Error Bounds for Discretized Optimal Transport and Its Reliable Efficient Numerical Solution

We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with homogeneous of degree one transport cost. 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 × 512, the proposed algorithm gives solutions within 0.2 ∼ 1.5 seconds on a single CPU, which is much faster than the state-of-the-art algorithms.

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Error Bounds for Discretized Optimal Transport and Its Reliable Efficient Numerical Solution

Cited by 2 publications

References 12 publications

Multi-Scale Algorithms for Optimal Transport

Multi-Scale Algorithms for Optimal Transport

Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances

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