“数通古今，学贯中外”学术讲座第六十八期【庞志峰教授】

报告人：庞志峰 河南大学数学与信息科学学院, 副教授
地点：研究生楼104
题目及摘要如下：
（一）5月26日：14:30-15:30
Proximal point method for a hybrid model in image restoration and image segmentation

Abstract: In this report we propose a hybrid total-variation-type model for the image restoration  problem based on combining advantages of  the ROF model with the LLT model.  Since two $L^1$-norm terms in the proposed model make it be difficultly solved by  using some classically numerical methods directly, we first employ the alternating direction method of multipliers (ADMM) to solve a general form  of proposed model. Then, based on the ADMM and the Moreau-Yosida decomposition theory, a more efficient method called the proximal point method (PPM) is proposed and the convergence of the proposed method  is proved. Some numerical results demonstrate the viability and efficiency of the proposed model and methods.

（二）5月26日：15:30-16:30
Unsupervised Data Clustering Based on Mumford-Shah-Potts Model

Abstract: The performance of data clustering highly relies on proposed models and  numerical algorithms. Following from the extension of the Mumford-Shah-Potts model in the spatially continuous setting, we  propose some efficient data clustering algorithms to solve it based on the alternating direction method of multipliers and the primal-dual method.  The convergence of the proposed data clustering algorithms is established  under the framework of variational inequalities. Some balanced and unbalanced clustering problems are tested, which demonstrate the efficiency of the proposed algorithms.

个人简介：庞志峰，博士，2010年博士毕业与湖南大学数学与计量经济学院, 2010.06-2011.03为南洋理工大学数学物理学院博士后, 2011.12-2012.12为香港城市大学电脑科学系做博士后, 2014年2月-2014年8月在中科院数学与系统科学研究生院做访问学者, 现为河南大学数学与信息科学学院, 副教授，硕士生导师。主要研究图像处理和机器学习中的数学理论与数值算法, 主持和参与国家自然科学基金各一项,参与河南省科技厅项目和国家973项目各一项。 现任杂志《Journal of Computational Intelligence and Electronic Systems》、《 International Journal of Numerical  Methodsand  Appli cations》和《图像与信号处理》的编委，美国《数学评论》(MR)评论员，已发表相关论文16篇(其中SCI收录11篇，EI收录3篇)。