The Total Variation-Wasserstein Problem
Antonin Chambolle (CEREMADE, MOKAPLAN), Vincent Duval (MOKAPLAN), Joao, Miguel Machado (CEREMADE, MOKAPLAN)
TL;DR
This paper investigates the Total Variation-Wasserstein minimization problem, offering a new derivation of optimality conditions, establishing regularity results, and proposing an algorithm with numerical experiments.
Contribution
It introduces an alternative derivation of optimality conditions and provides an algorithm for solving the Total Variation-Wasserstein problem.
Findings
Derived new optimality conditions with improved regularity
Proposed an effective algorithm for the problem
Validated the approach with numerical experiments
Abstract
In this work we analyze the Total Variation-Wasserstein minimization problem. We propose an alternative form of deriving optimality conditions from the approach of Calier\&Poon'18, and as result obtain further regularity for the quantities involved. In the sequel we propose an algorithm to solve this problem alongside two numerical experiments.
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Taxonomy
TopicsAdvanced Numerical Analysis Techniques · Geometric Analysis and Curvature Flows · Elasticity and Material Modeling