报告名称：Subdifferential of Quaternion Matrix Function and Nonconvex Low-Rank Quaternion Matrix Completion

主讲人：张立平 长聘副教授

邀请人：宋义生 教授

时间：2023年5月10日   16:30

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报告摘要

In recent years, quaternion matrix has demonstrated impressive results in color image impainting due to its ability to account for the interrelationships between RGB channels as a holistic entity rather than independent components. Most existing quaternion-based methods formulate a quaternion nuclear norm minimization problem. Nonetheless, the nuclear norm is insufficient to accurately approximate the rank function, thus limiting the efficacy of these models to approximate low rank attributes. To address this issue, we propose a novel nonconvex MCP relaxation model, and prove that this model is an exact penalty for the original low-rank model. To establish optimality conditions, we introduce the subdifferential of the composite function of MCP and the singular values of a quaternion matrix via an elegant Fenchel conjugacy formula. We also propose a globally convergent Quaternion Block Coordinate Descent (QBCD) algorithm to solve our model. The effectiveness and superiority of our proposed method are demonstrated by experiments conducted on authentic visual data sets.

专家简介

张立平，清华大学长聘副教授，博士生导师，研究方向最优化理论算法及应用，在求解互补与变分不等式问题、半无限规划、张量优化等方面取得了一些有意义的结果。已在Mathematics of Computation, SIAM Journal of Matrix Analysis and Applications, SIAM Journal on Optimization, Applied Numerical Mathematics，中国科学等期刊发表高质量论文五十余篇、连续获得多项国家自然科学基金资助。曾获得教育部自然科学奖二等奖和北京市科学技术奖二等奖。