勷勤数学•领军学者报告

题      目：Generalized variational framework with minimax optimization for parametric blind deconvolution

报  告  人：韩德仁  教授  (邀请人：陈艳男)

                                 北京航空航天大学

时      间：12月15日  09：30-10：30

地     点：数科院西楼二楼会议室

报告人简介:

       韩德仁，教授，博士生导师，北京航空航天大学数学科学学院院长、教育部数学类专业教指委秘书长。从事大规模优化、变分不等式问题及其应用研究工作，发表多篇学术论文。曾获中国运筹学会青年科技奖，江苏省科学技术奖等奖项;主持国家自然科学基金重点项目、杰出青年基金项目等多项项目。担任中国运筹学会副理事长；《数值计算与计算机应用》、《Journal of the Operations Research Society of China》、《Journal of Global Optimization》、《Asia-Pacific Journal of Operational Research》编委。

摘      要：

       Blind deconvolution (BD), which aims to separate unknown colvolved signals, is a fundamental problem in signal processing. Due to the ill-posedness and underdetermination of the convolution system, it is a challenging nonlinear inverse problem. This talk presents the algorithmic studies of parametric BD, which is typically applied to recover images from ad hoc optical modalities. We propose a generalized variational framework for parametric BD with various priors and potential functions. By using the conjugate theory in convex analysis, the framework can be cast into a nonlinear saddle point problem. We employ the recent advances in minimax optimization to solve the parametric BD by the nonlinear primal-dual hybrid gradient method, with all subproblems admitting closed-form solutions. Numerical simulations on synthetic and real datasets demonstrate the compelling performance of the minimax optimization approach for solving parametric BD.

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