VECTOR-VALUED OPTIMAL MASS TRANSPORT
VECTOR-VALUED OPTIMAL MASS TRANSPORT
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DOI：
10.1137/17m1130897
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发表时间：
2018-01-01
影响因子：
1.9
通讯作者：
Tannenbaum, Allen
中科院分区：
文献类型：
--
作者：
Chen, Yongxin;Georgiou, Tryphon T.;Tannenbaum, Allen
我们介绍了向量值分布的传输问题。在这一点上，一个显著的特征是质量可以在矢量条目之间流动，也可以跨越空间(离散或连续)流动。该理论依赖于在图上定义最优运输的适当概念所采取的第一步。分布之间的对应距离很容易通过凸优化计算，并提供了Wasserstein型度量的适当推广。在此基础上，我们定义了连续空间和图上支持的向量值分布上的Wasserstein型度量。发展矢量值质量传输的动力来自于诸如彩色图像处理、多模成像、偏振雷达以及资源可能是矢量的网络问题等应用。
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 color image processing, multimodality imaging, polarimetric radar, as well as network problems where resources may be vectorial.