报告题目：Tensor Completion via A Generalized Transformed Tensor T-ProductDecomposition without t-SVD

报告人：凌晨 教授/博导，杭州电子科技大学

报告时间：2026年6月9日（周二）10:30

报告地点：数理楼306学术报告厅

主办单位：123AV

报告对象：全校感兴趣的老师、研究生

报告摘要：Matrix and tensor nuclear norms have been successfully used to promote thelow-rankness of tensors in low-rank tensor completion. However, singular valuedecomposition (SVD), which is computationally expensive for large-scale matrices,frequently appears in solving these nuclear norm minimization models. Based on thetensor-tensor product (T-product), in this talk, we first establish the equivalence betweenthe so-called transformed tubal nuclear norm for a third order tensor and the minimum ofthe sum of two factor tensors’ squared Frobenius norms under a general invertible lineartransform. Gainfully, we introduce a spatio-temporal regularized tensor completionmodel that is able to maximally preserve the hidden structures of tensors. Then, wepropose an implementable alternating minimization algorithm to solve the underlyingoptimization model. It is remarkable that our approach does not require any SVDs andall subproblems of our algorithm have closed-form solutions. A series of numericalexperiments on traffic data recovery, color images and videos inpainting demonstratethat our SVD-free approach takes less computing time to achieve satisfactory accuracythan some state-of-the-art tensor nuclear norm minimization approaches.

报告人简介：凌晨, 杭州电子科技大学理学院教授（二级），博士生导师。曾任：杭州电子科技大学理学院院长，中国运筹学会数学规划分会副理事长、中国经济数学与管理数学研究会副理事长、中国运筹学会理事、中国系统工程学会理事、浙江省数学会常务理事等。现任国际期刊Pacific Journal of Optimization 编委、Statistics,Optimization & Information Computing 编委。近十余年来，主持国家自科基金和浙江省自科基金多项(其中省基金重点项目1 项)。在Math. Program.、SIAM J.on Optim.和SIAM J.on Matrix Anal.and Appl.、COAP、JOTA、JOGO 等国内外重要刊物发表论文多篇。