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：

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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。