Welsch M-估计在视频重构与背景减除中的应用
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摘要
针对监控视频在压缩采样过程中混入冲击噪声后的背景减除问题,提出一种基于Welsch M-估计与张量分解正则化的鲁棒视频重构与分解模型。为削弱冲击噪声对重构性能的影响,引入Welsch M-估计替代均方差作为衡量重建误差的代价函数。在张量框架下,将背景在不同维度、不同场景下的低秩差异性先验引入背景建模,得到重构与分解模型,并基于半二次理论和多块交替方向乘子方法给出相应的优化求解算法。实验结果表明,与SpaRCS、CS-L1PCA等算法相比,该算法在混入冲击噪声情况下,仍能保持视频重构与分解的鲁棒性。
Aiming at the background subtraction problem of surveillance video mixed with impact noise during compression sampling,a robust video reconstruction and decomposition model based on Welsch M-estimation and tensor decomposition regularization is proposed. In order to reduce the impact of effect noise on reconstruction performance,Welsch M-estimation is used to replace the mean square error as a cost function to measure the reconstruction error,and a more robust reconstruction model is constructed. Under the tensor framew ork,the low-rank difference priors of the background in different dimensions and different scenarios are introduced into the background modeling to obtain the reconstruction and decomposition model,and based on half-quadratic theory and multi-block ADM M method,the corresponding optimization algorithm is given. Experimental results show that compared with the algorithms such as SpaRCS and CS-L1 PCA,the algorithm can maintain the robustness of video reconstruction and decomposition under the condition of mixed impact noise.
Aiming at the background subtraction problem of surveillance video mixed with impact noise during compression sampling,a robust video reconstruction and decomposition model based on Welsch M-estimation and tensor decomposition regularization is proposed. In order to reduce the impact of effect noise on reconstruction performance,Welsch M-estimation is used to replace the mean square error as a cost function to measure the reconstruction error,and a more robust reconstruction model is constructed. Under the tensor framew ork,the low-rank difference priors of the background in different dimensions and different scenarios are introduced into the background modeling to obtain the reconstruction and decomposition model,and based on half-quadratic theory and multi-block ADM M method,the corresponding optimization algorithm is given. Experimental results show that compared with the algorithms such as SpaRCS and CS-L1 PCA,the algorithm can maintain the robustness of video reconstruction and decomposition under the condition of mixed impact noise.
引文
[1]邱联奎,刘启亮,雷文龙.基于背景减除与三帧差分相融合的运动检测[J].合肥工业大学学报(自然科学版),2014,(5):572-577.
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[23]SHEN Y,WEN Z,ZHANG Y.Augmented lagrangian alternating direction method for matrix separation based on low-rank factorization[J].Optimization M ethods&Softw are,2014,29(2):239-263.
[24]KOLDA T,BADER B.Tensor decompositions and applications[J].SIAM Review,2009,51(3):455-500.
[25]PHAM D S,VENKATESH S.Improved image recovery from compressed data contaminated with impulsive noise[J].IEEETransactions on Image Processing A Publication of the IEEESignal Processing Society,2012,21(1):397-405.
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[28]GUO H,QIU C,VASWANI N.An online algorithm for separating sparse and low-dimensional signal sequences from their sum[J].IEEE Transactions on Signal Processing,2013,62(16):4284-4297.
[2]孙吉花.背景减除的算法研究[D].长沙:国防科学技术大学,2006.
[3]谌湘倩,马绍惠,须文波.基于背景差分检测和改进GM-PHD滤波器的多目标跟踪[J].计算机工程,2017,43(1):253-258.
[4]CANDES E J,ROMBERG J,TAO T.Robust uncertainty principles:exact signal reconstruction from highly incomplete frequency information[J].IEEE Transactions on Information Theory,2006,52(2):489-509.
[5]DPNOHO D L.Compressed sensing[J].IEEE Transactions on Information Theory,2006,52(4):1289-1306.
[6]DONOHO D L.An introduction to compressive sampling[J].IEEE Signal Processing M agazine,2008,25(2):21-30.
[7]CARRILLO R E,BARNER K E,AYSAL T C.Robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise[J].IEEE Journal of Selected Topics in Signal Processing,2010,4(2):392-408.
[8]HE R,ZHENG W S,TAN T,et al.Half-quadratic-based iterative minimization for robust sparse representation[J].IEEE Transactions on Pattern Analysis&Machine Intelligence,2014,36(2):261-275.
[9]孙双侠.基于矩阵分解的鲁棒推荐算法研究[D].秦皇岛:燕山大学,2013.
[10]JIANG H,DENG W,SHEN Z.Surveillance video processing using compressive sensing[J].Inverse Problems&Imaging,2013,6(2):201-214.
[11]CAO W,WANG Y,SUN J,et al.Total variation regularized tensor RPCA for background subtraction from compressive measurements[J].IEEE Transactions on Image Processing,2016,25(9):4075-4090.
[12]汪太月,戴燕青.一种改进的非凸秩最小化算法及其在矩阵恢复中的应用[J].湖北理工学院学报,2015,31(1):21-26.
[13]CAI J F,CANDES E J,SHEN Z.A Singular value thresholding algorithm for matrix completion[J].SIAMJournal on Optimization,2008,20(4):1956-1982.
[14]CHARTRAND R.Exact reconstruction of sparse signals via nonconvex minimization[J].IEEE Signal Processing Letters,2007,14(10):707-710.
[15]TRZASKO J,MANDUCA A.Highly undersampled magnetic resonance image reconstruction via homotopic L0-minimization[J].IEEE Transactions on M edical Imaging,2009,28(1):106-121.
[16]DONG W,SHI G,LI X,et al.Compressive sensing via nonlocal low-rank regularization[J].IEEE Transactions on Image Processing,2014,23(8):3618-3632.
[17]NIKOLOVA M,NG M.Analysis of half-quadratic minimization methods for signal and image recovery[M].[S.1.]:Society for Industrial and Applied Mathematics,2005:937-966.
[18]YUANG X T,HU B G.Robust feature extraction via information theoretic learning[C]//Proceedings of IEEEInternational Conference on M achine Learning.Washington D.C.,USA:IEEE Press,2009:1193-1200.
[19]BOYD S,PARIKH N,CHU E,et al.Distributed aptimization and statistical learning via the alternating direction method of multipliers[J].Foundations and Trends in M achine Learning,2010,3(1):1-12.
[20]DENG W,LAI M J,PENG Z,et al.Parallel multi-block ADM M w ith O(1/k)convergence[J].Journal of Scientific Computing,2017,71(2):712-736.
[21]HONG M,LUO Z.On the linear convergence of the alternating direction method of multipliers[J].M athematical Programming,2017,162(1/2):165-199.
[22]MOTA J F C,XAVIER J M F,AGUIAR P M Q,et al.D-ADMM:a communication-efficient distributed algorithm for separable optimization[J].IEEE Transactions on Signal Processing,2013,61(10):2718-2723.
[23]SHEN Y,WEN Z,ZHANG Y.Augmented lagrangian alternating direction method for matrix separation based on low-rank factorization[J].Optimization M ethods&Softw are,2014,29(2):239-263.
[24]KOLDA T,BADER B.Tensor decompositions and applications[J].SIAM Review,2009,51(3):455-500.
[25]PHAM D S,VENKATESH S.Improved image recovery from compressed data contaminated with impulsive noise[J].IEEETransactions on Image Processing A Publication of the IEEESignal Processing Society,2012,21(1):397-405.
[26]WATERS A E,SANKARANARAYANAN A C,BARANIUK RG.SpaRCS:recovering low-rank and sparse matrices from compressive measurements[C]//Proceedings of Inter-national Conference on Neural Information Processing Systems.Washington D.C.,USA:IEEE Press,2011:1089-1097.
[27]LIU Y,PADOS D A.Compressed-sensed-domain L1-PCAvideo surveillance[C]//Proceedings of IEEE SPIE’15.Washington D.C.,USA:IEEE Press,2015:351-363.
[28]GUO H,QIU C,VASWANI N.An online algorithm for separating sparse and low-dimensional signal sequences from their sum[J].IEEE Transactions on Signal Processing,2013,62(16):4284-4297.