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

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...

Full description

Saved in:
Bibliographic Details
Published inThe Visual computer Vol. 38; no. 2; pp. 477 - 491
Main Authors Rolet, Antoine, Seguy, Vivien
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2022
Springer Nature B.V
Subjects
Algorithms
Approximation
Artificial Intelligence
Coefficients
Computer Graphics
Computer Science
Dictionaries
Entropy
Euclidean geometry
Filtration
Image Processing and Computer Vision
Optimization
Original Article
Regularization
Sparsity
Wasserstein distance
Coefficient shrinkage
Sparse decomposition
Optimal transport
Wavelet thresholding
Denoising
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0178-2789
1432-2315
DOI:10.1007/s00371-020-02029-7