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Low-tubal-rank Tensor Analysis: Theory, Algorithms and Applications
作者:      發布時間:2019-09-16       點擊數:
報告時間 2019年9月19日09:00 報告地點 數學與統計學學院201報告廳
報告人 王建軍(西南大學)

報告名稱Low-tubal-rank Tensor Analysis: Theory, Algorithms and Applications

主辦單位:數學與統計學學院

報告專家:王建軍

專家所在單位:西南大學

報告時間:2019年9月19日(周四)上午9:00-11:00

報告地點:數學與統計學學院201報告廳

專家簡介:王建軍,博士,教授(研究員)天津11选5走势图,博士生導師,CSIAM全國大數據與人工智能專家委員會委員,重慶市工業與應用數學學會副理事長天津11选5走势图,美國數學評論評論員天津11选5走势图,重慶數學會理事,重慶市統計學重點學科學術帶頭人,重慶市學術技術帶頭人,西南大學統計學博士一級學科負責人天津11选5走势图,以第一完成人申報的階段性成果《復雜結構性高維數據稀疏建模的方法與算法應用》榮獲重慶市自然科學三等獎天津11选5走势图,西南大學人工智能學院副院長。主要研究方向為:高維數據建模天津11选5走势图、機器學習(深度學習)、數據挖掘、壓縮感知、張量分析、函數逼近論等。在神經網絡逼近復雜性和稀疏逼近等方面有一定的學術積累。主持并完成國家自然科學基金4項,教育部科學技術重點項目1項,重慶市自然科學基金1項,主研8項國家自然、社會科學基金天津11选5走势图;現主持國家自然科學基金面上項目一項,參與國家重點基礎研究發展‘973’計劃一項天津11选5走势图,多次出席國際天津11选5走势图、國內重要學術會議,并應邀做大會特邀報告16次。已在Neural Networks, Applied and Computational Harmonic Analysis,Signal Processing,IEEE Signal Processing letters,Neurocomputing,中國科學(A,F輯),數學學報,計算機學報,電子學報等專業期刊發表80余篇學術論文,其中SCI、EI檢索65篇?!吨袊茖W》,IEEE Trans.Signal Process, image Process. Neural Networks and learning system及IEEE等系列刊物,Signal Processing,Neural networks,Pattern Recognization,計算機學報,電子學報,數學學報等知名期刊審稿人天津11选5走势图。

報告摘要:This talk will share our two recent results on low-tubal-rank tensor analysis. (1)LRTR:we establish aregularizedtensor nuclear norm minimization (RTNNM) model for low-tubal-rank tensor recovery (LRTR). Then, we initiatively define a novel tensor restricted isometry property (t-RIP) based on tensor singular value decomposition (t-SVD). Besides, our theoretical results show that any third-order tensor whose tubal rank is at most can stably be recovered from its as few as measurements with a bounded noise constraint via the RTNNM model, if the linear map obeys t-RIP with for certain fixed.(2)TRPCA:by incorporating prior information including the column and row space knowledge, we investigate the tensor robust principal component analysis (TRPCA) problem based on t-SVD. We establish sufficient conditions to ensure that under significantly weaker incoherence assumptions than tensor principal components pursuit method (TPCP), our proposed Modified-TPCP solution perfectly recovers the low-tubal-rank and the sparse components with high probability, provided that the available prior subspace information is accurate. In addition, we present an efficient algorithm by modifying the alternating direction method of multipliers (ADMM) to solve the Modified-TPCP program. Numerical experiments show that the Modified-TPCP based on prior subspace information does allow us to recover under weaker conditions than TPCP. The application of color video and face denoising task suggests the superiority of the proposed method over the existing state-of-the-art methods.

邀請人:鄒斌


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