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Optimal Transport-Based Total Variation for Functional Lifting and Q-Ball Imaging

Presented by: 
Thomas Vogt Universität zu Lübeck
Friday 8th September 2017 - 14:00 to 14:50
INI Seminar Room 1
Co-Author: Jan Lellmann (Institute of Mathematics and Image Computing, University of Lübeck)

One strategy in functional lifting is to consider probability measures on the label space of interest, which can be discrete or continuous. The considered functionals often make use of a total variation regularizer which, when lifted, allows for a dual formulation introducing a Lipschitz constraint. In our recent work, we proposed to use a similar formulation of total variation for the restoration of so-called Q-Ball images. In this talk, we present a mathematical framework for total variation regularization that is inspired from the theory of Optimal Transport and that covers all of the previous cases, including probability measures on discrete and continuous label spaces and on manifolds. This framework nicely explains the above-mentioned Lipschitz constraint and comes with a robust theoretical background.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons