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Multilevel Optimal Transport: A Fast Approximation of Wasserstein-1 Distances
SIAM Journal on Scientific Computing ( IF 3.0 ) Pub Date : 2021-01-12 , DOI: 10.1137/18m1219813
Jialin Liu , Wotao Yin , Wuchen Li , Yat Tin Chow

SIAM Journal on Scientific Computing, Volume 43, Issue 1, Page A193-A220, January 2021.
We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with transport cost homogeneous of degree one. Our algorithm is built on multilevel primal-dual algorithms. Several numerical examples and a complexity analysis are provided to demonstrate its computational speed. On some commonly used image examples of size $512\times512$, the proposed algorithm gives solutions within $0.2\sim 1.5$ seconds on a single CPU, which is much faster than the state-of-the-art algorithms.


中文翻译:

多级最优传输:Wasserstein-1距离的快速逼近

SIAM科学计算杂志,第43卷,第1期,第A193-A220页,2021年1月。
我们提出了一种用于计算Wasserstein-1距离的快速算法,Wasserstein-1距离是一种最优运输距离的特殊类型,运输成本的度数为度一。我们的算法建立在多级原始对偶算法上。提供了几个数值示例和复杂度分析以证明其计算速度。在一些大小为$ 512 \ times512 $的常用图像示例中,所提出的算法在单个CPU上在$ 0.2 \ sim 1.5 $秒内提供解决方案,这比最新算法要快得多。
更新日期:2021-01-13
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