Generalized singular value thresholding operator based nonconvex low-rank and sparse decomposition for moving object detection

Yang, Zhenzhen; Lü, Fan; Yang, Yongpeng; Yang, Zhen; Gui, Guan

doi:10.1016/j.jfranklin.2019.09.017

Cited by 29 publications

(8 citation statements)

References 33 publications

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“…where ∆ 0 ′ ≜ 2 − 2 , and ∆ ≜ 2 − ( + 2) 2 . Then, we define ∆ ≜ 2 − ( + 2) 2 . Combining (27) and (28), it can be concluded that can be defined by the following equation…”

Section: B Mean Squared Steady State Analysis Of the Bsls-lms Algorithmmentioning

confidence: 99%

“…Signal reconstruction technologies have attracted much attention in the fields of channel estimation, image recovery, sparse unknown system identification [1][2][3][4][5][6]. In many cases, sparse unknown systems have only a few nonzero entries, and these limited nonzero or large coefficients response appear independently in different locations over a long pulse.…”

Section: Introductionmentioning

confidence: 99%

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Block-Sparsity Log-Sum-Induced Adaptive Filter for Cluster Sparse System Identification

et al. 2020

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In this work, an effective adaptive block-sparsity log-sum least mean square (BSLS-LMS) algorithm is proposed to improve the convergence performance of cluster sparse system identification. The main idea of the proposed scheme is to add a new block-sparsity induced term into the cost function of the LMS algorithm. We utilize the 1 norm of adaptive tap weights and log-sum as a mixed constraint, via optimizing the cost function through the gradient descent method, the proposed adaptive filtering method can iteratively move the identified signals towards the optimal solutions, and finally identify the unknown system accurately. The cluster-sparse system response, with block length and arbitrary average sparsity, is generated by a Markov-Gaussian (M-G) model. For the white Gaussian input data, the theoretical formulas of the steady-state mis-adjustment and convergence behaviors of the BSLS-LMS are derived in a general sparse system and a block sparse system, respectively. Numerical experiments demonstrate that the proposed adaptive BSLS-LMS algorithm achieves much better convergence behavior than conventional sparse signal recovery solutions. The experimental study also verifies the consistency between the simulation results and the theoretical analysis.

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Section: B Mean Squared Steady State Analysis Of the Bsls-lms Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Block-Sparsity Log-Sum-Induced Adaptive Filter for Cluster Sparse System Identification

et al. 2020

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“…The key issue is how to improve nonlinear approximation capacity as much as possible [23]- [25]. It is demonstrated that classic AR, ARMA and ARIMA can only seizure both linearity and short range dependencies (SRD) hidden between video data, but are powerless to LRD, which leads to weak performance in video traffic prediction [26].…”

Section: Introductionmentioning

confidence: 99%

Smoothing-Aided Support Vector Machine Based Nonstationary Video Traffic Prediction Towards B5G Networks

Wang

Sun

et al. 2020

IEEE Trans. Veh. Technol.

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Video services have hold a surprising proportion of the whole network traffic in wireless communication networks. Accurate prediction of video traffic can endow networks with intelligence in resource management, especially for the forthcoming beyond the fifth-generation (B5G) networks. However, the existing approaches fail to accurately predict video traffic with all types of frames, due to the natures of strong long-range dependence, self-similarity and burstiness. Obviously, it is unable to meet the QoS and QoE requirements of dynamic bandwidth allocation. In this paper, we propose the feasibility of advanced machine learning methodology applied in nonstationary video traffic prediction, i.e., smoothing-aided support vector machine (SSVM) model. The model utilizes classical smoothing methods to preprocess video traffic by relieving the drastic fluctuation of video stream. It can provide an effective association for the subsequent support vector regression, as the preprocessed data becomes more smooth and continuous than the original unprocessed one. Experimental results show that our proposed model significantly outperforms the state of the art model, i.e., logistic smooth transition autoregressive, in prediction performance. The superior nonlinear approximation capacity is further demonstrated by visualized statistical analysis.

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“…Ma et al [39] showed that the nuclear normminimization is the convex relaxation of low rank minimization which leads to good denoising results and applied the weighted nuclear norm minimization to image denoising. Based on this fact, Yang et al proposed the nonconvex nonsmooth weighted nuclear norm (NNWNN) [25]and the non-convex low-rank and sparse decomposition (NonLRSD) methods [28]. The NNWNN and the NonLRSD methods use nonconvex nonsmooth weighted nuclear norm and the non-convex generalized singular value threshold operator to approximate the rank function in the LRSD model, respectively.…”

Section: Introductionmentioning

confidence: 99%

Foreground-Background Separation via Generalized Nuclear Norm and Structured Sparse Norm Based Low-Rank and Sparse Decomposition

Yang

et al. 2020

IEEE Access

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Low-rank and sparse decomposition (LRSD) has attracted wide attention in video foregroundbackground separation and many other fields. However, the traditional LRSD methods have many tough problems, such as the problems of the low accuracy of the surrogate functions of rank and sparsity, ignoring the spatial information of the videos and sensitivity to noise, etc. To deal with these problems, this paper proposes the generalized nuclear norm and structured sparse norm (GNNSSN) method based LRSD for video foreground-background separation, which introduces the generalized nuclear norm (GNN) and the structured sparse norm (SSN) to approximate the rank function and the l 0 -norm of the LRSD method. In addition, we extend our proposed model to a robust model against noise for practical applications, and we called the extended method as the robust generalized nuclear norm and structured sparse norm (RGNNSSN) method. At last, we use the alternating direction method of multipliers (ADMM) to solve our proposed two methods. Experimental results and discussions on video foreground-background separation demonstrate that our proposed two methods have better performances than other LRSD based foreground-background separation methods.INDEX TERMS Low-rank and sparse decomposition, generalized nuclear norm, structured sparse norm, alternating direction method of multipliers, foreground-background separation.

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Generalized singular value thresholding operator based nonconvex low-rank and sparse decomposition for moving object detection

Cited by 29 publications

References 33 publications

Block-Sparsity Log-Sum-Induced Adaptive Filter for Cluster Sparse System Identification

Block-Sparsity Log-Sum-Induced Adaptive Filter for Cluster Sparse System Identification

Smoothing-Aided Support Vector Machine Based Nonstationary Video Traffic Prediction Towards B5G Networks

Foreground-Background Separation via Generalized Nuclear Norm and Structured Sparse Norm Based Low-Rank and Sparse Decomposition

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