报告题目: A Penalty Relaxation Method for Image Processing Using Euler's Elastica Model 

报告人：王晓  鹏城实验室

报告时间：9月27日 周三 10:00

报告地点：管理楼1418

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 paper, we propose 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 advantage 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.

个人简介：王晓，鹏城实验室智能计算研究部副研究员、博士生导师。本科毕业于山东大学数学基地班，博士毕业于中国科学院数学与系统科学研究院计算数学专业。2012年至2021年任职于中国科学院大学365英国上市官网。2021年底加入鹏城实验室。研究方向为非线性优化理论与算法。研究成果发表在SIAM J. Optim., Math. Comput., SIAM J. Imaging Sci., SIAM J. Numer. Anal., J. Sci. Comput.等国际知名期刊。先后入选中国科协第四届青年人才托举工程、中国科学院青年创新促进会会员、广东省珠江人才计划青年拔尖人才、获聘深圳市鹏城孔雀特聘岗位。荣获第八届中国运筹学会青年科技奖、中国科学院大学领雁银奖。先后主持三项国家自然科学基金项目三项、鹏城实验室重大攻关项目子课题一项。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。