沈立新教授受邀进行讲座
发布时间: 2018-12-18 19:06:34
题 目：Structured Sparsity Promoting Functions and Proximity Algorithms
报告人：沈立新教授 Syracuse University
时 间：2018-12-17 10:30--11:30
地 点：学院401
报告人简介:
沈立新现为美国雪城大学数学系终身教授，美国空军高级顾问。他于1987年本科毕业于北京大学，1990年在北京大学取得硕士学位，1996年在中山大学获数学博士学位。博士毕业后曾在新加坡国立大学、美国西密西根大学等工作，后于2006年加盟美国雪城大学数学系。其研究兴趣包括图像处理、最优化算法、计算调和分析等。已在国际知名期刊如：Appl. Comput.Harmon. Anal.，Inverse Problems, SIAM J. Imaging Sci.等发表近50篇论文。曾任IEEE Trans. Signal Process.，Advan. Compt. Math. 杂志副主编。
摘 要：
This talk is divided into two parts. In the first part, we introduce a simple scheme to construct structured semiconvex sparsity promoting functions from convex sparsity promoting functions and their Moreau envelopes. Properties of these functions are discussed by leveraging their structures. In particular, we provide sparsity guarantees for the general family of functions. We further study the behavior of the proximity operators of several special functions including indicator functions of closed convex sets, piece-wise quadratic functions, and the linear combinations of them. In the second part, we first give an overview of proximity operators and their essential properties. We then present our work on proximity algorithms for a class of optimization problems arising from image processing.
