Numerical analysis of constrained total variation flows

Abstract

In this paper, we consider total variation flow with values constrained to a Riemannian manifold (constrained total variation flow), which appears in several fields of mathematical sciences. In particular, we consider the constrained total variation flow on the space of piecewise constant functions and construct a numerical scheme based on the minimizing movement scheme. We present a mathematical result on the convergence of our numerical scheme and a result of the numerical experiment. This paper is based on the joint work with Yoshikazu Giga (The University of Tokyo), Kazutoshi Taguchi (ARISE analytics Inc.), and Masaaki Uesaka (Arithmer Inc./The University of Tokyo), and a full version of this paper has been published in [7].