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A fast $\ell_1$-solver and its applications to robust face recognition
1. | Sun Yat-sen Univeristy, NO.135 Xiguangxi Road, Guangzhou 510275, China, China, China |
2. | Curtin University, GPO Box U1987, Perth, WA 6845, Australia, Australia |
3. | Qufu Normal University, Rizhao 276800, Shandong, China |
References:
[1] |
M. S. Bartlett, J. R. Movellan and T. J. Sejnowski, Face recognition by independent component analysis,, IEEE Transactions on Neural Networks, 6 (2002), 1450.
doi: 10.1109/TNN.2002.804287. |
[2] |
M. S. Bazaraa and C. M. Shetty, "Nonlinear Programming: Theory and Algorithms,", John Wiley & Sons, (1979).
|
[3] |
P. N. Belhumeur, J. Hespanha and D. J. Kriegman, Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 7 (1997), 711.
doi: 10.1109/34.598228. |
[4] |
E. van den Berg and M. P. Friedlander, Probing the Pareto frontier for basis pursuit solutions,, SIAM Journal on Scientific Computing, 31 (): 890.
|
[5] |
S. Boyd and L. Vandenberghe, "Convex Optimization,", Cambridge University Press, (2004).
|
[6] |
R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, A limited memory algorithm for bound constrained optimization,, SIAM Journal on Scientific Computing, 16 (1995), 1190.
doi: 10.1137/0916069. |
[7] |
E. J. Candès, J. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,, IEEE Transactions on Information Theory, 52 (2006), 489.
doi: 10.1109/TIT.2005.862083. |
[8] |
E. J. Candès and M. Wakin, An introduction to compressive sampling,, IEEE Signal Processing Magazine, 2 (2008), 21. Google Scholar |
[9] |
E. J. Candès and J. Romberg, The code package $\mathcall_1$ -magic:, , (). Google Scholar |
[10] |
R. Chellappa, P. Sinha and P. J. Phillips, Face recognition by computers and humans,, Computer, 2 (2010), 46.
doi: 10.1109/MC.2010.37. |
[11] |
I. Dagher and R. Nachar, Face recognition using IPCA-ICA algorithm,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6 (2006), 996.
doi: 10.1109/TPAMI.2006.118. |
[12] |
D. L. Donoho, Compressed sensing,, IEEE Transactions on Information Theory, 52 (2006), 1289.
doi: 10.1109/TIT.2006.871582. |
[13] |
M. A. T. Figueiredo, R. D. Nowak and S. J. Wright, Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,, Selected Topics in IEEE Journal of Signal Processing, 4 (2007), 586.
doi: 10.1109/JSTSP.2007.910281. |
[14] |
J.-J. Fuchs, On sparse representations in arbitrary redundant bases,, IEEE Transactions on Information Theory, 50 (2004), 1341.
doi: 10.1109/TIT.2004.828141. |
[15] |
J.-J. Fuchs, Recovery of exact sparse representations in the presence of noise,, Proceedings of the IEEE International Conference on Acoustics, 2 (2004). Google Scholar |
[16] |
J.-J. Fuchs, Fast implementation of a $mathcall_1$-$\mathcall_1$ regularized sparse representations algorithm,, Proceedings of the IEEE International Conference on Acoustics, (2009), 3329. Google Scholar |
[17] |
X. He, S. Yan, Y. Hu, P. Niyogi and H. Zhang, Face recognition using laplacianfaces,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 3 (2005), 328. Google Scholar |
[18] |
K. Koh, S.-J. Kim and S. Boyd, The code package $\mathcall_1-\mathcall_s$:, , (). Google Scholar |
[19] |
D. D. Lee and H. S. Seung, Learning the parts of objects by non-negative matrix factorization,, Nature, 6755 (1999), 788. Google Scholar |
[20] |
S. Z. Li, X. Hou, H. Zhang and Q. Cheng, Learning spatially localized, parts-based representation,, Proceedings of 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'01), 1 (2001). Google Scholar |
[21] |
P. J. Phillips, P. J. Flynn, T. Scruggs, K. W. Bowyer, J. Chang, K. Hoffman, J. Marques, J. Min and W. Worek, Overview of the face recognition grand challenge,, Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), 1 (2005), 947. Google Scholar |
[22] |
P. J. Phillips, P. J. Flynn, T. Scruggs, K. W. Bowyer and W. Worek, Preliminary face recognition grand challenge results,, The 7th International Conference on Automatic Face and Gesture Recognition (AFGR'06), (2006), 15. Google Scholar |
[23] |
J. Lu, K. N. Plataniotis and A. N. Venetsanopoulos, Face recognition using LDA-based algorithms,, IEEE Transactions on Neural Networks, 1 (2003), 195. Google Scholar |
[24] |
O. L. Mangasarian and R. R. Meyer, Nonlinear perturbation of linear programs,, SIAM Journal on Control and Optimization, 17 (1979), 745.
doi: 10.1137/0317052. |
[25] |
A. M. Martinez and A. C. Kak, PCA versus LDA,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2 (2001), 228.
doi: 10.1109/34.908974. |
[26] |
A. J. O'Toole, P. J. Phillips and A. Narvekar, FRVT 2002 evaluation report,, NISTIR TR-6965, (2003). Google Scholar |
[27] |
P. J. Phillips, W. T. Scruggs, A. J. O'Toole, P. J. Flynn, K. W. Bowyer, C. L. Schott and M. Sharpe, FRVT 2006 and ICE 2006 large-scale experimental results,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 5 (2010), 831.
doi: 10.1109/TPAMI.2009.59. |
[28] |
M. Turk and A. Pentland, Eigenfaces for recognition,, Journal of Cognitive Neuroscience, 1 (1991), 71.
doi: 10.1162/jocn.1991.3.1.71. |
[29] |
H.-Y. Wang and X.-J. Wu, Weighted PCA space and its application in face recognition,, Proceedings of 2005 International Conference on Machine Learning and Cybernetics, 7 (2005), 4522. Google Scholar |
[30] |
X.-G. Wang and X.-O. Tang, A unified framework for subspace face recognition,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 9 (2004), 1222.
doi: 10.1109/TPAMI.2004.57. |
[31] |
Y. Wang, G. Zhou, L. Caccetta and W. Liu, An alternative Lagrange-dual based algorithm for sparse signal reconstruction,, IEEE Transactions on Signal Processing, 4 (2011), 1895.
doi: 10.1109/TSP.2010.2103066. |
[32] |
J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry and Yi Ma, Robust face recognition via sparse representation,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2 (2009), 210.
doi: 10.1109/TPAMI.2008.79. |
[33] |
S. J. Wright, R. D. Nowak and M. Figueiredo, Sparse reconstruction by separable approximation,, IEEE Transactions on Signal Processing, 57 (2009), 2479.
doi: 10.1109/TSP.2009.2016892. |
[34] |
J. Yang and Y. Zhang, Alternating direction algorithms for $\mathcall_1$ problems in compressive sensing,, SIAM Journal on Scientific Computing, 33 (2011), 250.
doi: 10.1137/090777761. |
[35] |
S. Yan, D. Xu, B. Zhang, H.-J. Zhang, Q. Yang and S. Lin, Graph embedding and extensions: A general framework for dimensionality reduction,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1 (2007), 40.
doi: 10.1109/TPAMI.2007.250598. |
[36] |
W. Zhao, R. Chellappa, P. J. Phillips and A. Rosenfeld, Face recognition: A literature survey,, ACM Computing Surveys, 4 (2003), 399.
doi: 10.1145/954339.954342. |
show all references
References:
[1] |
M. S. Bartlett, J. R. Movellan and T. J. Sejnowski, Face recognition by independent component analysis,, IEEE Transactions on Neural Networks, 6 (2002), 1450.
doi: 10.1109/TNN.2002.804287. |
[2] |
M. S. Bazaraa and C. M. Shetty, "Nonlinear Programming: Theory and Algorithms,", John Wiley & Sons, (1979).
|
[3] |
P. N. Belhumeur, J. Hespanha and D. J. Kriegman, Eigenfaces vs. Fisherfaces: Recognition using class specific linear projection,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 7 (1997), 711.
doi: 10.1109/34.598228. |
[4] |
E. van den Berg and M. P. Friedlander, Probing the Pareto frontier for basis pursuit solutions,, SIAM Journal on Scientific Computing, 31 (): 890.
|
[5] |
S. Boyd and L. Vandenberghe, "Convex Optimization,", Cambridge University Press, (2004).
|
[6] |
R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, A limited memory algorithm for bound constrained optimization,, SIAM Journal on Scientific Computing, 16 (1995), 1190.
doi: 10.1137/0916069. |
[7] |
E. J. Candès, J. Romberg and T. Tao, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,, IEEE Transactions on Information Theory, 52 (2006), 489.
doi: 10.1109/TIT.2005.862083. |
[8] |
E. J. Candès and M. Wakin, An introduction to compressive sampling,, IEEE Signal Processing Magazine, 2 (2008), 21. Google Scholar |
[9] |
E. J. Candès and J. Romberg, The code package $\mathcall_1$ -magic:, , (). Google Scholar |
[10] |
R. Chellappa, P. Sinha and P. J. Phillips, Face recognition by computers and humans,, Computer, 2 (2010), 46.
doi: 10.1109/MC.2010.37. |
[11] |
I. Dagher and R. Nachar, Face recognition using IPCA-ICA algorithm,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6 (2006), 996.
doi: 10.1109/TPAMI.2006.118. |
[12] |
D. L. Donoho, Compressed sensing,, IEEE Transactions on Information Theory, 52 (2006), 1289.
doi: 10.1109/TIT.2006.871582. |
[13] |
M. A. T. Figueiredo, R. D. Nowak and S. J. Wright, Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,, Selected Topics in IEEE Journal of Signal Processing, 4 (2007), 586.
doi: 10.1109/JSTSP.2007.910281. |
[14] |
J.-J. Fuchs, On sparse representations in arbitrary redundant bases,, IEEE Transactions on Information Theory, 50 (2004), 1341.
doi: 10.1109/TIT.2004.828141. |
[15] |
J.-J. Fuchs, Recovery of exact sparse representations in the presence of noise,, Proceedings of the IEEE International Conference on Acoustics, 2 (2004). Google Scholar |
[16] |
J.-J. Fuchs, Fast implementation of a $mathcall_1$-$\mathcall_1$ regularized sparse representations algorithm,, Proceedings of the IEEE International Conference on Acoustics, (2009), 3329. Google Scholar |
[17] |
X. He, S. Yan, Y. Hu, P. Niyogi and H. Zhang, Face recognition using laplacianfaces,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 3 (2005), 328. Google Scholar |
[18] |
K. Koh, S.-J. Kim and S. Boyd, The code package $\mathcall_1-\mathcall_s$:, , (). Google Scholar |
[19] |
D. D. Lee and H. S. Seung, Learning the parts of objects by non-negative matrix factorization,, Nature, 6755 (1999), 788. Google Scholar |
[20] |
S. Z. Li, X. Hou, H. Zhang and Q. Cheng, Learning spatially localized, parts-based representation,, Proceedings of 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'01), 1 (2001). Google Scholar |
[21] |
P. J. Phillips, P. J. Flynn, T. Scruggs, K. W. Bowyer, J. Chang, K. Hoffman, J. Marques, J. Min and W. Worek, Overview of the face recognition grand challenge,, Proceedings of 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), 1 (2005), 947. Google Scholar |
[22] |
P. J. Phillips, P. J. Flynn, T. Scruggs, K. W. Bowyer and W. Worek, Preliminary face recognition grand challenge results,, The 7th International Conference on Automatic Face and Gesture Recognition (AFGR'06), (2006), 15. Google Scholar |
[23] |
J. Lu, K. N. Plataniotis and A. N. Venetsanopoulos, Face recognition using LDA-based algorithms,, IEEE Transactions on Neural Networks, 1 (2003), 195. Google Scholar |
[24] |
O. L. Mangasarian and R. R. Meyer, Nonlinear perturbation of linear programs,, SIAM Journal on Control and Optimization, 17 (1979), 745.
doi: 10.1137/0317052. |
[25] |
A. M. Martinez and A. C. Kak, PCA versus LDA,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2 (2001), 228.
doi: 10.1109/34.908974. |
[26] |
A. J. O'Toole, P. J. Phillips and A. Narvekar, FRVT 2002 evaluation report,, NISTIR TR-6965, (2003). Google Scholar |
[27] |
P. J. Phillips, W. T. Scruggs, A. J. O'Toole, P. J. Flynn, K. W. Bowyer, C. L. Schott and M. Sharpe, FRVT 2006 and ICE 2006 large-scale experimental results,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 5 (2010), 831.
doi: 10.1109/TPAMI.2009.59. |
[28] |
M. Turk and A. Pentland, Eigenfaces for recognition,, Journal of Cognitive Neuroscience, 1 (1991), 71.
doi: 10.1162/jocn.1991.3.1.71. |
[29] |
H.-Y. Wang and X.-J. Wu, Weighted PCA space and its application in face recognition,, Proceedings of 2005 International Conference on Machine Learning and Cybernetics, 7 (2005), 4522. Google Scholar |
[30] |
X.-G. Wang and X.-O. Tang, A unified framework for subspace face recognition,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 9 (2004), 1222.
doi: 10.1109/TPAMI.2004.57. |
[31] |
Y. Wang, G. Zhou, L. Caccetta and W. Liu, An alternative Lagrange-dual based algorithm for sparse signal reconstruction,, IEEE Transactions on Signal Processing, 4 (2011), 1895.
doi: 10.1109/TSP.2010.2103066. |
[32] |
J. Wright, A. Y. Yang, A. Ganesh, S. S. Sastry and Yi Ma, Robust face recognition via sparse representation,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2 (2009), 210.
doi: 10.1109/TPAMI.2008.79. |
[33] |
S. J. Wright, R. D. Nowak and M. Figueiredo, Sparse reconstruction by separable approximation,, IEEE Transactions on Signal Processing, 57 (2009), 2479.
doi: 10.1109/TSP.2009.2016892. |
[34] |
J. Yang and Y. Zhang, Alternating direction algorithms for $\mathcall_1$ problems in compressive sensing,, SIAM Journal on Scientific Computing, 33 (2011), 250.
doi: 10.1137/090777761. |
[35] |
S. Yan, D. Xu, B. Zhang, H.-J. Zhang, Q. Yang and S. Lin, Graph embedding and extensions: A general framework for dimensionality reduction,, IEEE Transactions on Pattern Analysis and Machine Intelligence, 1 (2007), 40.
doi: 10.1109/TPAMI.2007.250598. |
[36] |
W. Zhao, R. Chellappa, P. J. Phillips and A. Rosenfeld, Face recognition: A literature survey,, ACM Computing Surveys, 4 (2003), 399.
doi: 10.1145/954339.954342. |
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