报告题目：Robust quaternion matrix completion with applications to image inpainting

报告摘要：In this paper, we study robust quaternion matrix completion and provide a rigorous analysis for provable estimation of quaternion matrix from a random subset of their corrupted entries. In order to generalize the results from real matrix completion to quaternion matrix completion, we derive some new formulas to handle noncommutativity of quaternions. We solve a convex optimization problem, which minimizes a nuclear norm of quaternion matrix that is a convex surrogate for the quaternion matrix rank, and the 𝓁1 -norm of sparse quaternion matrix entries. We show that, under incoherence conditions, a quaternion matrix can be recovered exactly with overwhelming probability, provided that its rank is sufficiently small and that the corrupted entries are sparsely located. The quaternion framework can be used to represent red, green, and blue channels of color images. The results of missing/noisy color image pixels as a robust quaternion matrix completion problem are given to show that the performance of the proposed approach is better than that of the testing methods, including image inpainting methods, the tensor-based completion method, and the quaternion completion method using semidefinite programming.

报告时间：2019年6月14日10：00—11：00

报告地点：我院213会议室

专家简介：贾志刚，江苏师范大学教授、硕士生导师。2009年毕业于华东师范大学数学系，获理学博士学位。主要研究方向为数值代数与图像处理，至今已在SIAM J. Matrix Anal. Appl., SIAM J. Imaging Sci., J. Sci. Comput., Numer. Linear Algebra Appl.等国际知名期刊上发表学术论文30余篇，出版译著1部、教材1部，主持国家自然科学基金项目2项、省部级科研项目1项，参加国家和省自然科学项目4项。先后入选江苏师范大学“第一批高层次人才队伍后备人选”、“三育人先进个人”、“校先进工作者”等。曾经到英国曼彻斯特大学、香港浸会大学等高校数学系进行为期一年的访问。现兼职为中国高等教育学会教育数学专业委员会团体理事、江苏省工业与应用数学会理事、江苏省计算数学学会理事、美国SIAM正式会员，美国Math Review评论员，和SIMAX，Inverse Problem，Automatic等学术期刊的审稿人。