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Bayesian image restoration for mosaic active imaging
1. | LTCI, CNRS UMR5141, Institut Mines-Télécom, Télécom ParisTech, Paris, France |
2. | IMT, CNRS UMR5219, Université de Toulouse, Toulouse, France |
3. | ONERA - The French Aerospace Lab, F-31055 Toulouse, France, France |
References:
[1] |
J. Bect, L. Blanc-Féraud, G. Aubert and A. Chambolle, A L1-unified variational framework for image restoration, in Computer Vision - ECCV 2004, Lecture Notes in Computer Science, 3024, Springer-Verlag, Berlin Heidelberg, 2004, 1-13. |
[2] |
D. Bertsekas, Nonlinear Programming, 2nd edition, Athena Scientific, 2003. |
[3] |
Y. Boykov and V. Kolmogorov, An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision, Pattern Analysis And Machine Intelligence, 26 (2004), 1124-1137.
doi: 10.1109/TPAMI.2004.60. |
[4] |
A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, 20 (2004), 89-97. |
[5] |
A. Chambolle, Total variation minimization and a class of binary MRF models, in Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in Computer Science, Vol. 3757, Springer, 2005, 136-152.
doi: 10.1007/11585978_10. |
[6] |
A. Chambolle and J. Darbon, On total variation minimization and surface evolution using parametric maximum flows, International Journal of Computer Vision, 84 (2009), 288-307.
doi: 10.1007/s11263-009-0238-9. |
[7] |
A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging, Journal of Mathematical Imaging and Vision, 40 (2011), 120-145.
doi: 10.1007/s10851-010-0251-1. |
[8] |
T. Chan and J. Shen, Variational image inpainting, Communications in Pure and Applied Math., 58 (2005), 579-619.
doi: 10.1002/cpa.20075. |
[9] |
F. Chassat, Optical Propagation through Atmospheric Turbulence: Moral Study and Application of Anisoplanatism in Adaptive Optics, PhD thesis, University of Paris Sud, 1992. |
[10] |
R. R. Coifman and A. Sowa, Combining the calculus of variations and wavelets for image enhancement, Applied and Computational Harmonic Analysis, 9 (2000), 1-18.
doi: 10.1006/acha.2000.0299. |
[11] |
J. Darbon and M. Sigelle, Image restoration with discrete constrained total variation. I. Fast and exact optimization, Journal of Mathematical Imaging and Vision, 26 (2006), 261-276.
doi: 10.1007/s10851-006-8803-0. |
[12] |
G. Demoment, Image reconstruction and restoration: Overview of common estimation structures and problems, IEEE, Transactions on Acoustics, Speech and Signal Processing, 37 (1989), 2024-2036.
doi: 10.1109/29.45551. |
[13] |
M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, Springer, New York, 2010.
doi: 10.1007/978-1-4419-7011-4. |
[14] |
R. Fante, Electromagnetic beam propagation in turbulent media, Proceedings of the IEEE, 63 (1975), 1669-1692.
doi: 10.1109/PROC.1975.10035. |
[15] |
D. Fried, Optical resolution through a randomly inhomogeneous medium for very long and very short exposures, Journal of the Optical Society of America, 56 (1966), 1372-1379.
doi: 10.1364/JOSA.56.001372. |
[16] |
D. Greig, B. Porteous and A. Seheult, Exact maximum a posteriori estimation for binary images, Journal of the Royal Statistical Society, 51 (1989), 271-279. |
[17] |
D. Hamoir, Procédé et système d'imagerie active à champ large: Method and system for active imaging with a large field, Patent WO 2010119225, 2010. |
[18] |
L. Hespel, M.-T. Velluet, A. Bonnefois, N. Rivière, M. Fraces, D. Hamoir, B. Tanguy, B. Duchenne and J. Isbert, Comparison of a physics-based BIL simulator with experiments, in International Symposium on Photoelectronic Detection and Imaging, Society of Photo-Optical Instrumentation Engineers, 2009, 73822T-73822T-10. |
[19] |
J. Kiefer, Sequential minimax search for a maximum, Proceedings of the American Mathematical Society, 4 (1953), 502-506.
doi: 10.1090/S0002-9939-1953-0055639-3. |
[20] |
A. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Doklady Akademii Nauk SSSR, 66 (1949), 825; English translation in Turbulence: Classic Papers on Statistical Theory (eds. S. K. Friedlander and L. Topper), Interscience Publishers, Inc., New York, 1961, 151. |
[21] |
V. Kolmogorov and R. Zabih, What energy functions can be minimized via graph cuts?, Pattern Analysis And Machine Intelligence, 26 (2004), 147-159.
doi: 10.1109/TPAMI.2004.1262177. |
[22] |
F. Luisier, T. Blu and M. Unser, Image denoising in mixed Poisson-Gaussian noise, IEEE Transactions on Image Processing, 20 (2011), 696-708.
doi: 10.1109/TIP.2010.2073477. |
[23] |
F. Malgouyres and F. Guichard, Edge direction preserving image zooming: A mathematical and numerical analysis, SIAM Journal on Numerical Analysis, 39 (2001), 1-37.
doi: 10.1137/S0036142999362286. |
[24] |
Y. Mao and J. Gilles, Non rigid geometric distortions correction - Application to atmospheric turbulence stabilization, Inverse Problems and Imaging, 6 (2012), 531-546.
doi: 10.3934/ipi.2012.6.531. |
[25] |
Y. Meyer, Oscillating Patterns in Image Processing and in Some Nonlinear Evolution Equations, The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures, University Lecture Series, 22, AMS, Providence, RI, 2001. |
[26] |
M. Mäkitalo and A. Foi, Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise, IEEE Transactions on Image Processing, 22 (2013), 91-103.
doi: 10.1109/TIP.2012.2202675. |
[27] |
M. Nikolova, Local strong homogeneity of a regularized estimator, SIAM Journal of Applied Mathematics, 61 (2000), 633-658.
doi: 10.1137/S0036139997327794. |
[28] |
J. Picard and H. Ratliff, Minimum cuts and related problems, Networks, 5 (1975), 357-370.
doi: 10.1002/net.3230050405. |
[29] |
N. Rivière, L. Hespel, M.-T. Velluet, Y.-M. Frédéric, P. Barillot and F. Hélias, Modeling of an active burst illumination imaging system: Comparison between experimental and modelled 3d scene, in Society of Photo-Optical Instrumentation Engineers, International Symposium on Photoelectronic Detection and Imaging, Vol. 7382, 2010, 783509-783509-11.
doi: 10.1117/12.864694. |
[30] |
F. Roddier, The effects of atmospheric turbulence in optical astronomy, Progress in Optics, 19 (1981), 281-376.
doi: 10.1016/S0079-6638(08)70204-X. |
[31] |
L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
show all references
References:
[1] |
J. Bect, L. Blanc-Féraud, G. Aubert and A. Chambolle, A L1-unified variational framework for image restoration, in Computer Vision - ECCV 2004, Lecture Notes in Computer Science, 3024, Springer-Verlag, Berlin Heidelberg, 2004, 1-13. |
[2] |
D. Bertsekas, Nonlinear Programming, 2nd edition, Athena Scientific, 2003. |
[3] |
Y. Boykov and V. Kolmogorov, An experimental comparison of min-cut/max-flow algorithms for energy minimization in vision, Pattern Analysis And Machine Intelligence, 26 (2004), 1124-1137.
doi: 10.1109/TPAMI.2004.60. |
[4] |
A. Chambolle, An algorithm for total variation minimization and applications, Journal of Mathematical Imaging and Vision, 20 (2004), 89-97. |
[5] |
A. Chambolle, Total variation minimization and a class of binary MRF models, in Energy Minimization Methods in Computer Vision and Pattern Recognition, Lecture Notes in Computer Science, Vol. 3757, Springer, 2005, 136-152.
doi: 10.1007/11585978_10. |
[6] |
A. Chambolle and J. Darbon, On total variation minimization and surface evolution using parametric maximum flows, International Journal of Computer Vision, 84 (2009), 288-307.
doi: 10.1007/s11263-009-0238-9. |
[7] |
A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging, Journal of Mathematical Imaging and Vision, 40 (2011), 120-145.
doi: 10.1007/s10851-010-0251-1. |
[8] |
T. Chan and J. Shen, Variational image inpainting, Communications in Pure and Applied Math., 58 (2005), 579-619.
doi: 10.1002/cpa.20075. |
[9] |
F. Chassat, Optical Propagation through Atmospheric Turbulence: Moral Study and Application of Anisoplanatism in Adaptive Optics, PhD thesis, University of Paris Sud, 1992. |
[10] |
R. R. Coifman and A. Sowa, Combining the calculus of variations and wavelets for image enhancement, Applied and Computational Harmonic Analysis, 9 (2000), 1-18.
doi: 10.1006/acha.2000.0299. |
[11] |
J. Darbon and M. Sigelle, Image restoration with discrete constrained total variation. I. Fast and exact optimization, Journal of Mathematical Imaging and Vision, 26 (2006), 261-276.
doi: 10.1007/s10851-006-8803-0. |
[12] |
G. Demoment, Image reconstruction and restoration: Overview of common estimation structures and problems, IEEE, Transactions on Acoustics, Speech and Signal Processing, 37 (1989), 2024-2036.
doi: 10.1109/29.45551. |
[13] |
M. Elad, Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing, Springer, New York, 2010.
doi: 10.1007/978-1-4419-7011-4. |
[14] |
R. Fante, Electromagnetic beam propagation in turbulent media, Proceedings of the IEEE, 63 (1975), 1669-1692.
doi: 10.1109/PROC.1975.10035. |
[15] |
D. Fried, Optical resolution through a randomly inhomogeneous medium for very long and very short exposures, Journal of the Optical Society of America, 56 (1966), 1372-1379.
doi: 10.1364/JOSA.56.001372. |
[16] |
D. Greig, B. Porteous and A. Seheult, Exact maximum a posteriori estimation for binary images, Journal of the Royal Statistical Society, 51 (1989), 271-279. |
[17] |
D. Hamoir, Procédé et système d'imagerie active à champ large: Method and system for active imaging with a large field, Patent WO 2010119225, 2010. |
[18] |
L. Hespel, M.-T. Velluet, A. Bonnefois, N. Rivière, M. Fraces, D. Hamoir, B. Tanguy, B. Duchenne and J. Isbert, Comparison of a physics-based BIL simulator with experiments, in International Symposium on Photoelectronic Detection and Imaging, Society of Photo-Optical Instrumentation Engineers, 2009, 73822T-73822T-10. |
[19] |
J. Kiefer, Sequential minimax search for a maximum, Proceedings of the American Mathematical Society, 4 (1953), 502-506.
doi: 10.1090/S0002-9939-1953-0055639-3. |
[20] |
A. Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Doklady Akademii Nauk SSSR, 66 (1949), 825; English translation in Turbulence: Classic Papers on Statistical Theory (eds. S. K. Friedlander and L. Topper), Interscience Publishers, Inc., New York, 1961, 151. |
[21] |
V. Kolmogorov and R. Zabih, What energy functions can be minimized via graph cuts?, Pattern Analysis And Machine Intelligence, 26 (2004), 147-159.
doi: 10.1109/TPAMI.2004.1262177. |
[22] |
F. Luisier, T. Blu and M. Unser, Image denoising in mixed Poisson-Gaussian noise, IEEE Transactions on Image Processing, 20 (2011), 696-708.
doi: 10.1109/TIP.2010.2073477. |
[23] |
F. Malgouyres and F. Guichard, Edge direction preserving image zooming: A mathematical and numerical analysis, SIAM Journal on Numerical Analysis, 39 (2001), 1-37.
doi: 10.1137/S0036142999362286. |
[24] |
Y. Mao and J. Gilles, Non rigid geometric distortions correction - Application to atmospheric turbulence stabilization, Inverse Problems and Imaging, 6 (2012), 531-546.
doi: 10.3934/ipi.2012.6.531. |
[25] |
Y. Meyer, Oscillating Patterns in Image Processing and in Some Nonlinear Evolution Equations, The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures, University Lecture Series, 22, AMS, Providence, RI, 2001. |
[26] |
M. Mäkitalo and A. Foi, Optimal inversion of the generalized Anscombe transformation for Poisson-Gaussian noise, IEEE Transactions on Image Processing, 22 (2013), 91-103.
doi: 10.1109/TIP.2012.2202675. |
[27] |
M. Nikolova, Local strong homogeneity of a regularized estimator, SIAM Journal of Applied Mathematics, 61 (2000), 633-658.
doi: 10.1137/S0036139997327794. |
[28] |
J. Picard and H. Ratliff, Minimum cuts and related problems, Networks, 5 (1975), 357-370.
doi: 10.1002/net.3230050405. |
[29] |
N. Rivière, L. Hespel, M.-T. Velluet, Y.-M. Frédéric, P. Barillot and F. Hélias, Modeling of an active burst illumination imaging system: Comparison between experimental and modelled 3d scene, in Society of Photo-Optical Instrumentation Engineers, International Symposium on Photoelectronic Detection and Imaging, Vol. 7382, 2010, 783509-783509-11.
doi: 10.1117/12.864694. |
[30] |
F. Roddier, The effects of atmospheric turbulence in optical astronomy, Progress in Optics, 19 (1981), 281-376.
doi: 10.1016/S0079-6638(08)70204-X. |
[31] |
L. Rudin, S. Osher and E. Fatemi, Nonlinear total variation based noise removal algorithms, Physica D, 60 (1992), 259-268.
doi: 10.1016/0167-2789(92)90242-F. |
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