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Computations of Optimal Transport Distance with Fisher Information Regularization

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Abstract

We propose a fast algorithm to approximate the optimal transport distance. The main idea is to add a Fisher information regularization into the dynamical setting of the problem, originated by Benamou and Brenier. The regularized problem is shown to be smooth and strictly convex, thus many classical fast algorithms are available. In this paper, we adopt Newton’s method, which converges to the minimizer with a quadratic rate. Several numerical examples are provided.

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Acknowledgements

We would like to thank Professors Shui-Nee Chow, Wilfrid Gangbo and Haomin Zhou for many discussions on related topics.

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Authors and Affiliations

  1. University of California, Los Angeles, Los Angeles, CA, USA

    Wuchen Li, Penghang Yin & Stanley Osher

Authors
  1. Wuchen Li
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  2. Penghang Yin
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  3. Stanley Osher
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Corresponding author

Correspondence to Wuchen Li.

Additional information

This work is partially supported by ONR Grants N000141410683, N000141210838 and DOE Grant DE-SC00183838.

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Li, W., Yin, P. & Osher, S. Computations of Optimal Transport Distance with Fisher Information Regularization. J Sci Comput 75, 1581–1595 (2018). https://doi.org/10.1007/s10915-017-0599-0

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  • DOI: https://doi.org/10.1007/s10915-017-0599-0

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