学术报告

报告题目：Low Rank Tensor Completion with PoissonObservations

报告人：张雄军（华中师范大学）

报告时间：2021年12月30日（星期四）10:00-12:00

腾讯会议：638-930-569

参加人员：教师、研究生、本科生

报告摘要：Poisson observations for videos are important models in video processing and computer vision. In this paper, we study thethird-order tensor completion problem with Poisson observations. The main aim is to recover a tensor based on a small number of itsPoisson observation entries. A existing matrix-based method may be applied to this problem via the matricized version of the tensor.

However, this method does not leverage on the global low-rankness of a tensor and may be substantially suboptimal. Our approach is to consider the maximum likelihood estimate of the Poisson distribution, and utilize the Kullback-Leibler divergence for the data-fitting term to measure the observations and the underlying tensor. Moreover, we propose to employ a transformed tensor nuclear norm ball constraint and a bounded constraint of each entry, where the transformed tensor nuclear norm is used to get a lower transformed multi-rank tensor with suitable unitary transformation matrices. We show that the upper bound of the error of the estimator of the proposed model is less than that of the existing matrix-based method. Also an information theoretic lower error bound is established. An alternating direction method of multipliers is developed to solve the resulting convex optimization model. Extensive numerical experiments on synthetic data and real-world datasets are presented to demonstrate the effectiveness of our proposed model compared with existing tensor completion methods.

报告人简介：张雄军, 华中师范大学数学与统计学学院副教授，博士生导师。2017年博士毕业于湖南大学, 2015年11月-2016年11月香港浸会大学博士交换生, 2020年-2021年香港大学博士后。目前主持国家自然科学基金青年基金和面上项目一项，完成主持湖北省自然科学基金青年一项。2019年获湖南省优秀博士学位论文。主要研究方向包括图像处理、张量优化、机器学习, 目前已在包括SIAM J.Image Sciences, SIAM J. Scientific Computing, TPAMI, ITNNLS, Inverse Problems等期刊发表论文20篇。