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Iterated quasi-reversibility method applied to elliptic and parabolic data completion problems
Ghost imaging in the random paraxial regime
1. | Laboratoire de Probabilités et Modèles Aléatoires & Laboratoire Jacques-Louis Lions, Université Paris Diderot, 75205 Paris Cedex 13 |
References:
[1] |
D. G. Alfaro Vigo, J.-P. Fouque, J. Garnier and A. Nachbin, Robustness of time reversal for waves in time-dependent random media, Stochastic Process. Appl., 113 (2004), 289-313.
doi: 10.1016/j.spa.2004.04.002. |
[2] |
G. Bal and L. Ryzhik, Stability of time reversed waves in changing media, Disc. Cont. Dyn. Syst. A, 12 (2005), 793-815.
doi: 10.3934/dcds.2005.12.793. |
[3] |
P. Blomgren, G. Papanicolaou and H. Zhao, Super-resolution in time-reversal acoustics, J. Acoust. Soc. Amer., 111 (2002), 230-248.
doi: 10.1121/1.1421342. |
[4] |
M. Born and E. Wolf, Principles of Optics, Cambridge University Press, Cambridge, 1999.
doi: 10.1017/CBO9781139644181. |
[5] |
J. Cheng, Ghost imaging through turbulent atmosphere, Opt. Express, 17 (2009), 7916-7921.
doi: 10.1364/OE.17.007916. |
[6] |
M. Fink, Time reversed acoustics, Scientific American, 281 (1999), 91-97. |
[7] |
J.-P. Fouque, J. Garnier, G. Papanicolaou and K. Sølna, Wave Propagation and Time Reversal in Randomly Layered Media, Springer, New York, 2007.
doi: 10.1007/978-0-387-49808-9_4. |
[8] |
J. Garnier and G. Papanicolaou, Pulse propagation and time reversal in random waveguides, SIAM J. Appl. Math., 67 (2007), 1718-1739.
doi: 10.1137/060659235. |
[9] |
J. Garnier and G. Papanicolaou, Passive sensor imaging using cross correlations of noisy signals in a scattering medium, SIAM J. Imaging Sciences, 2 (2009), 396-437.
doi: 10.1137/080723454. |
[10] |
J. Garnier and G. Papanicolaou, Resolution analysis for imaging with noise, Inverse Problems, 26 (2010), 074001, 22pp.
doi: 10.1088/0266-5611/26/7/074001. |
[11] |
J. Garnier and G. Papanicolaou, Fluctuation theory of ambient noise imaging, CRAS Geoscience, 343 (2011), 502-511.
doi: 10.1016/j.crte.2011.01.004. |
[12] |
J. Garnier and K. Sølna, Coupled paraxial wave equations in random media in the white-noise regime, Ann. Appl. Probab., 19 (2009), 318-346.
doi: 10.1214/08-AAP543. |
[13] |
J. Garnier and K. Sølna, Fourth-moment analysis for wave propagation in the white-noise paraxial regime, Arch. Rational Mech. Anal., 220 (2016), 37-81.
doi: 10.1007/s00205-015-0926-2. |
[14] |
N. D. Hardy and J. H. Shapiro, Reflective Ghost Imaging through turbulence, Phys. Rev. A, 84 (2011), 063824.
doi: 10.1103/PhysRevA.84.063824. |
[15] |
P. Hariharan, Optical Holography, Cambridge University Press, Cambridge, 1996.
doi: 10.1017/CBO9781139174039. |
[16] |
A. Ishimaru, Wave Propagation and Scattering in Random Media, IEEE Press, Piscataway, 1997. |
[17] |
O. Katz, Y. Bromberg and Y. Silberberg, Compressive ghost imaging, Appl. Phys. Lett., 95 (2009), 131110.
doi: 10.1063/1.3238296. |
[18] |
C. Li, T. Wang, J. Pu, W. Zhu and R. Rao, Ghost imaging with partially coherent light radiation through turbulent atmosphere, Appl. Phys. B, 99 (2010), 599-604.
doi: 10.1007/s00340-010-3969-y. |
[19] |
L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, Cambridge, 1995. |
[20] |
J. H. Shapiro, Computational ghost imaging, Phys. Rev. A, 78 (2008), 061802(R).
doi: 10.1364/IQEC.2009.IThK7. |
[21] |
J. H. Shapiro and R. W. Boyd, The physics of ghost imaging, Quantum Inf. Process., 11 (2012), 949-993.
doi: 10.1007/s11128-011-0356-5. |
[22] |
F. D. Tappert, The parabolic approximation method, in Wave Propagation and Underwater Acoustics, Springer Lecture Notes in Physics, 70 (1977), 224-287. |
[23] |
V. I. Tatarski, Wave Propagation in a Turbulent Medium, Dover, New York, 1961. |
[24] |
B. J. Uscinski, The Elements of Wave Propagation in Random Media, McGraw Hill, New York, 1977. |
[25] |
A. Valencia, G. Scarcelli, M. D'Angelo and Y. Shih, Two-photon imaging with thermal light, Phys. Rev. Lett., 94 (2005), 063601. |
[26] |
P. Zhang, W. Gong, X. Shen and S. Han, Correlated imaging through atmospheric turbulence, Phys. Rev. A, 82 (2010), 033817.
doi: 10.1103/PhysRevA.82.033817. |
show all references
References:
[1] |
D. G. Alfaro Vigo, J.-P. Fouque, J. Garnier and A. Nachbin, Robustness of time reversal for waves in time-dependent random media, Stochastic Process. Appl., 113 (2004), 289-313.
doi: 10.1016/j.spa.2004.04.002. |
[2] |
G. Bal and L. Ryzhik, Stability of time reversed waves in changing media, Disc. Cont. Dyn. Syst. A, 12 (2005), 793-815.
doi: 10.3934/dcds.2005.12.793. |
[3] |
P. Blomgren, G. Papanicolaou and H. Zhao, Super-resolution in time-reversal acoustics, J. Acoust. Soc. Amer., 111 (2002), 230-248.
doi: 10.1121/1.1421342. |
[4] |
M. Born and E. Wolf, Principles of Optics, Cambridge University Press, Cambridge, 1999.
doi: 10.1017/CBO9781139644181. |
[5] |
J. Cheng, Ghost imaging through turbulent atmosphere, Opt. Express, 17 (2009), 7916-7921.
doi: 10.1364/OE.17.007916. |
[6] |
M. Fink, Time reversed acoustics, Scientific American, 281 (1999), 91-97. |
[7] |
J.-P. Fouque, J. Garnier, G. Papanicolaou and K. Sølna, Wave Propagation and Time Reversal in Randomly Layered Media, Springer, New York, 2007.
doi: 10.1007/978-0-387-49808-9_4. |
[8] |
J. Garnier and G. Papanicolaou, Pulse propagation and time reversal in random waveguides, SIAM J. Appl. Math., 67 (2007), 1718-1739.
doi: 10.1137/060659235. |
[9] |
J. Garnier and G. Papanicolaou, Passive sensor imaging using cross correlations of noisy signals in a scattering medium, SIAM J. Imaging Sciences, 2 (2009), 396-437.
doi: 10.1137/080723454. |
[10] |
J. Garnier and G. Papanicolaou, Resolution analysis for imaging with noise, Inverse Problems, 26 (2010), 074001, 22pp.
doi: 10.1088/0266-5611/26/7/074001. |
[11] |
J. Garnier and G. Papanicolaou, Fluctuation theory of ambient noise imaging, CRAS Geoscience, 343 (2011), 502-511.
doi: 10.1016/j.crte.2011.01.004. |
[12] |
J. Garnier and K. Sølna, Coupled paraxial wave equations in random media in the white-noise regime, Ann. Appl. Probab., 19 (2009), 318-346.
doi: 10.1214/08-AAP543. |
[13] |
J. Garnier and K. Sølna, Fourth-moment analysis for wave propagation in the white-noise paraxial regime, Arch. Rational Mech. Anal., 220 (2016), 37-81.
doi: 10.1007/s00205-015-0926-2. |
[14] |
N. D. Hardy and J. H. Shapiro, Reflective Ghost Imaging through turbulence, Phys. Rev. A, 84 (2011), 063824.
doi: 10.1103/PhysRevA.84.063824. |
[15] |
P. Hariharan, Optical Holography, Cambridge University Press, Cambridge, 1996.
doi: 10.1017/CBO9781139174039. |
[16] |
A. Ishimaru, Wave Propagation and Scattering in Random Media, IEEE Press, Piscataway, 1997. |
[17] |
O. Katz, Y. Bromberg and Y. Silberberg, Compressive ghost imaging, Appl. Phys. Lett., 95 (2009), 131110.
doi: 10.1063/1.3238296. |
[18] |
C. Li, T. Wang, J. Pu, W. Zhu and R. Rao, Ghost imaging with partially coherent light radiation through turbulent atmosphere, Appl. Phys. B, 99 (2010), 599-604.
doi: 10.1007/s00340-010-3969-y. |
[19] |
L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press, Cambridge, 1995. |
[20] |
J. H. Shapiro, Computational ghost imaging, Phys. Rev. A, 78 (2008), 061802(R).
doi: 10.1364/IQEC.2009.IThK7. |
[21] |
J. H. Shapiro and R. W. Boyd, The physics of ghost imaging, Quantum Inf. Process., 11 (2012), 949-993.
doi: 10.1007/s11128-011-0356-5. |
[22] |
F. D. Tappert, The parabolic approximation method, in Wave Propagation and Underwater Acoustics, Springer Lecture Notes in Physics, 70 (1977), 224-287. |
[23] |
V. I. Tatarski, Wave Propagation in a Turbulent Medium, Dover, New York, 1961. |
[24] |
B. J. Uscinski, The Elements of Wave Propagation in Random Media, McGraw Hill, New York, 1977. |
[25] |
A. Valencia, G. Scarcelli, M. D'Angelo and Y. Shih, Two-photon imaging with thermal light, Phys. Rev. Lett., 94 (2005), 063601. |
[26] |
P. Zhang, W. Gong, X. Shen and S. Han, Correlated imaging through atmospheric turbulence, Phys. Rev. A, 82 (2010), 033817.
doi: 10.1103/PhysRevA.82.033817. |
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