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Surveillance video processing using compressive sensing
1.  Bell Labs, AlcatelLucent, 700 Mountain Ave, Murray Hill, NJ 07974, United States 
2.  Dept. of Computational and Applied Math., Rice University, Houston, TX 77005, United States 
3.  Dept. of Math., National Univ. of Singapore, 119076, Singapore 
References:
[1] 
Y. Benezeth, P. M. Jodoin, B. Emile, H. Laurent and C. Rosenberger, Comparative study of background subtraction algorithms, J. Electron. Imaging, 19 (2010), 033003. doi: 10.1117/1.3456695. 
[2] 
J.F. Cai, E. J. Candès and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, 20 (2010), 19561982. doi: 10.1137/080738970. 
[3] 
J.F. Cai, S. Osher and Z. Shen, Split Bregman methods and frame based image restoration,, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 8 (): 337. 
[4] 
E.J. Candès, X. Li, Y. Ma and J. Wright, Robust principal component analysis?, Journal of ACM, 58 (2011), Art. 11, 37 pp. 
[5] 
E. J. Candès, J. Romberg and T. Tao, Stable signal recovery from incomplete and inaccurate measurements, Comm. Pure Appl. Math., 59 (2006), 12071223. doi: 10.1002/cpa.20124. 
[6] 
V. Cevher, A. Sankaranarayanan, M. Duarte, D. Reddy, R. Baraniuk and R. Chellappa, Compressive sensing for background subtraction, Computer VisionECCV 2008, (2008), 155168. 
[7] 
I. Daubechies, B. Han, A. Ron and Z. Shen, Framelets: MRAbased constructions of wavelet frames, Applied and Computational Harmonic Analysis, 14 (2003), 146. doi: 10.1016/S10635203(02)005110. 
[8] 
W. Deng, W. Yin and Y. Zhang, "Group Sparse Optimization by Alternating Direction Method," TR1106, Department of Computational and Applied Mathematics, Rice University, 2011. 
[9] 
B. Dong and Z. Shen, "MRABased Wavelet Frames and Applications," IAS Lecture Notes Series, Summer Program on The Mathematics of Image Processing, Park City Mathematics Institute, 2010. 
[10] 
Y. Dong, G. N. DeSouza and T. X. Han, Illumination invariant foreground detection using multisubspace learning, International Journal of Knowledgebased and Intelligent Engineering Systems, 14 (2010), 3141. 
[11] 
D. Donoho, Compressed sensing, IEEE Trans. on Information Theory, 52 (2006), 12891306. doi: 10.1109/TIT.2006.871582. 
[12] 
M. Fornasier and H. Rauhut, Recovery algorithms for vectorvalued data with joint sparsity constraints, SIAM J. Numer. Anal., 46 (2008), 577613. doi: 10.1137/0606668909. 
[13] 
H. Gao, J. F. Cai, Z. Shen and H. Zhao, Robust principal component analysisbased fourdimensional computed tomography, Physics in Medicine and Biology, 56 (2011), 3181. doi: 10.1088/00319155/56/11/002. 
[14] 
R. Glowinski and P. Le Tallec, "Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics," SIAM Studies in Applied Mathematics, 9, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1989. doi: 10.1137/1.9781611970838. 
[15] 
T. Goldstein and S. Osher, The split Bregman method for L1regularized problems, SIAM J. Imaging Sci., 2 (2009), 323343. doi: 10.1137/080725891. 
[16] 
H. Jiang, Chengbo Li, Raziel HaimiCohen, Paul Wilford and Yin Zhang, Scalable video coding using compressive sensing, Bell Labs Technical Journal, 16 (2012). 
[17] 
H. Jiang, B. Mathews and P. Wilford, Compressive sensing for sound localization in wireless sensor network, accepted for presentation at SENSORNET2012, The First International Conference on Sensor Networks, February 2426, Rome, Italy, 2012. 
[18] 
H. Jiang, Z. Shen, W. Deng and P. Wilford, Adaptive low rank and sparse decomposition in compressive sensing of surveillance video, submitted, 2011. 
[19] 
C. Li, H. Jiang, P. A., Wilford and Y. Zhang, Video coding using compressive sensing for wireless communications, IEEE Wireless Communications and Networking Conference (WCNC), (2011), 20772082. doi: 10.1109/WCNC.2011.5779474. 
[20] 
V. Mahadevan and N. Vasconcelos, Spatiotemporal saliency in highly dynamic scenes, IEEE Trans. on Pattern Analysis and Machine Intelligence, 32 (2010), 171177. doi: 10.1109/TPAMI.2009.112. 
[21] 
M. Piccardi, Background subtraction techniques: A review, IEEE International Conference on Systems, Man and Cybernetics, 4 (2004), 30993104. 
[22] 
A. Ron and Z. Shen, Affine systems in $L_2(R^d)$: The analysis of the analysis operator, Journal of Functional Analysis, 148 (1997), 408447. doi: 10.1006/jfan.1996.3079. 
[23] 
M. Rudelson and R. Vershynin, On sparse reconstruction from Fourier and Gaussian measurements, Communications on Pure and Applied Mathematics, 61 (2008), 10251045. doi: 10.1002/cpa.20227. 
[24] 
Z. Shen, Wavelet frames and image restorations, "Proceedings of the International Congress of Mathematicians," IV (ed. Rajendra Bhatia), Hindustan Book Agency, New Delhi, (2010), 28342863. 
[25] 
C. Stauffer and W. E. L Grimson, Adaptive background mixture models for realtime tracking, Computer Vision and Pattern Recognition, 2 (1999), 252258. 
[26] 
E. Sutter, The Fast $m$Transform: A fast computation of crosscorrelations with binary $m$sequences, SIAM J. Comput., 20 (1991), 686694. doi: 10.1137/0220043. 
[27] 
, EC Funded CAVIAR project/IST 2001 37540,, 2003. Available from: \url{http://homepages.inf.ed.ac.uk/rbf/CAVIAR/}., (). 
show all references
References:
[1] 
Y. Benezeth, P. M. Jodoin, B. Emile, H. Laurent and C. Rosenberger, Comparative study of background subtraction algorithms, J. Electron. Imaging, 19 (2010), 033003. doi: 10.1117/1.3456695. 
[2] 
J.F. Cai, E. J. Candès and Z. Shen, A singular value thresholding algorithm for matrix completion, SIAM Journal on Optimization, 20 (2010), 19561982. doi: 10.1137/080738970. 
[3] 
J.F. Cai, S. Osher and Z. Shen, Split Bregman methods and frame based image restoration,, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 8 (): 337. 
[4] 
E.J. Candès, X. Li, Y. Ma and J. Wright, Robust principal component analysis?, Journal of ACM, 58 (2011), Art. 11, 37 pp. 
[5] 
E. J. Candès, J. Romberg and T. Tao, Stable signal recovery from incomplete and inaccurate measurements, Comm. Pure Appl. Math., 59 (2006), 12071223. doi: 10.1002/cpa.20124. 
[6] 
V. Cevher, A. Sankaranarayanan, M. Duarte, D. Reddy, R. Baraniuk and R. Chellappa, Compressive sensing for background subtraction, Computer VisionECCV 2008, (2008), 155168. 
[7] 
I. Daubechies, B. Han, A. Ron and Z. Shen, Framelets: MRAbased constructions of wavelet frames, Applied and Computational Harmonic Analysis, 14 (2003), 146. doi: 10.1016/S10635203(02)005110. 
[8] 
W. Deng, W. Yin and Y. Zhang, "Group Sparse Optimization by Alternating Direction Method," TR1106, Department of Computational and Applied Mathematics, Rice University, 2011. 
[9] 
B. Dong and Z. Shen, "MRABased Wavelet Frames and Applications," IAS Lecture Notes Series, Summer Program on The Mathematics of Image Processing, Park City Mathematics Institute, 2010. 
[10] 
Y. Dong, G. N. DeSouza and T. X. Han, Illumination invariant foreground detection using multisubspace learning, International Journal of Knowledgebased and Intelligent Engineering Systems, 14 (2010), 3141. 
[11] 
D. Donoho, Compressed sensing, IEEE Trans. on Information Theory, 52 (2006), 12891306. doi: 10.1109/TIT.2006.871582. 
[12] 
M. Fornasier and H. Rauhut, Recovery algorithms for vectorvalued data with joint sparsity constraints, SIAM J. Numer. Anal., 46 (2008), 577613. doi: 10.1137/0606668909. 
[13] 
H. Gao, J. F. Cai, Z. Shen and H. Zhao, Robust principal component analysisbased fourdimensional computed tomography, Physics in Medicine and Biology, 56 (2011), 3181. doi: 10.1088/00319155/56/11/002. 
[14] 
R. Glowinski and P. Le Tallec, "Augmented Lagrangian and Operator Splitting Methods in Nonlinear Mechanics," SIAM Studies in Applied Mathematics, 9, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1989. doi: 10.1137/1.9781611970838. 
[15] 
T. Goldstein and S. Osher, The split Bregman method for L1regularized problems, SIAM J. Imaging Sci., 2 (2009), 323343. doi: 10.1137/080725891. 
[16] 
H. Jiang, Chengbo Li, Raziel HaimiCohen, Paul Wilford and Yin Zhang, Scalable video coding using compressive sensing, Bell Labs Technical Journal, 16 (2012). 
[17] 
H. Jiang, B. Mathews and P. Wilford, Compressive sensing for sound localization in wireless sensor network, accepted for presentation at SENSORNET2012, The First International Conference on Sensor Networks, February 2426, Rome, Italy, 2012. 
[18] 
H. Jiang, Z. Shen, W. Deng and P. Wilford, Adaptive low rank and sparse decomposition in compressive sensing of surveillance video, submitted, 2011. 
[19] 
C. Li, H. Jiang, P. A., Wilford and Y. Zhang, Video coding using compressive sensing for wireless communications, IEEE Wireless Communications and Networking Conference (WCNC), (2011), 20772082. doi: 10.1109/WCNC.2011.5779474. 
[20] 
V. Mahadevan and N. Vasconcelos, Spatiotemporal saliency in highly dynamic scenes, IEEE Trans. on Pattern Analysis and Machine Intelligence, 32 (2010), 171177. doi: 10.1109/TPAMI.2009.112. 
[21] 
M. Piccardi, Background subtraction techniques: A review, IEEE International Conference on Systems, Man and Cybernetics, 4 (2004), 30993104. 
[22] 
A. Ron and Z. Shen, Affine systems in $L_2(R^d)$: The analysis of the analysis operator, Journal of Functional Analysis, 148 (1997), 408447. doi: 10.1006/jfan.1996.3079. 
[23] 
M. Rudelson and R. Vershynin, On sparse reconstruction from Fourier and Gaussian measurements, Communications on Pure and Applied Mathematics, 61 (2008), 10251045. doi: 10.1002/cpa.20227. 
[24] 
Z. Shen, Wavelet frames and image restorations, "Proceedings of the International Congress of Mathematicians," IV (ed. Rajendra Bhatia), Hindustan Book Agency, New Delhi, (2010), 28342863. 
[25] 
C. Stauffer and W. E. L Grimson, Adaptive background mixture models for realtime tracking, Computer Vision and Pattern Recognition, 2 (1999), 252258. 
[26] 
E. Sutter, The Fast $m$Transform: A fast computation of crosscorrelations with binary $m$sequences, SIAM J. Comput., 20 (1991), 686694. doi: 10.1137/0220043. 
[27] 
, EC Funded CAVIAR project/IST 2001 37540,, 2003. Available from: \url{http://homepages.inf.ed.ac.uk/rbf/CAVIAR/}., (). 
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