题 目：Inertial Proximal Difference-of-Convex Algorithm with Convergent Bregman Plug-and-Play for Nonconvex Imaging
内容简介：Imaging tasks are typically tackled using a structured optimization framework. This paper delves into a class of algorithms for difference-of-convex (DC) structured optimization, focusing on minimizing a DC function along with a possibly nonconvex function. Existing DC algorithm (DCA) versions often fail to effectively handle nonconvex functions or exhibit slow convergence rates. We propose a novel inertial proximal DC algorithm in Bregman geometry, named iBPDCA, designed to address nonconvex terms and enhance convergence speed through inertial techniques. We provide a detailed theoretical analysis, establishing both subsequential and global convergence of iBPDCA via the Kurdyka- Lojasiewicz property. Additionally, we introduce a Plug-and-Play variant, PnP-iBPDCA, which employs a deep neural network-based prior for greater flexibility and robustness while ensuring theoretical convergence. We also establish that the Gaussian gradient step denoiser used in our method is equivalent to evaluating the Bregman proximal operator for an implicitly weakly convex functional. We extensively validate our method on Rician noise and phase retrieval. We demonstrate that iBPDCA surpasses existing state-of-the-art methods.
报告人：吴中明
报告人简介：南京信息工程大学副教授，香港中文大学博士后，新加坡国立大学访问学者。研究方向为最优化算法及图像应用。在SIAM Journal on Imaging Sciences, IEEE Transactions on Signal Processing, Mathematics of Computation, European Journal of Operational Research等期刊发表论文四十余篇。入选南京信息工程大学首届“青年科技之星”，江苏省“双创博士”，人社部“香江学者计划”。担任中国运筹学会宣传工作委员会委员，中国运筹学会数学规划分会青年理事，江苏省运筹学会理事、副秘书长。主持国家自然科学基金面上、青年项目，江苏省自然科学基金面上项目，教育部人文社科基金青年项目，中国博士后面上资助项目等。
时 间：2024年11月8日（周五）下午15：00开始
地 点：南海楼224室
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