報告人：龐志峰 河南大學數(shù)學與信息科學學院, 副教授
地點：研究生樓104
題目及摘要如下：
（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.

個人簡介：龐志峰,，博士，2010年博士畢業(yè)與湖南大學數(shù)學與計量經(jīng)濟學院, 2010.06-2011.03為南洋理工大學數(shù)學物理學院博士后, 2011.12-2012.12為香港城市大學電腦科學系做博士后, 2014年2月-2014年8月在中科院數(shù)學與系統(tǒng)科學研究生院做訪問學者, 現(xiàn)為河南大學數(shù)學與信息科學學院, 副教授,，碩士生導(dǎo)師。主要研究圖像處理和機器學習中的數(shù)學理論與數(shù)值算法, 主持和參與國家自然科學基金各一項,參與河南省科技廳項目和國家973項目各一項,。 現(xiàn)任雜志《Journal of Computational Intelligence and Electronic Systems》,、《 International Journal of Numerical  Methodsand  Appli cations》和《圖像與信號處理》的編委，美國《數(shù)學評論》(MR)評論員,，已發(fā)表相關(guān)論文16篇(其中SCI收錄11篇,，EI收錄3篇),。