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2021首發(fā),西南大學(xué)王建軍教授:1-比特低管秩張量魯棒恢復(fù)的模型、理論與算法

日期:2021-03-24 10:32

2021年中國自動(dòng)化學(xué)會(huì)云講座正式起航!首期云講座將于3月29日15:00-16:00開講,本期云講座邀請到西南大學(xué)王建軍教授,為大家?guī)韴?bào)告:ROBUST ONE-BIT LOW-TUBAL-RANK TENSOR RECOVERY(1-比特低管秩張量魯棒恢復(fù)的模型、理論與算法),敬請期待!

 

報(bào)告人:西南大學(xué)教授 王建軍

 

報(bào)告題目:

ROBUST ONE-BIT LOW-TUBAL-RANK TENSOR RECOVERY

1-比特低管秩張量魯棒恢復(fù)的模型、理論與算法

報(bào)告摘要:

This talk focuses on the recovery of low-tubal-rank tensors from binary measurements based on tensor-tensor product (or t-product) and tensor Singular Value Decomposition (t-SVD). Two types of recovery models are considered, one is the tensor hard singular tube thresholding and the other one is the tensor nuclear norm minimization. In the case no random dither exists in the measurements, our research shows that the direction of tensor XR^(n1×n2×n3) with tubal rank r can be well approximated from O(r(n1+n2)n3) random Gaussian measurements. In the case nonadaptive dither exists in the measurements, it is proved that both the direction and the magnitude of X can be simultaneously recovered. As we will see, under the nonadaptive measurement scheme, the recovery errors of two reconstruction procedures decay at the rate of polynomial of the oversampling factor λ=m/"r(n1+n2)n3" (m is the random Gaussian measurements). In order to obtain faster decay rate, we introduce a recursive strategy and allow the dithers in quantization to be adaptive to previous measurements for each iterations. Under this quantization scheme, two iterative recovery algorithms are proposed which establish recovery errors decaying at the rate of exponent of the oversampling factor λ. Numerical experiments on both synthetic and real-world data sets are conducted and demonstrate the validity of our theoretical results and the superiority of our algorithms.

報(bào)告人簡介:

王建軍,博士,西南大學(xué)三級(jí)教授,博士生導(dǎo)師,重慶市學(xué)術(shù)帶頭人,重慶市創(chuàng)新創(chuàng)業(yè)領(lǐng)軍人才,巴渝學(xué)者特聘教授,重慶工業(yè)與應(yīng)用數(shù)學(xué)學(xué)會(huì)副理事長,CSIAM全國大數(shù)據(jù)與人工智能專家委員會(huì)委員,美國數(shù)學(xué)評(píng)論評(píng)論員,曾獲重慶市自然科學(xué)獎(jiǎng)勵(lì)。主要研究方向?yàn)椋焊呔S數(shù)據(jù)建模、機(jī)器學(xué)習(xí)(深度學(xué)習(xí))、數(shù)據(jù)挖掘、壓縮感知、張量分析、函數(shù)逼近論等。在神經(jīng)網(wǎng)絡(luò)(深度學(xué)習(xí))逼近復(fù)雜性和高維數(shù)據(jù)稀疏建模等方面有一定的學(xué)術(shù)積累。主持國家自然科學(xué)基金5項(xiàng),教育部科學(xué)技術(shù)重點(diǎn)項(xiàng)目1項(xiàng),重慶市自然科學(xué)基金1項(xiàng),主研8項(xiàng)國家自然、社會(huì)科學(xué)基金;現(xiàn)主持國家自然科學(xué)基金面上項(xiàng)目2項(xiàng),參與國家重點(diǎn)基礎(chǔ)研究發(fā)展‘973’計(jì)劃一項(xiàng), 多次出席國際、國內(nèi)重要學(xué)術(shù)會(huì)議,并應(yīng)邀做大會(huì)特邀報(bào)告22余次。 

已在IEEE Transactions on Pattern Analysis and Machine Intelligence(2), IEEE Transactions on Neural Networks and Learning System(2),Applied and Computational Harmonic Analysis(2),Inverse Problems, Neural Networks, Signal Processing(2), IEEE Signal Processing letters(2), Journal of Computational and applied mathematics, ICASSP,IET Image processing(2), IET Signal processing(4),中國科學(xué)(A,F輯)(4), 數(shù)學(xué)學(xué)報(bào), 計(jì)算機(jī)學(xué)報(bào), 電子學(xué)報(bào)(3)等知名專業(yè)期刊發(fā)表90余篇學(xué)術(shù)論文,IEEE等系列刊物,National Science Review 及Signal Processing,Neural Networks,Pattern Recognization,中國科學(xué), 計(jì)算機(jī)學(xué)報(bào),電子學(xué)報(bào),數(shù)學(xué)學(xué)報(bào)等知名期刊審稿人。

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來源:學(xué)會(huì)秘書處