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arXiv · 1611.09946

Vector-Valued Optimal Mass Transport

Yongxin Chen·Tryphon T. Georgiou·Allen Tannenbaum
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Abstract

We introduce the problem of transporting vector-valued distributions. In this, a salient feature is that mass may flow between vectorial entries as well as across space (discrete or continuous). The theory relies on a first step taken to define an appropriate notion of optimal transport on a graph. The corresponding distance between distributions is readily computable via convex optimization and provides a suitable generalization of Wasserstein-type metrics. Building on this, we define Wasserstein-type metrics on vector-valued distributions supported on continuous spaces as well as graphs. Motivation for developing vector-valued mass transport is provided by applications such as multi-color image processing, polarimetric radar, as well as network problems where resources may be vectorial.

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BibTeXRIS

Yongxin Chen, Tryphon T. Georgiou, Allen Tannenbaum. 2016-11-30. Vector-Valued Optimal Mass Transport. https://arxiv.org/abs/1611.09946

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