A Penalty Relaxation Method for Image Processing Using Euler's Elastica Model
报告专家：王晓
报告时间：9月20日星期二晚上8：30-9：30
报告地点：腾讯会议：983-932-275
摘要：Euler's elastica model has been widely used in image processing. Since it is a challenging nonconvex and nonsmooth optimization model, most existing algorithms do not have convergence theory for it. In this talk, I will introduce a penalty relaxation algorithm with mathematical guarantee to find a stationary point of Euler's elastica model. To deal with the nonsmoothness of Euler's elastica model, we first introduce a smoothing relaxation problem, and then propose an exact penalty method to solve it. We establish the relationships between Euler's elastica model, the smoothing relaxation problem and the penalty problem in theory regarding optimal solutions and stationary points. Moreover, we propose an efficient block coordinate descent algorithm to solve the penalty problem by taking advantages of convexity of its subproblems. We prove global convergence of the algorithm to a stationary point of the penalty problem. Finally we apply the proposed algorithm to denoise the optical coherence tomography images with real data from an optometry clinic and show the efficiency of the method for image processing using Euler's elastica model.
专家简介：王晓，鹏城实验室副研究员、博士生导师。2007年本科毕业于山东大学数学基地班信息与计算科学专业。2012年博士毕业于中科院数学与系统科学研究院计算数学专业(师从袁亚湘院士)。2012.7至2021.11任职于中国科学院大学数学科学学院。研究方向为非线性优化理论与算法。论文发表在包括SIAM J. Optim., Math. Comput., SIAM J. Imaging Sci., SIAM Numer. Anal.等的国际知名期刊。入选中国科协第四届青年人才托举工程(2018)、中国科学院青年创新促进会第十批会员(2020)、广东省珠江人才计划(2022)、深圳鹏城孔雀特聘计划(2022)。现主持一项国家自然科学基金面上项目、一项鹏城实验室重大攻关项目子课题。目前担任中国运筹学会智能工业数据解析与优化专业委员会理事、中国运筹学会数学规划分会青年理事。
