报告题目：An accelerated preconditioned proximal gradient algorithm with a generalized Nesterov momentum for PET image reconstruction

报告人：韩德仁 教授/博导，北京航空航天大学

报告时间：2025年5月15日（周四）下午14:30-15:30

报告地点：数理楼306会议室

主办单位：999策略手机论坛版

报告对象：全校感兴趣的老师和学生

报告摘要：We present an accelerated preconditioned proximal gradient algorithm (APPGA) for effectively solving a class of positron emission tomography (PET) image reconstruction models with differentiable regularizers. We establish the convergence of APPGA with the generalized Nesterov (GN) momentum scheme, demonstrating its ability to converge to a minimizer of the objective function with sublinear rates in terms of the function value and the distance between consecutive iterates. To achieve an efficient algorithm with high-order convergence rate for the higher-order isotropic total variation (ITV) regularized PET image reconstruction model, we replace the ITV term by its smoothed version and subsequently apply APPGA to solve the smoothed model. Numerical results indicate that APPGA exhibits superior performance compared to the preconditioned proximal gradient algorithm and the preconditioned Krasnoselskii-Mann algorithm. The extension of the GN momentum technique for solving a more complex optimization model with multiple nondifferentiable terms is also discussed.

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。从事大规模优化问题、变分不等式问题及其在交通规划、磁共振成像中的应用研究，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。