Mixed geometry information regularization for image deblurring with multiplicative noise
数学专题报告
报告题目(Title)：Mixed geometry information regularization for image deblurring with multiplicative noise
报告人(Speaker)：郭志昌 教授 （哈尔滨工业大学）
地点(Place)：后主楼1223
时间(Time)：2025年10月11日（周六）11：00-12：00
邀请人(Inviter)：刘君
报告摘要
We propose a variational model for the simultaneous removal of multiplicative noise and blur. Variational regularization techniques have been widely employed in various image processing tasks. However, designing models that incorporate sufficient geometric priors remains a challenging problem. To address this issue, we introduce a mixed geometry regularization that integrates both area and curvature terms as priors. Due to the high-order and nonlinear nature of the model, minimizing the associated functional is nontrivial. To overcome this challenge, we adopt the additive operator splitting method and a relaxed scalar auxiliary variable (RSAV) approach, with the latter showing higher computational accuracy for our model. The unconditional stability of these algorithms allows the use of a large time step. Furthermore, we discuss several theoretical properties of the RSAV method. Numerical experiments demonstrate the effectiveness of the proposed model and the efficiency of the corresponding algorithm.
主讲人简介
2010年博士毕业于吉林大学，现任哈尔滨工业大学数学学院教授、博士生导师、计算数学系副主任，中国工业与应用数学学会数学与医学交叉学科专业委员会委员、中国生物医学工程学会人工智能分会青年委员。主要从事偏微分方程及图像处理、人工智能（计算机视觉，大数据分析，股票趋势量化）研究工作。主持国家自然科学基金面上项目、黑龙江省自然科学基金、广东省基础与应用基础研究基金、国家自然科学基金青年基金、教育部新教师基金，哈尔滨工业大学校创新基金等项目；作为主要参与人参与国自然联合基金重点项目、黑龙江省基金重点项目、相关研究成果发表在SIAM、IEEE TIP、NIPS、JSC等高水平刊物上，累计发表论文60余篇，出版专著/教材3部，授权发明专利5项。
