Fast optimal transport regularized projection and application to coefficient shrinkage and filtering

Abstract

This paper explores solutions to the problem of regularized projections with respect to the optimal transport metric. Expanding recent works on optimal transport dictionary learning and non-negative matrix factorization, we derive general purpose algorithms for projecting on any set of vectors with any regularization, and we further propose fast algorithms for the special cases of projecting onto invertible or orthonormal bases. Noting that pass filters and coefficient shrinkage can be seen as regularized projections under the Euclidean metric, we show how to use our algorithms to perform optimal transport pass filters and coefficient shrinkage. We give experimental evidence that using the optimal transport distance instead of the Euclidean distance for filtering and coefficient shrinkage leads to reduced artifacts and improved denoising results.