Extrapolated Plug-and-Play Splitting Methods for Nonconvex Optimization with Applications to Image Restoration




报告摘要:We focus on the convergence properties and applications of the three-operator splitting (DYS) method, also known as Davis-Yin splitting (DYS) method, integrated with extrapolation and Plug-and-Play (PnP) denoiser within a nonconvex framework. We first propose an extrapolated DYS method to effectively solve a class of structural nonconvex optimization problems that involve minimizing the sum of three possibly nonconvex functions. Our approach provides an algorithmic framework that encompasses both extrapolated forward-backward splitting and extrapolated Douglas-Rachford splitting methods. To establish the convergence of the proposed method, we rigorouslyanalyze its behavior based on the Kurdyka-Lojasiewicz property, subject to some tight parameterconditions. Moreover, we introduce two extrapolated PnP-DYS methods with convergence guarantee, where the traditional regularization step is replaced by a gradient step-based denoiser. This denoiser is designed using a differentiable neural network and can be reformulated as the proximal operator of a specific nonconvex functional. We conduct extensive experiments on image deblurringand image super-resolution problems, where our numerical results showcase the advantage of the extrapolation strategy and the superior performance of the learning-based model that incorporatesthe PnP denoiser in terms of achieving high-quality recovery images.

专家简介:吴中明,南京信息工程大学副教授,硕士生导师,香港中文大学博士后。博士毕业于东南大学,博士期间前往新加坡国立大学联合培养一年。入选南京信息工程大学“青年科技之星”,江苏省“双创博士”,人社部“香江学者”。主持国家自然科学青年基金、中国博士后面上资助项目。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。在COAP、JOTA、JOGO、IEEE TSP、IEEE TIM、Math. Comput.、ANOR等期刊发表学术论文三十余篇。