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Alternating algorithms for total variation image reconstruction from random projections
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1. | Institute for Mathematics and Its Applications, University of Minnesota, 425 Lind Hall 207 Church Street SE, Minneapolis, MN 55455-0134, United States |
2. | Department of Mathematics, University of California Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095-1555, United States |
References:
[1] |
M. S. C. Almeida and L. B. Almeida, Blind and semi-blind deblurring of natural images, IEEE Transactions on Image Processing, 19 (2010), 36-52.
doi: 10.1109/TIP.2009.2031231. |
[2] |
M. Aubailly, M. A. Vorontsov, G. W. Carhat and M. T. Valley, "Automated Video Enhancement from a Stream of Atmospherically-Distorted Images: the Lucky-Region Fusion Approach," Proceedings of SPIE, 7463 (2009). |
[3] |
M. J. Black and P. Anandan, The robust estimation of multiple motions: Parametric and piecewise-smooth flow fields, Comput Vision and Image Understanding, 63 (1996), 75-104.
doi: 10.1006/cviu.1996.0006. |
[4] |
J. Y. Bouguet, "Pyramidal Implementation of the Lucas Kanade Feature Tracker Description of the Algorithm," Intel Corporation Microprocessor Research Labs, 2000. Available from: http://robots.stanford.edu/cs223b04/algo_tracking.pdf. |
[5] |
A. Buades, B. Coll and J. M. Morel, A review of image denoising algorithms, with a new one, Multiscale Model Sim, 4 (2005), 490-530. |
[6] |
J. F. Cai, S. Osher and Z. Shen, Linearized Bregman iterations for frame-based image deblurring, SIAM Journal on Imaging Sciences, 2 (2009), 226-252. |
[7] |
J. F. Cai, S. Osher and Z. Shen, Split Bregman methods and frame based image restoration, Multiscale Modeling and Simulation, 8 (2009), 337-369. |
[8] |
T. F. Chan and C. K. Wong, Convergence of the alternating minimization algorithm for blind deconvolution, Linear Algebra Appl., 316 (2000), 259-285.
doi: 10.1016/S0024-3795(00)00141-5. |
[9] |
T. F. Chan, A. M. Yip and F. E. Park, Simultaneous total variation image inpainting and blind deconvolution, International Journal of Imaging Systems and Technology, 15 (2005), 92-102.
doi: 10.1002/ima.20041. |
[10] |
P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model Sim., 4 (2005), 1168-1200. |
[11] |
D. Frakes, J. Monaco and M. Smith, "Suppression of Atmospheric Turbulence in Video Using an Adaptive Control Grid Interpolation Approach," Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 2001. |
[12] |
S. Gepshtein, A. Shteinman and B. Fishbain, "Restoration of Atmospheric Turbulent Video Containing Real Motion Using Rank Filtering and Elastic Image Registration," Proceedings of the Eusipco, 2004. |
[13] |
G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Model Sim., 7 (2008), 1005-1028. |
[14] |
J. Gilles, T. Dagobert and C. De Franchis, Atmospheric turbulence restoration by diffeomorphic image registration and blind deconvolution, in "Proceedings of Advanced Concepts for Intelligent Vision Systems,'' 2008. |
[15] |
D. Goldfarb and W. Yin, Parametric maximum flow algorithms for fast total variation minimization, SIAM J. Sci. Comput., 31 (2009), 3712-3743.
doi: 10.1137/070706318. |
[16] |
T. Goldstein and S. Osher, The split Bregman method for L1 regularized problems, SIAM Journal on Imaging Sciences, 2 (2009), 323-343. |
[17] |
L. He, A. Marquina and S. Osher, Blind deconvolution using TV regularization and Bregman iteration, International Journal of Imaging Systems and Technology, 15 (2005), 74-83.
doi: 10.1002/ima.20040. |
[18] |
M. Hirsch, S. Sra, B. Scholkopf and S. Harmeling, "Efficient Filter Flow for Space-variant Multiframe Blind Deconvolution," Computer Vision and Pattern Recognition Conference, 2010. |
[19] |
M. Lemaitre, "Etude de la Turbulence Atmosphérique en Vision Horizontale Lointaine et Restauration de Séquences Dégradées Dans le Visible et L'infrarouge,'' Ph. D Thesis, Université de Bourgogne, 2007. |
[20] |
D. Li, R. M. Mersereau and S. Simske, Atmospheric turbulence-degraded image restoration using principal components analysis, IEEE Geoscience and Remote Sensing Letters, 4 (2007), 340-344. |
[21] |
P. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM Journal on Numerical Analysis, 16 (1979), 964-979.
doi: 10.1137/0716071. |
[22] |
Y. Mao, B. P. Fahimian, S. Osher and J. Miao, Development and optimization of regularized tomographic reconstruction algorithms utilizing equally-sloped tomography, IEEE Transactions on Image Processing, 19 (2010), 1259-1268.
doi: 10.1109/TIP.2009.2039660. |
[23] |
S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin, An iterative regularization method for total variation-based image restoration, Multiscale Model Sim., 4 (2005), 460-489. |
[24] |
G. B. Passty, Ergodic convergence to a zero of the sum of monotone operators in Hilbert space, J. Math. Anal. Appl., 72 (1979), 383-390.
doi: 10.1016/0022-247X(79)90234-8. |
[25] |
L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[26] |
D. Sun, S. Roth, J. Lewis and M. J. Black, "Learning Optical Flow," Computer Vision-ECCV, 2008. |
[27] |
M. Tahtali, A. Lambert and D. Fraser, "Self-tuning Kalman Filter Estimation of Atmospheric Warp," Proceedings of SPIE, 2008. |
[28] |
X. Zhang, M. Burger, X. Bresson and S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction, SIAM Journal on Imaging Sciences, 3 (2010), 253-276. |
[29] |
X. Zhang, M. Burger and S. Osher, A unified primal-dual algorithm framework based on Bregman iteration, Journal of Scientific Computing, 46 (2010), 1-27. |
[30] |
X. Zhu and P. Milanfar, "Image Reconstruction from Videos Distorted by Atmospheric Turbulence," SPIE Electronic Imaging, Conference 7543 on Visual Information Processing and Communication, 2010. |
show all references
References:
[1] |
M. S. C. Almeida and L. B. Almeida, Blind and semi-blind deblurring of natural images, IEEE Transactions on Image Processing, 19 (2010), 36-52.
doi: 10.1109/TIP.2009.2031231. |
[2] |
M. Aubailly, M. A. Vorontsov, G. W. Carhat and M. T. Valley, "Automated Video Enhancement from a Stream of Atmospherically-Distorted Images: the Lucky-Region Fusion Approach," Proceedings of SPIE, 7463 (2009). |
[3] |
M. J. Black and P. Anandan, The robust estimation of multiple motions: Parametric and piecewise-smooth flow fields, Comput Vision and Image Understanding, 63 (1996), 75-104.
doi: 10.1006/cviu.1996.0006. |
[4] |
J. Y. Bouguet, "Pyramidal Implementation of the Lucas Kanade Feature Tracker Description of the Algorithm," Intel Corporation Microprocessor Research Labs, 2000. Available from: http://robots.stanford.edu/cs223b04/algo_tracking.pdf. |
[5] |
A. Buades, B. Coll and J. M. Morel, A review of image denoising algorithms, with a new one, Multiscale Model Sim, 4 (2005), 490-530. |
[6] |
J. F. Cai, S. Osher and Z. Shen, Linearized Bregman iterations for frame-based image deblurring, SIAM Journal on Imaging Sciences, 2 (2009), 226-252. |
[7] |
J. F. Cai, S. Osher and Z. Shen, Split Bregman methods and frame based image restoration, Multiscale Modeling and Simulation, 8 (2009), 337-369. |
[8] |
T. F. Chan and C. K. Wong, Convergence of the alternating minimization algorithm for blind deconvolution, Linear Algebra Appl., 316 (2000), 259-285.
doi: 10.1016/S0024-3795(00)00141-5. |
[9] |
T. F. Chan, A. M. Yip and F. E. Park, Simultaneous total variation image inpainting and blind deconvolution, International Journal of Imaging Systems and Technology, 15 (2005), 92-102.
doi: 10.1002/ima.20041. |
[10] |
P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model Sim., 4 (2005), 1168-1200. |
[11] |
D. Frakes, J. Monaco and M. Smith, "Suppression of Atmospheric Turbulence in Video Using an Adaptive Control Grid Interpolation Approach," Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, 2001. |
[12] |
S. Gepshtein, A. Shteinman and B. Fishbain, "Restoration of Atmospheric Turbulent Video Containing Real Motion Using Rank Filtering and Elastic Image Registration," Proceedings of the Eusipco, 2004. |
[13] |
G. Gilboa and S. Osher, Nonlocal operators with applications to image processing, Multiscale Model Sim., 7 (2008), 1005-1028. |
[14] |
J. Gilles, T. Dagobert and C. De Franchis, Atmospheric turbulence restoration by diffeomorphic image registration and blind deconvolution, in "Proceedings of Advanced Concepts for Intelligent Vision Systems,'' 2008. |
[15] |
D. Goldfarb and W. Yin, Parametric maximum flow algorithms for fast total variation minimization, SIAM J. Sci. Comput., 31 (2009), 3712-3743.
doi: 10.1137/070706318. |
[16] |
T. Goldstein and S. Osher, The split Bregman method for L1 regularized problems, SIAM Journal on Imaging Sciences, 2 (2009), 323-343. |
[17] |
L. He, A. Marquina and S. Osher, Blind deconvolution using TV regularization and Bregman iteration, International Journal of Imaging Systems and Technology, 15 (2005), 74-83.
doi: 10.1002/ima.20040. |
[18] |
M. Hirsch, S. Sra, B. Scholkopf and S. Harmeling, "Efficient Filter Flow for Space-variant Multiframe Blind Deconvolution," Computer Vision and Pattern Recognition Conference, 2010. |
[19] |
M. Lemaitre, "Etude de la Turbulence Atmosphérique en Vision Horizontale Lointaine et Restauration de Séquences Dégradées Dans le Visible et L'infrarouge,'' Ph. D Thesis, Université de Bourgogne, 2007. |
[20] |
D. Li, R. M. Mersereau and S. Simske, Atmospheric turbulence-degraded image restoration using principal components analysis, IEEE Geoscience and Remote Sensing Letters, 4 (2007), 340-344. |
[21] |
P. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators, SIAM Journal on Numerical Analysis, 16 (1979), 964-979.
doi: 10.1137/0716071. |
[22] |
Y. Mao, B. P. Fahimian, S. Osher and J. Miao, Development and optimization of regularized tomographic reconstruction algorithms utilizing equally-sloped tomography, IEEE Transactions on Image Processing, 19 (2010), 1259-1268.
doi: 10.1109/TIP.2009.2039660. |
[23] |
S. Osher, M. Burger, D. Goldfarb, J. Xu and W. Yin, An iterative regularization method for total variation-based image restoration, Multiscale Model Sim., 4 (2005), 460-489. |
[24] |
G. B. Passty, Ergodic convergence to a zero of the sum of monotone operators in Hilbert space, J. Math. Anal. Appl., 72 (1979), 383-390.
doi: 10.1016/0022-247X(79)90234-8. |
[25] |
L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D: Nonlinear Phenomena, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
[26] |
D. Sun, S. Roth, J. Lewis and M. J. Black, "Learning Optical Flow," Computer Vision-ECCV, 2008. |
[27] |
M. Tahtali, A. Lambert and D. Fraser, "Self-tuning Kalman Filter Estimation of Atmospheric Warp," Proceedings of SPIE, 2008. |
[28] |
X. Zhang, M. Burger, X. Bresson and S. Osher, Bregmanized nonlocal regularization for deconvolution and sparse reconstruction, SIAM Journal on Imaging Sciences, 3 (2010), 253-276. |
[29] |
X. Zhang, M. Burger and S. Osher, A unified primal-dual algorithm framework based on Bregman iteration, Journal of Scientific Computing, 46 (2010), 1-27. |
[30] |
X. Zhu and P. Milanfar, "Image Reconstruction from Videos Distorted by Atmospheric Turbulence," SPIE Electronic Imaging, Conference 7543 on Visual Information Processing and Communication, 2010. |
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