题  目：Tensor completion via a generalized transformed tensor T-product decomposition without t-SVD

报告人：凌 晨

单  位：杭州电子科技大学 理学院

时  间：2023年10月11日 15：00

地  点：河南大学龙子湖校区九章学堂C座301

摘要：Matrix and tensor nuclear norms have been successfully used to promote the low-rankness of tensors in low-rank tensor completion. However, singular value decomposition (SVD), which is computationally expensive for large-scale matrices, frequently appears in solving these nuclear norm minimization models. Based on the tensor-tensor product (T-product), in this talk, we first establish the equivalence between the so-called transformed tubal nuclear norm for a third order tensor and the minimum of the sum of two factor tensors’ squared Frobenius norms under a general invertible linear transform. Gainfully, we introduce a spatio-temporal regularized tensor completion model that is able to maximally preserve the hidden structures of tensors. Then, we propose an implementable alternating minimization algorithm to solve the underlying optimization model. It is remarkable that our approach does not require any SVDs and all subproblems of our algorithm have closed-form solutions. A series of numerical experiments on traffic data recovery, color images and videos inpainting demonstrate that our SVD-free approach takes less computing time to achieve satisfactory accuracy than some state-of-the-art tensor nuclear norm minimization approaches.This is a joint work with H. J. He and W. H. Xie.

报告人简介：凌晨 : 杭州电子科技大学理学院教授，博士生导师。现任中国经济数学与管理数学研究会副理事长，曾任中国运筹学会数学规划分会副理事长、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。近十多年来，主持国家自科基金和浙江省自科基金各多项、其中省基金重点项目。 在Math. Program.、SIAM J. on Optim.、SIAM J.on Matrix Anal.and Appl. 、COAP、JOTA、JOGO等国内外重要刊物发表论文多篇。