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ROBUST INEXACT ALTERNATING OPTIMIZATION FOR MATRIX COMPLETION WITH OUTLIERS

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Journal of Computational Mathematics 2020年第2期38卷 337-354页

作者： Ji Li jian-feng cai Hongkai Zhao Beijing Computational Science Research Center Beijing 100193China Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong Kong Department of Mathematics University of CaliforniaIrvineCAUSA

We investigate the problem of robust matrix completion with a fraction of observation corrupted by sparsity outlier *** propose an algorithmic framework based on the ADMM algorithm for a non-convex optimization,whose objective function consists of an l1 norm data fidelity and a rank *** reduce the computational cost per iteration,two inexact schemes are developed to replace the most time-consuming step in the generic ADMM *** resulting algorithms remarkably outperform the existing solvers for robust matrix completion with outlier *** the noise is severe and the underlying matrix is ill-conditioned,the proposed algorithms are faster and give more accurate solutions than state-of-the-art robust matrix completion approaches.

关键词： Matrix completion ADMM Outlier noise Inexact projection

Data-Driven Tight Frame for Multi-channel Images and Its Application to Joint Color-Depth Image Reconstruction

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Journal of the Operations Research Society of China 2015年第2期3卷 99-115页

作者： Jin Wang jian-feng cai Beijing Key Laboratory of Multimedia and Intelligent Software Technology College of Metropolitan TransportationBeijing University of TechnologyBeijing 100124China Department of Mathematics University of IowaIowa CityIA 52242USA

In image restoration,we usually assume that the underlying image has a good sparse approximation under a certain *** tight frame system has been proven to be such an efficient system to sparsely approximate piecewise smooth ***,it has been widely used in many practical image restoration ***,images from different scenarios are so diverse that no static wavelet tight frame system can sparsely approximate all of *** overcome this,recently,cai ***.(Appl Comput Harmon Anal 37:89–105,2014)proposed a method that derives a data-driven tight frame adapted to the specific input image,leading to a better sparse *** data-driven tight frame has been applied successfully to image denoising and CT image *** this paper,we extend this data-driven tight frame construction method to multi-channel *** construct a discrete tight frame system for each channel and assume their sparse coefficients have a joint *** multi-channel data-driven tight frame construction scheme is applied to joint color and depth image *** results show that the proposed approach has a better performance than state-of-the-art joint color and depth image reconstruction approaches.

关键词： Data-driven tight frame Group sparsity Image reconstruction

MODIFIED NEWTON＇S ALGORITHM FOR COMPUTING THE GROUP INVERSES OF SINGULAR TOEPLITZ MATRICES

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维普期刊数据库

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Journal of Computational Mathematics 2006年第5期24卷 647-656页

作者： jian-feng cai Michael K. Ng Yi-min Wei Department of Mathematics The Chinese University of Hong Kong Hong Kong Department of Mathematics Hong Kong Baptist University Hong Kong School of Mathematical Sciences Fudan University Shanghai 200433 China ~ Key Laboratory of Mathematics for Nonlinear Sciences (Fudan University) Ministry of Education

Newton＇s iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration, the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix, the matrix-vector multiplication involved in Newton＇s iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.

关键词： Newton's iteration Group inverse Toeplitz matrix Displacement rank.

Relationship Between Differential Interference Angle and Parameter of Experiment in Molecular Beam

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维普期刊数据库

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Communications in Theoretical Physics 2006年第2X期46卷 294-296页

作者： LI Yong-Qing LI jian MA feng-cai Department of Physics Liaoning University Shenyang 110036 China

Collisional quantum interference （CQI） was observed in the intramolecular rotational energy transfer in the experiment of the static cell, and the integral interference angles were measured. To observe more precise information, the experiment in the molecular beam should be taken,from which the relationship between the differential interference angle and the scattering angle can be obtained. In this paper, the theoretical model of CQI is described in an atom-diatom system in the condition of the molecular beam, based on the first-Born approximation of time-dependent perturbation theory, taking into accounts the long-range interaction potential. The method of observing and measuring correctly the differential interference angle is presented. The changing tendency of the differential interference angle with the impact parameter and relative velocity is discussed. The changing tendencies of the differential interference angle with the parameter of experiment in the molecular beam, including the impact parameter and the velocity are discussed. This theoretical model is important to understand or perform the experiment in the molecular beam.

关键词： differential interference angle quantum interference rotational energy transfer

Gradient Descent for Symmetric Tensor Decomposition

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Annals of Applied Mathematics 2022年第4期38卷 385-413页

作者： jian-feng cai Haixia Liu Yang Wang Department of Mathematics The Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina School of Mathematics and Statistics&Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and TechnologyWuhanHubei 430074China

Symmetric tensor decomposition is of great importance in *** studies have employed a greedy approach,where the main idea is to first find a best rank-one approximation of a given tensor,and then repeat the process to the residual tensor by subtracting the rank-one *** this paper,we focus on finding a best rank-one approximation of a given orthogonally order-3 symmetric *** give a geometric landscape analysis of a nonconvex optimization for the best rank-one approximation of orthogonally symmetric *** show that any local minimizer must be a factor in this orthogonally symmetric tensor decomposition,and any other critical points are linear combinations of the ***,we propose a gradient descent algorithm with a carefully designed initialization to solve this nonconvex optimization problem,and we prove that the algorithm converges to the global minimum with high probability for orthogonal decomposable *** result,combined with the landscape analysis,reveals that the greedy algorithm will get the tensor CP low-rank *** results are provided to verify our theoretical results.

关键词： Gradient descent random initialization symmetric tensor decomposition CP decomposition linear convergence

The Global Landscape of Phase Retrieval Ⅱ:Quotient Intensity Models

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Annals of Applied Mathematics 2022年第1期38卷 62-114页

作者： jian-feng cai Meng Huang Dong Li Yang Wang Department of Mathematics The Hong Kong University of Science and TechnologyClear Water BayKowloonHong Kong SUSTech International Center for Mathematics and Department of Mathematics Southern University of Science and TechnologyShenzhenGuangdong 518055China

A fundamental problem in phase retrieval is to reconstruct an unknown signal from a set of magnitude-only *** this work we introduce three novel quotient intensity models(QIMs) based on a deep modification of the traditional intensity-based models.A remarkable feature of the new loss functions is that the corresponding geometric landscape is benign under the optimal sampling *** the measurements ai∈Rn are Gaussian random vectors and the number of measurements m≥Cn,the QIMs admit no spurious local minimizers with high probability,i.e.,the target solution x is the unique local minimizer(up to a global phase) and the loss function has a negative directional curvature around each saddle *** benign geometric landscape allows the gradient descent methods to find the global solution x(up to a global phase) without spectral initialization.

关键词： Phase retrieval landscape analysis non-convex optimization.

The Global Landscape of Phase Retrieval I:Perturbed Amplitude Models

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Annals of Applied Mathematics 2021年第4期37卷 437-512页

作者： jian-feng cai Meng Huang Dong Li Yang Wang Department of Mathematics The Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina SUSTech International Center for Mathematics and Department of Mathematics Southern University of Science and TechnologyShenzhenGuangdong 518055China

A fundamental task in phase retrieval is to recover an unknown signal x∈R^(n) from a set of magnitude-only measurements y_(i)=|〈a_(i),x〉|,i=1,…,*** this paper,we propose two novel perturbed amplitude models(PAMs)which have a non-convex and quadratic-type loss *** the measurements a_(i)∈R^(n) are Gaussian random vectors and the number of measurements m≥Cn,we rigorously prove that the PAMs admit no spurious local minimizers with high probability,i.e.,the target solution x is the unique local minimizer(up to a global phase)and the loss function has a negative directional curvature around each saddle *** to the well-tamed benign geometric landscape,one can employ the vanilla gradient descent method to locate the global minimizer x(up to a global phase)without spectral *** carry out extensive numerical experiments to show that the gradient descent algorithm with random initialization outperforms state-of-the-art algorithms with spectral initialization in empirical success rate and convergence speed.

关键词： Phase retrieval landscape analysis non-convex optimization

Carboniferous-Early Permian heterogeneous distribution of porous carbonate reservoirs in the Central Uplift of the South Yellow Sea Basin and its hydrocarbon potential analysis

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China Geology 2025年第1期8卷 58-76页

作者： Shu-yu Wu Jun Liu jian-wen Chen Qi-liang Sun Yin-guo Zhang Jie Liang Yong-cai feng School of Engineering China University of GeoscienceWuhan 430074China Yantai Center of Coastal Zone Geological Survey China Geological SurveyMinistry of Natural ResourcesYantai 264001China Key Laboratory of Submarine Geosicences Ministry of Natural ResourcesHangzhou 310012China Chinese Academy of Geological Sciences China Geological SurveyMinistry of Natural ResourcesBeijing 100037China Laboratory for Marine Mineral Resources Qingdao National Laboratory for Marine Science and TechnologyQingdao 266061China The Key Laboratory of Gas Hydrate Ministry of Natural ResourcesQingdao Institute of Marine GeologyChina Geological SurveyMinistry of Natural ResourcesQingdao 266071China College of Marine Science and Technology China University of GeoscienceWuhan 430074China

Mesozoic-Palaeozoic marine carbonate rocks are crucial hydrocarbon reservoirs in the Central Uplift area of the South Yellow Sea Basin(SYSB).Due to the scarcity of boreholes and the significant heterogeneity of carbonate reservoirs,the distribution of porous carbonate reservoirs and their related key controlling factors remain *** this study,factors affecting the distribution of porous Carboniferous-Early Permian carbonate reservoirs in the SYSB were investigated through seismic inversion and isotope *** log-seismic characteristics of porous carbonate reservoirs,sensitive lithology parameters,and physical property parameters were extracted and *** pre-stack simultaneous inversion technique was applied to predict the lithology and physical properties of porous carbonate ***,the sedimentary of carbonate was analyzed using isotopes of carbon,oxygen,and *** results show that porous carbonate reservoirs are mainly developed in the open platform sediments with porosities of 3%-5%and are mainly distributed in the paleo-highland(Huanglong Formation and Chuanshan Formation)and the slope of paleo-highland(Hezhou Formation).The porous carbonate reservoirs of the Qixia Formation are only locally *** addition,the negativeδ13C excursions indicate a warm and humid tropical climate with three sea-level fluctuations in the study area from the Carboniferous to Early *** favorable conditions for developing porous carbonate rocks include the sedimentary environment and diagenetic *** primary pore tends to form in high-energy environments of the paleo-highland,and the secondary pore is increased by dissolution during the syngenetic or quasi-syngenetic *** to the hydrocarbon potential analysis,the Late Ordovician Wufeng Formation and Lower Silurian Gaojiabian Formation are the source rocks in the high-maturity-over-maturity stage,the Carboniferous-Lower Permian carbonate is the good reservoirs,and th

关键词： Sedimentary Heterogeneous porous carbonate reservoirs C-H-Sr isotope analysis Carboniferous-Early Permian Chuanshan Formation Huanglong Formation Pre-stack simultaneous inversion technique Oil-gas exploration engineering Hydrocarbon accumulation Hydrocarbon potential Central Uplift of the South Yellow Sea Basin

Uncovering the oxidation mechanism of sphalerite(ZnS)in the absence and presence of water:A first-principles investigation

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International Journal of Mining Science and Technology 2025年第1期35卷 149-157页

作者： Yuanjia Luo Wei Sun Haisheng Han jian Peng feng jiang School of Minerals Processing and Bioengineering Central South UniversityChangsha 410083China

Herein,a first-principles investigation was innovatively conducted to research the surface oxidation of ZnS-like sphalerite in the absence and presence of H_(2)O .The findings showed that single O_(2) was preferred to be dissociated adsorption on sphalerite surface by generating SAO and Zn AO bonds,and the S atom on the surface was the most energy-supported site for O_(2) adsorption,on which a≡Zn-O-S-O-Zn≡structure will be ***,dissociated adsorption of single H_(2)O will not *** was preferred to be adsorbed on the top Zn atom on sphalerite surface in molecular form through Zn-O ***,sphalerite oxidation can occur as if O_(2) was present regardless of the presence of H_(2)O ,and when H_(2)O and O_(2) coexisted,the formation of sulfur oxide(SO_(2) )needed a lower energy barrier and it was easier to form on sphalerite surface than that only O_(2) *** the absence of H_(2)O ,when SO_(2) was generated,further oxidation of which would form neutral zinc *** the presence of H_(2)O ,the formation of SO_(2) on sphalerite surface was easier and the rate of further oxidation to form sulfate was also ***,the occurrence of sphalerite oxidation was accelerated.

关键词： First-principles Oxidation Sphalerite H_(2)O Lower energy barrier