish convergence as the time step goes to zero to a solution of a fourth-order nonlinear evolution equation.
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https://hal.archives-ouvertes.fr/hal-01492343
Contributor : Guillaume Carlier <>
Submitted on : Saturday, March 18, 2017 - 3:28:46 PM
Last modification on : Thursday, April 26, 2018 - 10:28:41 AM
Long-term archiving on : Monday, June 19, 2017 - 12:30:49 PM

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Guillaume Carlier, Clarice Poon. On the total variation Wasserstein gradient flow and the TV-JKO scheme. 2017. ⟨hal-01492343⟩

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