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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

主持人外围买球app平台 顾先明博士

时间202119日(周10:00-11:30

直播平台及会议ID腾讯会议,304 709 057

主办单位:外围买球app平台  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-rank tensor 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 factor tensors in real-world imaging data, we propose to incorporate a hybrid regularization combining total variation and Tikhonov regularization into low-tubal-rank tensor factorization model for low-rank tensor completion problem. We also develop an efficient proximal alternating minimization (PAM) algorithm to tackle the corresponding minimization problem and establish a global convergence of the PAM algorithm. Numerical results on color images, color videos, and multi-spectral images (MSIs) are reported to illustrate the superiority of the proposed method over competing methods.