A duality based approach to the minimizing total variation flow in the space $H^{-s}$

Yoshikazu Giga; Monika Muszkieta; Piotr Rybka

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arXiv · 1706.03223

A duality based approach to the minimizing total variation flow in the space $H^{-s}$

Yoshikazu Giga·Monika Muszkieta·Piotr Rybka

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Abstract

We consider a gradient flow of the total variation in a negative Sobolev space $H^{-s}$ $(0\leq s \leq 1)$ under the periodic boundary condition. If $s=0$, the flow is nothing but the classical total variation flow. If $s=1$, this is the fourth order total variation flow. We consider a convex variational problem which gives an implicit-time discrete scheme for the flow. By a duality based method, we give a simple numerical scheme to calculate this minimizing problem numerically and discuss convergence of a forward-backward splitting scheme. Several numerical experiments are given.

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Yoshikazu Giga, Monika Muszkieta, Piotr Rybka. 2017-06-10. A duality based approach to the minimizing total variation flow in the space $H^{-s}$. https://arxiv.org/abs/1706.03223

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