主题：Low Rank Tensor Factorization with hybrid regularization for tensor completion in imaging data

主讲人：北京科学计算中心/深圳京鲁计算科学应用研究院林学磊博士后

主持人：经济555000jc赌船顾先明博士

时间：2021年1月9日（周六）10:00-11:30

直播平台及会议ID：腾讯会议，304 709 057

主办单位：经济555000jc赌船 科研处

主讲人简介：

林学磊，2014年在宁夏大学获得理学学士学位，2017年在澳门大学获得理学硕士学位，2020年获香港浸会大学攻读理学博士学位。主要从事数值线性代数方面的研究，包括偏微分方程数值解，结构线性系统的快速迭代法，张量计算在图像处理方面的应用，已在J. Comput. Phys., SIAM J. Matrix Anal. Appl., J. Sci. Comput., BIT. Numerical Mathematics, SIAM J. Numer. Anal., Comput. Math. Appl., J. Math. Imaging Vision等刊物以第一作者身份发表论文10余篇，曾在北京清华大学召开的“第八届世界华人数学家大会“上，获2019年”新世界数学奖“的优秀硕士论文银奖，是澳门首次获得该奖项，获”第十四届东亚工业与应用数学学会年会“优秀学生论文奖二等奖，获香港政府博士奖学金，获澳门研究生科技研发奖。

内容提要：

In this talk, a tensor factorization method with hybrid regularization is introduced for low-rank tensor completion in imaging data. Due to the underlying redundancy of real-world imaging data, the low-tubal-ranktensor factorization (the tensor-tensor product of two factor tensors) can be used to approximate such tensor tensors very well. Motivated by the spatial/temporal smoothness of factortensors in real-world imaging data, we propose to incorporate a hybrid regularization combining total variation and Tikhonov regularization into low-tubal-rank tensor factorization modelfor low-rank tensor completion problem. We also develop an efficient proximal alternating minimization (PAM) algorithm to tackle the corresponding minimization problem and establish aglobal convergence of the PAM algorithm. Numerical results on color images, color videos, andmulti-spectral images (MSIs) are reported to illustrate the superiority of the proposed methodover competing methods.