American Institute of Mathematical Sciences

Advanced
August  2012, 6(3): 531-546. doi: 10.3934/ipi.2012.6.531

Non rigid geometric distortions correction - Application to atmospheric turbulence stabilization

Yu Mao 1, and  Jérôme Gilles 2,

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

Received  July 2011 Revised  January 2012 Published  September 2012

A novel approach is presented to recover an image degraded by atmospheric turbulence. Given a sequence of frames affected by turbulence, we construct a variational model to characterize the static image. The optimization problem is solved by Bregman Iteration and the operator splitting method. Our algorithm is simple, efficient, and can be easily generalized for different scenarios.
Keywords: optical flow, Bregman iterations., Turbulence restoration, nonlocal total variation.
Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C3.
Citation: Yu Mao, Jérôme Gilles. Non rigid geometric distortions correction - Application to atmospheric turbulence stabilization. Inverse Problems & Imaging, 2012, 6 (3) : 531-546. doi: 10.3934/ipi.2012.6.531
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.  doi: 10.1109/TIP.2009.2031231.  Google Scholar

[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).   Google Scholar

[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.  doi: 10.1006/cviu.1996.0006.  Google Scholar

[4]

J. Y. Bouguet, "Pyramidal Implementation of the Lucas Kanade Feature Tracker Description of the Algorithm," Intel Corporation Microprocessor Research Labs,, 2000. Available from: , ().   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[7]

J. F. Cai, S. Osher and Z. Shen, Split Bregman methods and frame based image restoration,, Multiscale Modeling and Simulation, 8 (2009), 337.   Google Scholar

[8]

T. F. Chan and C. K. Wong, Convergence of the alternating minimization algorithm for blind deconvolution,, Linear Algebra Appl., 316 (2000), 259.  doi: 10.1016/S0024-3795(00)00141-5.  Google Scholar

[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.  doi: 10.1002/ima.20041.  Google Scholar

[10]

P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting,, Multiscale Model Sim., 4 (2005), 1168.   Google Scholar

[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, (2001).   Google Scholar

[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).   Google Scholar

[13]

G. Gilboa and S. Osher, Nonlocal operators with applications to image processing,, Multiscale Model Sim., 7 (2008), 1005.   Google Scholar

[14]

J. Gilles, T. Dagobert and C. De Franchis, Atmospheric turbulence restoration by diffeomorphic image registration and blind deconvolution,, in, (2008).   Google Scholar

[15]

D. Goldfarb and W. Yin, Parametric maximum flow algorithms for fast total variation minimization,, SIAM J. Sci. Comput., 31 (2009), 3712.  doi: 10.1137/070706318.  Google Scholar

[16]

T. Goldstein and S. Osher, The split Bregman method for L1 regularized problems,, SIAM Journal on Imaging Sciences, 2 (2009), 323.   Google Scholar

[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.  doi: 10.1002/ima.20040.  Google Scholar

[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).   Google Scholar

[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, (2007).   Google Scholar

[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.   Google Scholar

[21]

P. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators,, SIAM Journal on Numerical Analysis, 16 (1979), 964.  doi: 10.1137/0716071.  Google Scholar

[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.  doi: 10.1109/TIP.2009.2039660.  Google Scholar

[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.   Google Scholar

[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.  doi: 10.1016/0022-247X(79)90234-8.  Google Scholar

[25]

L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms,, Physica D: Nonlinear Phenomena, 60 (1992), 259.  doi: 10.1016/0167-2789(92)90242-F.  Google Scholar

[26]

D. Sun, S. Roth, J. Lewis and M. J. Black, "Learning Optical Flow,", Computer Vision-ECCV, (2008).   Google Scholar

[27]

M. Tahtali, A. Lambert and D. Fraser, "Self-tuning Kalman Filter Estimation of Atmospheric Warp,", Proceedings of SPIE, (2008).   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[30]

X. Zhu and P. Milanfar, "Image Reconstruction from Videos Distorted by Atmospheric Turbulence,", SPIE Electronic Imaging, (7543).   Google Scholar

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.  doi: 10.1109/TIP.2009.2031231.  Google Scholar

[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).   Google Scholar

[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.  doi: 10.1006/cviu.1996.0006.  Google Scholar

[4]

J. Y. Bouguet, "Pyramidal Implementation of the Lucas Kanade Feature Tracker Description of the Algorithm," Intel Corporation Microprocessor Research Labs,, 2000. Available from: , ().   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[7]

J. F. Cai, S. Osher and Z. Shen, Split Bregman methods and frame based image restoration,, Multiscale Modeling and Simulation, 8 (2009), 337.   Google Scholar

[8]

T. F. Chan and C. K. Wong, Convergence of the alternating minimization algorithm for blind deconvolution,, Linear Algebra Appl., 316 (2000), 259.  doi: 10.1016/S0024-3795(00)00141-5.  Google Scholar

[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.  doi: 10.1002/ima.20041.  Google Scholar

[10]

P. L. Combettes and V. R. Wajs, Signal recovery by proximal forward-backward splitting,, Multiscale Model Sim., 4 (2005), 1168.   Google Scholar

[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, (2001).   Google Scholar

[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).   Google Scholar

[13]

G. Gilboa and S. Osher, Nonlocal operators with applications to image processing,, Multiscale Model Sim., 7 (2008), 1005.   Google Scholar

[14]

J. Gilles, T. Dagobert and C. De Franchis, Atmospheric turbulence restoration by diffeomorphic image registration and blind deconvolution,, in, (2008).   Google Scholar

[15]

D. Goldfarb and W. Yin, Parametric maximum flow algorithms for fast total variation minimization,, SIAM J. Sci. Comput., 31 (2009), 3712.  doi: 10.1137/070706318.  Google Scholar

[16]

T. Goldstein and S. Osher, The split Bregman method for L1 regularized problems,, SIAM Journal on Imaging Sciences, 2 (2009), 323.   Google Scholar

[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.  doi: 10.1002/ima.20040.  Google Scholar

[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).   Google Scholar

[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, (2007).   Google Scholar

[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.   Google Scholar

[21]

P. Lions and B. Mercier, Splitting algorithms for the sum of two nonlinear operators,, SIAM Journal on Numerical Analysis, 16 (1979), 964.  doi: 10.1137/0716071.  Google Scholar

[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.  doi: 10.1109/TIP.2009.2039660.  Google Scholar

[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.   Google Scholar

[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.  doi: 10.1016/0022-247X(79)90234-8.  Google Scholar

[25]

L. I. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms,, Physica D: Nonlinear Phenomena, 60 (1992), 259.  doi: 10.1016/0167-2789(92)90242-F.  Google Scholar

[26]

D. Sun, S. Roth, J. Lewis and M. J. Black, "Learning Optical Flow,", Computer Vision-ECCV, (2008).   Google Scholar

[27]

M. Tahtali, A. Lambert and D. Fraser, "Self-tuning Kalman Filter Estimation of Atmospheric Warp,", Proceedings of SPIE, (2008).   Google Scholar

[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.   Google Scholar

[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.   Google Scholar

[30]

X. Zhu and P. Milanfar, "Image Reconstruction from Videos Distorted by Atmospheric Turbulence,", SPIE Electronic Imaging, (7543).   Google Scholar

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