Projected Gradient Method Combined with Homotopy Techniques for Volume-Measure-Preserving Optimal Mass Transportation Problems

Mei Heng Yueh, Tsung Ming Huang, Tiexiang Li*, Wen Wei Lin, Shing Tung Yau

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

摘要

Optimal mass transportation has been widely applied in various fields, such as data compression, generative adversarial networks, and image processing. In this paper, we adopt the projected gradient method, combined with the homotopy technique, to find a minimal volume-measure-preserving solution for a 3-manifold optimal mass transportation problem. The proposed projected gradient method is shown to be sublinearly convergent at a rate of O(1/k). Several numerical experiments indicate that our algorithms can significantly reduce transportation costs. Some applications of the optimal mass transportation maps—to deformations and canonical normalizations between brains and solid balls—are demonstrated to show the robustness of our proposed algorithms.

原文英語
文章編號64
期刊Journal of Scientific Computing
88
發行號3
DOIs
出版狀態已發佈 - 2021 九月

ASJC Scopus subject areas

  • 軟體
  • 理論電腦科學
  • 數值分析
  • 工程 (全部)
  • 計算機理論與數學
  • 計算數學
  • 應用數學

指紋

深入研究「Projected Gradient Method Combined with Homotopy Techniques for Volume-Measure-Preserving Optimal Mass Transportation Problems」主題。共同形成了獨特的指紋。

引用此