MULTILEVEL OPTIMAL TRANSPORT: A FAST APPROXIMATION OF WASSERSTEIN-1 DISTANCES

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 x 512, the proposed algorithm gives solutions within 0.2 similar to 1.5 seconds on a single CPU, which is much faster than the state-of-the-art algorithms.

Automated summary

The paper proposes a fast algorithm for calculating the Wasserstein-1 distance, based on multilevel primal-dual algorithms, and demonstrates its computational speed through numerical examples and complexity analysis. The proposed algorithm provides solutions within 0.2 to 1.5 seconds on a single CPU for commonly used image examples of size 512 x 512, which is much faster than state-of-the-art algorithms.