报告人：李晨（南京理工大学）
报告时间：2025年9月24日（星期三）14:30-16:00
报告地点：腾讯会议：123 340 517
报告摘要：Optimal transport (OT) theory and models have been widely applied in the fields of computer vision, machine learning and image analysis. Among three typical formulations of OT models, i.e., the Monge, Kantorovich, and dynamical ones. The Kantorovich formulation with entropic regularization is most commonly used in practical settings due to its computational convenience. The other two formulations are rarely regularized since adding regularization terms brings additional difficulties to their theoretical analysis and numerical algorithms. In this paper, we propose a regularized OT model based on the dynamic formulation. In precise, we incorporate a $W^{1,2}$ regularization term on the momentum field to promote smoothness, and a total variation (TV) regularization term on the density field to enhance robustness to noise. We establish the existence and uniqueness of solutions to the regularized dynamic OT model and provide a theoretical analysis based on $\Gamma$-convergence. Moreover, we develop a primal-dual algorithm to efficiently solve the resulting optimization problem. Numerical experiments on spatial-temporal image generation tasks demonstrate the effectiveness of the proposed model and the stability and efficiency of the proposed numerical algorithm. The proposed regularized dynamical OT model provides a flexible and theoretically grounded framework for image generation tasks in imaging science.
报告人简介：李晨博士毕业于南京大学数学系，现为南京理工大学博士后。其主要研究方向包括变分法、深度学习以及基于最优传输的医学图像处理算法与应用。目前主持江苏省自然科学基金青年项目，并获得博士后面上资助和国家博士后基金资助，同时参与多项国家自然科学基金项目。在 International Journal of Computer Vision、Medical Image Analysis、Medical Physics 等国际知名期刊上发表多篇研究论文。
邀请人：明炬
