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We propose a new algorithm to approximate the Earth Mover's distance (EMD).Our main idea is motivated by the theory of optimal transport, in which EMD canbe reformulated as a familiar $L_1$ type minimization. We use a regularizationwhich gives us a unique solution for this $L_1$ type problem. The newregularized minimization is very similar to problems which have been solved inthe fields of compressed sensing and image processing, where several fastmethods are available. In this paper, we adopt a primal-dual algorithm designedthere, which uses very simple updates at each iteration and is shown toconverge very rapidly. Several numerical examples are provided.

A fast algorithm for Earth Mover's Distance based on optimal transport and L1 type Regularization