金年会jinnianhuicom学术报告
Model Consistency of Iterative Regularization
梁经纬
（上海交通大学）
报告时间：2026年1月19日 星期一 下午15：30-16：30
报告地点：沙河校区E806
报告摘要：Regularization is vital in inverse problems to ensure well-defined solutions and control over noise. In particular, we study “model consistency”, which indicates that the reconstructed solution remains robust to small perturbations when the ground truth has low-complexity structure. This property is readily known to hold in variational regularization for linear inverse problems, where a balanced combination of a data-fidelity term and a suitable regularization term preserve key structural features. However, model consistency has remained an open question for iterative regularization methods, which rely on a proper stopping criterion to avoid overfitting. In this talk, we build on the concept of partial smoothness to prove that iterative schemes can achieve the same model consistency, provided the noise is sufficiently mild and the stopping time is chosen appropriately. We further establish a local linear convergence rate under these conditions. Numerical experiments will be presented to illustrate our theoretical findings.
报告人简介：梁经纬，副教授，上海交通大学自然科学研究院。梁经纬于2013年获得上海交通大学数学硕士学位，之后于2016年获得法国卡昂大学数学博士学位。2017至2020年，梁经纬在英国剑桥大学理论物理与应用数学系从事博士后研究工作，并于2020年底加入伦敦玛丽王后大学金年会jinnianhuicom任数据科学讲师。2021年7月，加入上海交通大学。梁经纬的主要研究兴趣为数学图像处理，非光滑优化和数据科学等。
邀请人：谢家新
