Article
Computer Science, Information Systems
Xue Guo, Feng Liu, Xuetao Tian
Summary: With the increasing railway mileage, technologies such as vision and optical-fiber sensing are widely used in automatic railway inspections. A vision-based system called on-board track inspection system (OBTIS) is designed for this purpose. This study focuses on improving the defect detection accuracy of images collected by OBTIS, by modeling the noise in the images and proposing a denoising model named RA-WNNM. Experimental results demonstrate the superiority of RA-WNNM in denoising and image classification.
MULTIMEDIA TOOLS AND APPLICATIONS
(2022)
Article
Geosciences, Multidisciplinary
Jingfei He, Yanyan Wang, Yatong Zhou
Summary: This paper proposes a method to recover 3D seismic data using truncated nuclear norm (TNN) in order to better utilize seismic information contained in small singular values. Experimental results demonstrate that the proposed method achieves superior reconstruction results than the traditional MSSA method.
JOURNAL OF APPLIED GEOPHYSICS
(2023)
Article
Engineering, Civil
Cheng Dai, Ying Zhang, Zhigao Zheng
Summary: Predicting traffic flow is essential in intelligent transportation systems, but missing information in traffic data affects performance. Nuclear Norm-based Tensor Completion algorithm tackles this issue through truncated nuclear norm minimization. However, the existing threshold may excessively penalize large singular values, resulting in accurate data missing. To solve this problem, a new method is proposed, considering prior rank information and retaining large singular values. Extensive experiments confirm better recovery accuracy with this method.
IEEE TRANSACTIONS ON INTELLIGENT TRANSPORTATION SYSTEMS
(2023)
Article
Computer Science, Artificial Intelligence
Kishan Wimalawarne, Hiroshi Mamitsuka
Summary: We investigate optimal conditions for inducing low-rankness of higher order tensors using convex tensor norms with reshaped tensors. Proposed reshaped tensor nuclear norm and reshaped latent tensor nuclear norm for regularization and combining multiple tensors, respectively. Through generalization bounds and experiments, the novel reshaping norms are shown to lead to lower complexities, favorably compared to existing tensor norms.
Article
Mathematics, Applied
Kaixin Gao, Zheng-Hai Huang, Lulu Guo
Summary: This paper proposes a new nonconvex surrogate N/F for approximating the rank of a matrix. The effectiveness and feasibility of the N/F method are demonstrated in both theoretical analysis and experimental results.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Engineering, Multidisciplinary
Yi Xu, Xiaorong Ren, Xihong Yan
Summary: This study investigates the method of approximately finding the global minimum of a positive semidefinite Hankel matrix under linear constraints, and provides a lower bound on the objective function based on conclusions from nonnegative polynomials, semi-infinite programming, and the dual theorem. It is proven that this lower bound is almost half of the number of linear constraints in the optimization problem.
MATHEMATICAL PROBLEMS IN ENGINEERING
(2021)
Article
Engineering, Aerospace
Jianuo Ran, Jiawen Bian, Gang Chen, Yilei Zhang, Wenping Liu
Summary: This study proposes a method for extracting trend and seasonal signals from GNSS coordinate time series by utilizing the low-rank characteristic of the Hankel matrix. The method utilizes truncated nuclear norm regularization and accelerated proximal gradient line-search to achieve accurate signal extraction, and experimental results demonstrate its competitive performance.
ADVANCES IN SPACE RESEARCH
(2022)
Article
Engineering, Electrical & Electronic
Yiwen Shan, Dong Hu, Zhi Wang, Tao Jia
Summary: This paper proposes a new multi-channel optimization model for color image denoising, which decomposes the color image into overlapping RGB patches and optimizes each patch to achieve denoising. The proposed model is effective in exploiting the information between color channels and outperforms state-of-the-art models.
Article
Radiology, Nuclear Medicine & Medical Imaging
Yujiao Zhao, Zheyuan Yi, Linfang Xiao, Vick Lau, Yilong Liu, Zhe Zhang, Hua Guo, Alex T. Leong, Ed X. Wu
Summary: This study develops a joint denoising method that effectively reduces noise in MR DWIs by exploiting natural information redundancy. The method utilizes matching image content and weighted nuclear norm minimization for denoising, and achieves good results.
MAGNETIC RESONANCE IN MEDICINE
(2022)
Article
Computer Science, Artificial Intelligence
Yanyun Qu, Wenjin Yang, Yuan Xie, Weiwei Wu, Yang Wu, Hanzi Wang
Summary: This paper presents a novel strategy for atmospheric turbulence removal by characterizing local smoothness, nonlocal similarity and low-rank property of natural images. Extensive experimental results show that our method can effectively mitigate geometric deformation as well as blur variations and outperforms several other state-of-the-art turbulence removal methods.
NEURAL COMPUTING & APPLICATIONS
(2023)
Article
Mathematics, Applied
Stanislav Morozov, Matvey Smirnov, Nikolai Zamarashkin
Summary: The problem of low rank approximation is common in science. Traditionally, it is solved using unitary invariant norms, but recent research has shown potential in the Chebyshev norm. This paper investigates the problem of building optimal rank-1 approximations in the Chebyshev norm and proposes an algorithm for its construction.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2023)
Article
Computer Science, Artificial Intelligence
Guorui Li, Guang Guo, Sancheng Peng, Cong Wang, Shui Yu, Jianwei Niu, Jianli Mo
Summary: This paper introduces a new approach to solve the low-rank matrix completion problem. By designing a new non-convex Schatten capped p norm, which balances between the rank and nuclear norm of the matrix, a matrix completion method is proposed. Through extensive experiments in image inpainting, the proposed method is shown to improve the accuracy of matrix completion compared with existing methods.
IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING
(2022)
Article
Computer Science, Interdisciplinary Applications
Yaohong Yang, Weihua Zhao, Lei Wang
Summary: In this paper, two-stage online regularized estimators with nuclear norm (NN) and adaptive nuclear norm (ANN) penalties are proposed for matrix regression with streaming data. The asymptotic properties of the resulting online regularized estimators are established, and rank selection consistency for the online ANN estimator is shown. Simulations and an application to Beijing Air Quality data set are conducted to study the finite-sample performance of the proposed estimators.
COMPUTATIONAL STATISTICS & DATA ANALYSIS
(2023)
Article
Geosciences, Multidisciplinary
Tiash Ghosh, Ratul Kishore Saha, Sanjai Kumar Singh, Mamata Jenamani, Aurobinda Routray
Summary: In this paper, the effectiveness of a combined low-rank and total variation-based denoising algorithm is explored for the first time in seismic data pre-processing. The algorithm is capable of restoring seismic data corrupted by severe degradation without smearing sharp edges and sharpening blurred edges in the data. The method is evaluated through synthetic and field datasets, and the results indicate its effectiveness and superiority over other state-of-the-art methods for seismic denoising.
JOURNAL OF APPLIED GEOPHYSICS
(2023)
Review
Acoustics
Dirceu Soares Jr, Alberto Luiz Serpa
Summary: This article explores some characteristics and applications of the Eigensystem Realization Algorithm in system identification, addressing the difficulty of parameter settings for the algorithm, proposing a new method for evaluating the identified system, and attempting to use a Pseudo Random Binary Sequence as an excitation signal for system identification. Through numerical simulations and result analysis, it is found that the settings of parameters play a crucial role in improving system identification.
JOURNAL OF VIBRATION AND CONTROL
(2022)
Article
Computer Science, Software Engineering
Yangjing Zhang, Ning Zhang, Defeng Sun, Kim-Chuan Toh
MATHEMATICAL PROGRAMMING
(2020)
Article
Computer Science, Software Engineering
Xudong Li, Defeng Sun, Kim-Chuan Toh
MATHEMATICAL PROGRAMMING
(2020)
Article
Computer Science, Software Engineering
Defeng Sun, Kim-Chuan Toh, Yancheng Yuan, Xin-Yuan Zhao
OPTIMIZATION METHODS & SOFTWARE
(2020)
Article
Operations Research & Management Science
Joao Gouveia, Ting Kei Pong, Mina Saee
JOURNAL OF GLOBAL OPTIMIZATION
(2020)
Article
Operations Research & Management Science
Chen Chen, Ting Kei Pong, Lulin Tan, Liaoyuan Zeng
JOURNAL OF GLOBAL OPTIMIZATION
(2020)
Article
Operations Research & Management Science
Xinxin Li, Ting Kei Pong, Hao Sun, Henry Wolkowicz
Summary: The paper introduces a new algorithm for solving the minimum cut problem, utilizing strengthened SDP and DNN relaxations to evaluate upper and lower bounds efficiently. The use of the Peaceman-Rachford splitting method accelerates the computation process, and empirical results demonstrate the efficiency and robustness of the proposed method on random datasets and vertex separator problems.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2021)
Article
Computer Science, Theory & Methods
Peiran Yu, Guoyin Li, Ting Kei Pong
Summary: The KL exponent is crucial in estimating the convergence rate of many first-order optimization methods, with a value of 1/2 indicating local linear convergence. It is generally difficult to estimate, but can be preserved through inf-projection. The KL exponent of important convex optimization models can be maintained at 1/2 under specific conditions, and for nonconvex models, can be derived from their majorant functions.
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
(2022)
Article
Operations Research & Management Science
Liaoyuan Zeng, Ting Kei Pong
Summary: This paper studies TR type methods and proposes a general regularized subproblem. It derives a strong duality theorem and necessary and sufficient optimality condition for the subproblem. An eigensolver-based algorithm is also proposed to solve the derived dual problem. Numerical results are presented to validate the effectiveness of the algorithm.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2022)
Article
Operations Research & Management Science
Shuqin Sun, Ting Kei Pong
Summary: We propose a new algorithmic framework for constrained compressed sensing models with nonconvex sparsity-inducing regularizers and nonconvex loss functions. Our framework efficiently solves subproblems using well-developed solvers and introduces a new termination criterion for infeasible solutions. Numerical comparisons demonstrate that our approaches outperform existing methods in terms of recovery errors and speed, particularly for badly scaled measurement matrices.
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Peiran Yu, Ting Kei Pong, Zhaosong Lu
Summary: This paper studies the sequential convex programming method with monotone line search (SCPls) for a class of difference-of-convex optimization problems with smooth inequality constraints. The convergence rate of the sequence generated by SCPls in nonconvex and convex settings under suitable Kurdyka-Lojasiewicz (KL) assumptions is analyzed. The paper also discusses how to deduce the KL exponent of the extended objective function from its Lagrangian in convex settings.
SIAM JOURNAL ON OPTIMIZATION
(2021)
Article
Mathematics, Applied
Liaoyuan Zeng, Peiran Yu, Ting Kei Pong
Summary: The paper explores the use of the l(1)/l(2) norm ratio in compressed sensing problems, proposes an algorithm for noise situations, and demonstrates through numerical experiments that the algorithm can recover the original sparse vectors with reasonable accuracy.
SIAM JOURNAL ON OPTIMIZATION
(2021)
Article
Mathematics, Applied
Tianxiang Liu, Ivan Markovsky, Ting Kei Pong, Akiko Takeda
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
(2020)
Article
Mathematics, Applied
Minglu Ye, Ting Kei Pong
SIAM JOURNAL ON OPTIMIZATION
(2020)
Article
Computer Science, Software Engineering
Shujun Bi, Shaohua Pan, Defeng Sun
MATHEMATICAL PROGRAMMING COMPUTATION
(2020)
Article
Automation & Control Systems
Ziyan Luo, Defeng Sun, Kim-Chuan Toh, Naihua Xiu
JOURNAL OF MACHINE LEARNING RESEARCH
(2019)