学术报告

题      目：Low Rank Learning Robust Quaternion Tensor Completion for Color Video Inpainting and Fast Algorithms

报  告  人：贾志刚   教授  (邀请人：彭小飞 )

                                    江苏师范大学

时      间：6月26日  10：00-11：00

地     点：数科院西楼111报告厅

报告人简介:

       贾志刚 ，江苏师范大学数学与统计学院，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；2021年入选“闽江学者”讲座教授；2022年在第九届世界华人数学家大会上作45分钟邀请报告。主要研究方向为数值代数与图像处理，至今已在IEEE Trans. Image Process.，SIAM J. Matrix Anal. Appl., SIAM J. Sci. Comput., SIAM J. Imaging Sci. 等期刊上发表学术论文40余篇，在科学出版社出版专著和译著各1部，主持国家自然科学基金项目3项、省高校自然科学研究重大项目1项，参加国家自然科学基金重大项目1项。曾先后到英国曼彻斯特大学、香港浸会大学、澳门大学等高校数学系进行学术访问。

摘      要：

       The robust quaternion tensor completion (RQTC) problem aims to recover the complete quaternion tensor from the observed quaternion tensor with missing or noisy entries. The unknown tensor is generally assumed to have a low rank structure. In this paper, we proposed two models to solve RQTC problem from global and local view. Firstly, we study the problem under a convex optimization framework, take advantages of robust principal component analysis and quaternion tensor completion. We propose solving algorithms with global convergence guarantees and give a sufficient condition for precise recovery of RQTC problem. Secondly, we formulate the minimization problem from local information by applying the two dimensional quaternion principal analysis (2DQPCA) technique. We apply 2DQPCA method to learn the better low rank structure adaptively and prove that it is numerical low rank from theoretical. Then alternating direction method of multipliers is used to divide the problem into several sub-problems with fast solutions. Numerical experimental results demonstrate that the proposed method outperform the state-of-the-art algorithms in color video or image inpainting.