×

Computational imaging through atmospheric turbulence. (English) Zbl 1531.68158

Summary: Since the seminal work of Andrey Kolmogorov in the early 1940’s, imaging through atmospheric turbulence has grown from a pure scientific pursuit to an important subject across a multitude of civilian, space-mission, and national security applications. Fueled by the recent advancement of deep learning, the field is further experiencing a new wave of momentum of applying these learning-based techniques to the problem. However, because of the complexity of the physics of atmospheric turbulence, significant gaps remain to be filled before the power of deep learning can be fully unleashed. In particular, the goal of building the most accurate turbulence model to mimic nature is gradually shifted to designing a compromised model that can maximize the image reconstruction performance. This leads to a new field which this book is trying to explain, Computational Imaging Through Atmospheric Turbulence.
The goal of this book is to present the basic concepts of turbulence physics while framing it under the theme of computational imaging. Emphasis is put on elaborating the principles of how waves propagate through atmospheric turbulence and propagation-free approaches to reproduce the effect without needing wave propagation equations. This allows for a much faster simulation while preserving the physics of turbulence, hence creating the possibility of integrating turbulence physics into the design of image reconstruction algorithms. The book is written for readers with an image processing background who are seeking to understand the physics of turbulence. Connections with deep learning are emphasized throughout the book.

MSC:

68U10 Computing methodologies for image processing
68T07 Artificial neural networks and deep learning
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
68-02 Research exposition (monographs, survey articles) pertaining to computer science
Full Text: DOI

References:

[1] R. Ahmad, C. A. Bouman, G. T. Buzzard, S. Chan, S. Liu, E. T. Reehorst, and P. Schniter, “Plug-and-play methods for magnetic resonance imaging: Using denoisers for image recovery,” IEEE Signal Processing Magazine, vol. 37, no. 1, pp. 105-116, 2020. doi: 10.1109/MSP.2019.2949470. · doi:10.1109/MSP.2019.2949470
[2] K. Akiyama, A. Alberdi, W. Alef, K. Asada, R. Azulay, A.-K. Baczko, D. Ball, M. Baloković, J. Barrett, D. Bintley, et al., “First m87 event horizon telescope results. iv. imaging the central supermassive black hole,” The Astrophysical Journal Letters, vol. 875, no. 1, p. L4, 2019.
[3] N. Anantrasirichai, “Atmospheric turbulence removal with comp-lex-valued convolutional neural network,” 2022. url: https:// arxiv.org/abs/2204.06989.
[4] N. Anantrasirichai, A. Achim, and D. Bull, “Atmospheric tur-bulence mitigation for sequences with moving objects using recursive image fusion,” in IEEE International Conference on Image Processing, pp. 2895-2899, Oct. 2018. doi: 10 . 1109 / ICIP.2018.8451755. · doi:10.1109/ICIP.2018.8451755
[5] N. Anantrasirichai, A. Achim, N. G. Kingsbury, and D. R. Bull, “Atmospheric turbulence mitigation using complex wavelet-based fusion,” IEEE Transactions on Image Processing, vol. 22, no. 6, pp. 2398-2408, Jun. 2013. doi: 10.1109/TIP.2013.2249078. References · Zbl 1373.94024 · doi:10.1109/TIP.2013.2249078
[6] N. Antipa, G. Kuo, R. Heckel, B. Mildenhall, E. Bostan, R. Ng, and L. Waller, “Diffusercam: Lensless single-exposure 3d imaging,” Optica, vol. 5, no. 1, pp. 1-9, Jan. 2018. doi: 10.1364/ OPTICA.5.000001. · doi:10.1364/OPTICA.5.000001
[7] E. Anzuola and S. Gladysz, “Modeling dynamic atmospheric turbulence using temporal spectra and Karhunen-Loève decom-position,” Optical Engineering, vol. 56, no. 7, p. 071 508, 2017. doi: 10.1117/1.OE.56.7.079803. · doi:10.1117/1.OE.56.7.079803
[8] M. Aubailly, M. A. Vorontsov, G. W. Carhart, and M. T. Valley, “Automated video enhancement from a stream of atmospherically-distorted images: The lucky-region fusion approach,” in Atmo-spheric Optics: Models, Measurements, and Target-in-the-Loop Propagation III, Proc. SPIE 7463, Aug. 2009. doi: 10 . 1117 / 12.828332. · doi:10.1117/12.828332
[9] S. Basu, J. E. McCrae, and S. T. Fiorino, “Estimation of the path averaged atmospheric refractive index structure constant from time lapse imagery,” in Laser Radar Technology and Applications XX; and Atmospheric Propagation XII, p. 94650T, Proc. SPIE 9465, May 2015. doi: 10.1117/12.2177330. · doi:10.1117/12.2177330
[10] M. Born and E. Wolf, Principles of Optics; Electromagnetic Theory of Propagation, Interference and Diffraction of Light, Seventh ed. Cambridge University Press, 1999. doi: 10.1017/ CBO9781139644181. · Zbl 1430.78001 · doi:10.1017/CBO9781139644181
[11] J. P. Bos and M. C. Roggemann, “Technique for simulating anisoplanatic image formation over long horizontal paths,” Opti-cal Engineering, vol. 51, no. 10, p. 101 704, 2012. doi: 10.1117/ 1.OE.51.10.101704. · doi:10.1117/1.OE.51.10.101704
[12] J. P. Bos, M. C. Roggemann, and V. S. R. Gudimetla, “Anisotropic non-kolmogorov turbulence phase screens with variable orienta-tion,” Applied Optics, vol. 54, no. 8, pp. 2039-2045, Mar. 2015. doi: 10.1364/AO.54.002039. · doi:10.1364/AO.54.002039
[13] ”Bridging the gap between computational photography and visual recognition: 5th UG2+ prize challenge,” Track 3. url: http://cvpr2022.ug2challenge.org/dataset22_t3.html.
[14] A. Buades, B. Coll, and J. Morel, “A non-local algorithm for image denoising,” in IEEE Conference on Computer Vision and Pattern Recognition, vol. 2, pp. 60-65, 2005. · Zbl 1108.94004
[15] W. P. Burckel and R. N. Gray, “Turbulence phase screens based on polar-logarithmic spectral sampling,” Applied Optics, vol. 52, no. 19, pp. 4672-4680, Jul. 2013. doi: 10.1364/AO.52.004672. · doi:10.1364/AO.52.004672
[16] J.-F. Cai, H. Ji, C. Liu, and Z. Shen, “Blind motion deblurring from a single image using sparse approximation,” in IEEE Con-ference on Computer Vision and Pattern Recognition, pp. 104-111, 2009.
[17] T. Çaliskan and N. Arica, “Atmospheric turbulence mitigation using optical flow,” in International Conference on Pattern Recog-nition, pp. 883-888, 2014. doi: 10.1109/ICPR.2014.162. · doi:10.1109/ICPR.2014.162
[18] W. H. Chak, C. P. Lau, and L. M. Lui, “Subsampled turbulence removal network,” Mathematics, Computation and Geometry of Data, vol. 1, pp. 1-33, 2021. doi: 10.4310/MCGD.2021.v1.n1.a1. · Zbl 1496.68354 · doi:10.4310/MCGD.2021.v1.n1.a1
[19] S. H. Chan, “Performance analysis of plug-and-play admm: A graph signal processing perspective,” IEEE Transactions on Computational Imaging, vol. 5, no. 2, pp. 274-286, 2019. doi: 10.1109/TCI.2019.2892123. · doi:10.1109/TCI.2019.2892123
[20] S. H. Chan, “Tilt-then-blur or blur-then-tilt? Clarifying the atmospheric turbulence model,” IEEE Signal Processing Letters, vol. 29, pp. 1833-1837, 2022. doi: 10.1109/LSP.2022.3200551. · doi:10.1109/LSP.2022.3200551
[21] S. H. Chan, X. Wang, and O. A. Elgendy, “Plug-and-play ADMM for image restoration: Fixed-point convergence and applications,” IEEE Transactions on Computational Imaging, vol. 3, no. 1, pp. 84-98, 2017. doi: 10.1109/TCI.2016.2629286. · doi:10.1109/TCI.2016.2629286
[22] G. A. Chanan, “Calculation of wave-front tilt correlations as-sociated with atmospheric turbulence,” Journal of the Optical Society of America A, vol. 9, no. 2, pp. 298-301, Feb. 1992. doi: 10.1364/JOSAA.9.000298. · doi:10.1364/JOSAA.9.000298
[23] M. Charnotskii, J. Gozani, V. Tatarskii, and V. Zavorotny, “Wave propagation theories in random media based on the path-integral approach,” Progress in Optics, vol. 32, pp. 203-266, 1993. doi: 10.1016/S0079-6638(08)70164-1. · doi:10.1016/S0079-6638(08)70164-1
[24] G. Chen, Z. Gao, Q. Wang, and Q. Luo, “U-net like deep au-toencoders for deblurring atmospheric turbulence,” Journal of Electronic Imaging, vol. 28, no. 5, p. 053 024, 2019. doi: 10.1117/ 1.JEI.28.5.053024. · doi:10.1117/1.JEI.28.5.053024
[25] N. Chimitt and S. H. Chan, “Simulating anisoplanatic turbu-lence by sampling intermodal and spatially correlated Zernike coefficients,” Optical Engineering, vol. 59, no. 8, p. 083 101, 2020. doi: 10.1117/1.OE.59.8.083101. · doi:10.1117/1.OE.59.8.083101
[26] N. Chimitt and S. H. Chan, “Anisoplanatic optical turbulence simulation for near-continuous C 2 n profiles without wave propa-gation,” 2023. url: https://arxiv.org/abs/2305.09036.
[27] N. Chimitt, X. Zhang, Y. Chi, and S. H. Chan, “Scattering and gathering for spatially varying blurs,” 2023. url: https:// arxiv.org/abs/2303.05687.
[28] N. Chimitt, X. Zhang, Z. Mao, and S. H. Chan, “Real-time dense field phase-to-space simulation of imaging through at-mospheric turbulence,” IEEE Transactions on Computational Imaging, 2022. doi: 10.1109/TCI.2022.3226293. · doi:10.1109/TCI.2022.3226293
[29] P. H. Christensen and W. Jarosz, “The path to path-traced movies,” Foundations and Trends ® in Computer Graphics and Vision, vol. 10, no. 2, pp. 103-175, 2016. doi: 10.1561/06000000 73. · doi:10.1561/0600000073
[30] W. A. Coles, J. P. Filice, R. G. Frehlich, and M. Yadlowsky, “Simulation of wave propagation in three-dimensional random media,” Applied Optics, vol. 34, no. 12, pp. 2089-2101, Apr. 1995. doi: 10.1364/AO.34.002089. · doi:10.1364/AO.34.002089
[31] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3D transform-domain collaborative filtering,” IEEE Transactions on Image Processing, vol. 16, no. 8, pp. 2080-2095, Aug. 2007. doi: 10.1109/TIP.2007.901238. · doi:10.1109/TIP.2007.901238
[32] R. Dashen, “Path integrals for waves in random media,” Journal of Mathematical Physics, vol. 20, no. 5, pp. 894-920, May 1979. doi: 10.1063/1.524138. · doi:10.1063/1.524138
[33] M. Delbracio and G. Sapiro, “Removing camera shake via weighted fourier burst accumulation,” IEEE Transactions on Image Pro-cessing, vol. 24, no. 11, pp. 3293-3307, 2015. doi: 10 . 1109 / TIP.2015.2442914. · Zbl 1408.94125 · doi:10.1109/TIP.2015.2442914
[34] D. R. Droege, R. C. Hardie, B. S. Allen, A. J. Dapore, and J. C. Blevins, “A real-time atmospheric turbulence mitigation and super-resolution solution for infrared imaging systems,” in In-frared Imaging Systems: Design, Analysis, Modeling, and Testing XXIII, Proc. SPIE 8355, 2012. doi: 10.1117/12.920323. · doi:10.1117/12.920323
[35] M. A. Ealey and J. A. Wellman, “Deformable mirrors: Design fundamentals, key performance specifications, and parametric trades,” in Active and Adaptive Optical Components, Proc. SPIE 1543, 1992. doi: 10.1117/12.51167. · doi:10.1117/12.51167
[36] B. Y. Feng, M. Xie, and C. A. Metzler, “TurbuGAN: An adver-sarial learning approach to spatially-varying multiframe blind deconvolution with applications to imaging through turbulence,” 2022. url: https://arxiv.org/pdf/2203.06764.pdf.
[37] R. Feng, J. Gu, Y. Qiao, and C. Dong, “Suppressing model overfitting for image super-resolution networks,” 2019. url: htt ps://arxiv.org/abs/1906.04809.
[38] R. Fergus, B. Singh, A. Hertzmann, S. Roweis, and W. Free-man, “Removing camera shake from a single photograph,” ACM Transactions on Graphics, vol. 25, pp. 787-794, Jul. 2006. doi: 10.1145/1141911.1141956. · Zbl 1371.94125 · doi:10.1145/1141911.1141956
[39] R. P. Feynman, The Feynman Lectures on Physics. Reading, Mass.: Addison-Wesley Pub. Co., 1963-1965., 1965 1963.
[40] R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals, ser. International series in pure and applied physics. McGraw-Hill, 1965. · Zbl 0176.54902
[41] D. H. Frakes, J. W. Monaco, and M. J. T. Smith, “Suppression of atmospheric turbulence in video using an adaptive control grid interpolation approach,” in IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 1881-1884, 2001.
[42] R. Frehlich, “Simulation of laser propagation in a turbulent atmosphere,” Applied Optics, vol. 39, no. 3, pp. 393-397, Jan. 2000. doi: 10.1364/AO.39.000393. · doi:10.1364/AO.39.000393
[43] D. Fried, “Anisoplanatism in adaptive optics,” Journal of the Optical Society of America, vol. 72, no. 1, pp. 52-61, 1982. doi: 10.1364/JOSA.72.000052. · doi:10.1364/JOSA.72.000052
[44] D. L. Fried, “Statistics of a geometric representation of wavefront distortion,” Journal of the Optical Society of America, vol. 55, no. 11, pp. 1427-1435, Nov. 1965. doi: 10.1364/JOSA.55.001427. · doi:10.1364/JOSA.55.001427
[45] D. L. Fried, “Optical resolution through a randomly inhomoge-neous medium for very long and very short exposures,” Journal of the Optical Society of America, vol. 56, no. 10, pp. 1372-1379, 1966. doi: 10.1364/JOSA.56.001372. · doi:10.1364/JOSA.56.001372
[46] D. L. Fried, “Probability of getting a lucky short-exposure image through turbulence,” Journal of the Optical Society of America, vol. 68, no. 12, pp. 1651-1658, Dec. 1978. doi: 10.1364/JOSA. 68.001651. · doi:10.1364/JOSA.68.001651
[47] D. L. Fried, “Differential angle of arrival: Theory, evaluation, and measurement feasibility,” Radio Science, vol. 10, no. 1, pp. 71-76, 1975. doi: 10.1029/RS010i001p00071. · doi:10.1029/RS010i001p00071
[48] D. L. Fried, “Varieties Of Isoplanatism,” in Imaging Through the Atmosphere, Proc. SPIE 0075, 1976.
[49] D. L. Fried and T. Clark, “Extruding kolmogorov-type phase screen ribbons,” Journal of the Optical Society of America A, vol. 25, no. 2, pp. 463-468, Feb. 2008. doi: 10.1364/JOSAA.25. 000463. · doi:10.1364/JOSAA.25.000463
[50] D. Fried, “Optical heterodyne detection of an atmospherically distorted signal wave front,” Proceedings of the IEEE, vol. 55, no. 1, pp. 57-77, 1967. doi: 10.1109/PROC.1967.5377. · doi:10.1109/PROC.1967.5377
[51] U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov. Cam-bridge University Press, 1995. doi: 10.1017/CBO9781139170666. · Zbl 0832.76001 · doi:10.1017/CBO9781139170666
[52] G. Gilles and S. Osher, “Wavelet burst accumulation for turbu-lence mitigation,” Journal of Electronic Imaging, vol. 25, no. 3, p. 033 003, 2016. doi: 10.1117/1.JEI.25.3.033003. · doi:10.1117/1.JEI.25.3.033003
[53] J. Gilles and N. B. Ferrante, “Open turbulent image set (OTIS),” Pattern Recognition Letters, vol. 86, pp. 38-41, 2017. doi: 10. 1016/j.patrec.2016.12.020. · doi:10.1016/j.patrec.2016.12.020
[54] J. W. Goodman, Introduction to Fourier Optics, Third ed. Roberts and Company, 2005.
[55] J. W. Goodman, Speckle Phenomena in Optics: Theory and Applications. Roberts & Company, 2007.
[56] J. W. Goodman, Statistical Optics, Second ed. John Wiley and Sons Inc., 2015.
[57] R. Gray, “Zernikecalc: A MATLAB function to work with zernike polynomials over circular and non-circular pupils,” url: https:// www.mathworks.com/matlabcentral/fileexchange/33330-zerni kecalc.
[58] D. P. Greenwood, “Bandwidth specification for adaptive optics systems,” Journal of the Optical Society of America, vol. 67, no. 3, pp. 390-393, Mar. 1977. doi: 10.1364/JOSA.67.000390. · doi:10.1364/JOSA.67.000390
[59] D. N. Groff, K. J. Miller, and T. W. D. Bosq, “Towards devel-opment of improved metrics for quantifying turbulence imposed degradation of long-range video,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXXII, p. 117400P, Proc. SPIE 11740, 2021. doi: 10.1117/12.2587971. · doi:10.1117/12.2587971
[60] K. K. Halder, M. Tahtali, and S. G. Anavatti, “Geometric cor-rection of atmospheric turbulence-degraded video containing moving objects,” Optics Express, vol. 23, no. 4, pp. 5091-5101, Feb. 2015. doi: 10.1364/OE.23.005091. · doi:10.1364/OE.23.005091
[61] R. C. Hardie, J. D. Power, D. A. LeMaster, D. R. Droege, S. Gladysz, and S. Bose-Pillai, “Simulation of anisoplanatic imaging through optical turbulence using numerical wave propagation with new validation analysis,” Optical Engineering, vol. 56, no. 7, p. 071 502, 2017. doi: 10.1117/1.OE.56.7.071502. · doi:10.1117/1.OE.56.7.071502
[62] R. C. Hardie, M. A. Rucci, S. R. Bose-Pillai, R. V. Hook, and B. K. Karch, “Modeling and simulation of multispectral imaging through anisoplanatic atmospheric optical turbulence,” Optical Engineering, vol. 61, no. 9, p. 093 102, 2022. doi: 10 . 1117 / 1.OE.61.9.093102. · doi:10.1117/1.OE.61.9.093102
[63] R. C. Hardie, M. A. Rucci, A. J. Dapore, and B. K. Karch, “Block matching and wiener filtering approach to optical turbulence mitigation and its application to simulated and real imagery with quantitative error analysis,” Optical Engineering, vol. 56, no. 7, p. 071 503, 2017. doi: 10.1117/1.OE.56.7.071503. References · doi:10.1117/1.OE.56.7.071503
[64] R. He, Z. Wang, Y. Fan, and D. Feng, “Atmospheric turbulence mitigation based on turbulence extraction,” in IEEE Interna-tional Conference on Acoustics, Speech, and Signal Processing, pp. 1442-1446, Mar. 2016. doi: 10.1109/ICASSP.2016.7471915. · doi:10.1109/ICASSP.2016.7471915
[65] E. Hecht, Optics, Fifth ed. Pearson Education, Inc., 2015.
[66] G. Heidbreder, “Image degradation with random wavefront tilt compensation,” IEEE Transactions on Antennas and Propaga-tion, vol. 15, no. 1, pp. 90-98, 1967. doi: 10.1109/TAP.1967. 1138846. · doi:10.1109/TAP.1967.1138846
[67] B. J. Herman and L. A. Strugala, “Method for inclusion of low-frequency contributions in numerical representation of atmo-spheric turbulence,” in Propagation of High-Energy Laser Beams Through the Earth’s Atmosphere, Proc. SPIE 1221, 1990. doi: 10.1117/12.18342. · doi:10.1117/12.18342
[68] M. Hirsch, S. Sra, B. Schölkopf, and S. Harmeling, “Efficient filter flow for space-variant multiframe blind deconvolution,” in IEEE Conference on Computer Vision and Pattern Recognition, pp. 607-614, 2010. doi: 10.1109/CVPR.2010.5540158. · doi:10.1109/CVPR.2010.5540158
[69] C. S. Huebner, “Turbulence mitigation of short exposure image data using motion detection and background segmentation,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXIII, Proc. SPIE 8355, May 2012. doi: 10.1117/12. 918255. · doi:10.1117/12.918255
[70] R. E. Hufnagel, “Propagation through atmospheric turbulence,” The Infrared Handbook, Chapter 6, 1978.
[71] R. E. Hufnagel and N. R. Stanley, “Modulation transfer function associated with image transmission through turbulent media,” Journal of the Optical Society of America, vol. 54, no. 1, pp. 52-61, Jan. 1964. doi: 10.1364/JOSA.54.000052. · doi:10.1364/JOSA.54.000052
[72] T.-W. Hui, X. Tang, and C. C. Loy, “LiteFlowNet: A Lightweight Convolutional Neural Network for Optical Flow Estimation,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 8981-8989, 2018.
[73] B. R. Hunt, A. L. Iler, C. A. Bailey, and M. A. Rucci, “Synthesis of atmospheric turbulence point spread functions by sparse and redundant representations,” Optical Engineering, vol. 57, no. 2, p. 024 101, 2018. doi: 10.1117/1.OE.57.2.024101. · doi:10.1117/1.OE.57.2.024101
[74] E. Ilg, N. Mayer, T. Saikia, M. Keuper, A. Dosovitskiy, and T. Brox, “Flownet 2.0: Evolution of optical flow estimation with deep networks,” in IEEE Conference on Computer Vision and Pattern Recognition, pp. 2462-2470, 2017. doi: 10.1109/ CVPR.2017.179. · doi:10.1109/CVPR.2017.179
[75] A. Ishimaru, “Theory and application of wave propagation and scattering in random media,” Proceedings of the IEEE, vol. 65, no. 7, pp. 1030-1061, 1977. doi: 10.1109/PROC.1977.10612. · doi:10.1109/PROC.1977.10612
[76] A. Ishimaru, Wave Propagation and Scattering in Random Media, vol. 2. New York: Academic Press, 1978. · Zbl 0873.65115
[77] J. D. Jackson, Classical Electrodynamics, Third ed. New York, NY: Wiley, 1999. · Zbl 0920.00012
[78] A. J. E. M. Janssen, “Extended nijboer-zernike approach for the computation of optical point-spread functions,” Journal of the Optical Society of America A, vol. 19, no. 5, pp. 849-857, May 2002. doi: 10.1364/JOSAA.19.000849. · doi:10.1364/JOSAA.19.000849
[79] D. Jin, Y. Chen, Y. Lu, J. Chen, P. Wang, Z. Liu, S. Guo, and X. Bai, “Neutralizing the impact of atmospheric turbulence on complex scene imaging via deep learning,” Nature Machine Intelligence, vol. 3, pp. 876-884, 2021. doi: 10.1038/s42256-021 -00392-1. · doi:10.1038/s42256-021-00392-1
[80] N. Joshi and M. F. Cohen, “Seeing Mt. Rainier: Lucky imaging for multi-image denoising, sharpening, and haze removal,” in IEEE International Conference on Computational Photography, pp. 1-8, 2010. doi: 10.1109/ICCPHOT.2010.5585096. · doi:10.1109/ICCPHOT.2010.5585096
[81] M. Khorasaninejad, W. T. Chen, R. C. Devlin, J. Oh, A. Y. Zhu, and F. Capasso, “Metalenses at visible wavelengths: Diffraction-limited focusing and subwavelength resolution imaging,” Science, vol. 352, no. 6290, pp. 1190-1194, 2016. doi: 10.1126/science. aaf6644. References · doi:10.1126/science.aaf6644
[82] A. N. Kolmogorov, “Dissipation of energy in the locally isotropic turbulence,” Doklady Akademii Nauk SSSR, vol. 32, pp. 16-18, 1941. · Zbl 0063.03292
[83] A. N. Kolmogorov, “The local structure of turbulence in incom-pressible viscous fluid for very large Reynolds numbers,” Doklady Akademii Nauk SSSR, vol. 30, pp. 301-305, 1941. · JFM 67.0850.06
[84] A. N. Kolmogorov, Foundations of the Theory of Probability, ser. AMS Chelsea Publishing Series. Chelsea Publishing Com-pany, 1956. · Zbl 0074.12202
[85] O. Korotkova, Random Light Beams. CRC Press, 2017.
[86] D. Krishnan, T. Tay, and R. Fergus, “Blind deconvolution using a normalized sparsity measure,” in IEEE Conference on Computer Vision and Pattern Recognition, IEEE, pp. 233-240, 2011. doi: 10.1109/CVPR.2011.5995521. · doi:10.1109/CVPR.2011.5995521
[87] S. L. Lachinova, M. A. Vorontsov, V. V. Dudorov, V. V. Kolosov, and M. T. Valley, “Anisoplanatic imaging through atmospheric turbulence: Brightness function approach,” in Atmospheric Op-tics: Models, Measurements, and Target-in-the-Loop Propagation, Proc. SPIE 6708, 2007. doi: 10.1117/12.738796. · doi:10.1117/12.738796
[88] S. L. Lachinova, M. A. Vorontsov, G. A. Filimonov, D. A. LeMas-ter, and M. E. Trippel, “Comparative analysis of numerical sim-ulation techniques for incoherent imaging of extended objects through atmospheric turbulence,” Optical Engineering, vol. 56, no. 7, 2017. doi: 10.1117/1.OE.56.7.071509. · doi:10.1117/1.OE.56.7.071509
[89] R. G. Lane, A. Glindemann, and J. C. Dainty, “Simulation of a Kolmogorov phase screen,” Waves in Random Media, vol. 2, no. 3, pp. 209-224, 1992. doi: 10.1088/0959-7174/2/3/003. · Zbl 0825.76348 · doi:10.1088/0959-7174/2/3/003
[90] C. P. Lau, Y. H. Lai, and L. M. Lui, “Restoration of atmo-spheric turbulence-distorted images via RPCA and quasicon-formal maps,” Inverse Problems, Mar. 2019. doi: 10 . 1088 / 1361-6420/ab0e4b. · Zbl 07079914 · doi:10.1088/1361-6420/ab0e4b
[91] C. P. Lau and L. M. Lui, “Subsampled turbulence removal network,” Mathematics, Computation and Geometry of Data, vol. 1, no. 1, pp. 1-33, 2021. doi: 10.4310/MCGD.2021.v1.n1.a1. · Zbl 1496.68354 · doi:10.4310/MCGD.2021.v1.n1.a1
[92] C. P. Lau, H. Souri, and R. Chellappa, “Atfacegan: Single face semantic aware image restoration and recognition from atmo-spheric turbulence,” IEEE Transactions on Biometrics, Behavior, and Identity Science, vol. 3, no. 2, pp. 240-251, Feb. 2021. doi: 10.1109/TBIOM.2021.3058316. · doi:10.1109/TBIOM.2021.3058316
[93] C. P. Lau, Y. H. Lai, and L. M. Lui, “Restoration of atmo-spheric turbulence-distorted images via RPCA and quasiconfor-mal maps,” Inverse Problems, Mar. 2019. · Zbl 07079914
[94] K. R. Leonard, J. Howe, and D. E. Oxford, “Simulation of atmospheric turbulence effects and mitigation algorithms on stand-off automatic facial recognition,” in Optics and Photonics for Counterterrorism, Crime Fighting, and Defence VIII, Proc. SPIE 8546, Oct. 2012. doi: 10.1117/12.979480. · doi:10.1117/12.979480
[95] A. Levin, “Blind motion deblurring using image statistics,” Ad-vances in Neural Information Processing Systems, vol. 19, 2006. doi: 10.7551/mitpress/7503.003.0110. · doi:10.7551/mitpress/7503.003.0110
[96] A. Levin, R. Fergus, F. Durand, and W. T. Freeman, “Image and depth from a conventional camera with a coded aperture,” ACM Transactions on Graphics, vol. 26, no. 3, 70-es, Jul. 2007. doi: 10.1145/1276377.1276464. · doi:10.1145/1276377.1276464
[97] A. Levin, Y. Weiss, F. Durand, and W. T. Freeman, “Under-standing blind deconvolution algorithms,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 33, no. 12, pp. 2354-2367, 2011. doi: 10.1109/TPAMI.2011.148. · doi:10.1109/TPAMI.2011.148
[98] N. Li, S. Thapa, C. Whyte, A. W. Reed, S. Jayasuriya, and J. Ye, “Unsupervised non-rigid image distortion removal via grid deformation,” in IEEE/CVF International Conference on Computer Vision, pp. 2522-2532, Oct. 2021.
[99] C. Liu, “Beyond pixels: Exploring new representations and appli-cations for motion analysis,” Ph.D. dissertation, Massachusetts Institute of Technology, Jan. 2009, 2009.
[100] Y. Lou, S. Ha Kang, S. Soatto, and A. Bertozzi, “Video stabi-lization of atmospheric turbulence distortion,” Inverse Problems and Imaging, vol. 7, no. 3, pp. 839-861, Aug. 2013. doi: 10.3934/ ipi.2013.7.839. · Zbl 1272.68436 · doi:10.3934/ipi.2013.7.839
[101] C. Macaskill and T. E. Ewart, “Computer simulation of two-dimensional random wave propagation,” IMA Journal of Applied Mathematics, vol. 33, no. 1, pp. 1-15, Jul. 1984. doi: 10.1093/ imamat/33.1.1. · Zbl 0596.76023 · doi:10.1093/imamat/33.1.1
[102] Y. Mao and J. Gilles, “Non rigid geometric distortions correction -application to atmospheric turbulence stabilization,” Inverse Problems and Imaging, vol. 3, pp. 531-546, 2012. doi: 10.3934/ ipi.2012.6.531. · Zbl 1287.94014 · doi:10.3934/ipi.2012.6.531
[103] Z. Mao, N. Chimitt, and S. H. Chan, “Image reconstruction of static and dynamic scenes through anisoplanatic turbulence,” IEEE Transactions on Computational Imaging, vol. 6, pp. 1415-1428, Oct. 2020. doi: 10.1109/TCI.2020.3029401. · doi:10.1109/TCI.2020.3029401
[104] Z. Mao, N. Chimitt, and S. H. Chan, “Accelerating atmospheric turbulence simulation via learned phase-to-space transform,” in IEEE/CVF International Conference on Computer Vision, pp. 14 759-14 768, Oct. 2021. doi: 10.1109/ICCV48922.2021. 01449. · doi:10.1109/ICCV48922.2021.01449
[105] Z. Mao, A. Jaiswal, Z. Wang, and S. H. Chan, “Single frame at-mospheric turbulence mitigation: A benchmark study and a new physics-inspired transformer model,” in European Conference on Computer Vision, 2022.
[106] J. M. Martin and S. M. Flatté, “Intensity images and statistics from numerical simulation of wave propagation in 3-d random media,” Applied Optics, vol. 27, no. 11, pp. 2111-2126, Jun. 1988. doi: 10.1364/AO.27.002111. · doi:10.1364/AO.27.002111
[107] B. L. McGlamery, “Restoration of turbulence-degraded images,” Journal of the Optical Society of America, vol. 57, no. 3, pp. 293-297, Mar. 1967. doi: 10.1364/JOSA.57.000293. · doi:10.1364/JOSA.57.000293
[108] T. Michaeli and M. Irani, “Blind deblurring using internal patch recurrence,” in European Conference on Computer Vision, Springer, pp. 783-798, 2014. doi: 10.1007/978-3-319-10578-9_51. · doi:10.1007/978-3-319-10578-9_51
[109] K. J. Miller and T. D. Bosq, “A machine learning approach to improving quality of atmospheric turbulence simulation,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Test-ing XXXII, p. 117400N, Proc. SPIE 11740, 2021. doi: 10.1117/ 12.2587749. · doi:10.1117/12.2587749
[110] K. J. Miller, B. Preece, T. W. D. Bosq, and K. R. Leonard, “A data-constrained algorithm for the emulation of long-range turbulence-degraded video,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXX, G. C. Holst and K. A. Krapels, Eds., International Society for Optics and Photonics, vol. 11001, 110010J, SPIE, 2019. doi: 10.1117/12.2519069. · doi:10.1117/12.2519069
[111] N. G. Nair, K. Mei, and V. M. Patel, “AT-DDPM: Restoring faces degraded by atmospheric turbulence using denoising diffu-sion probabilistic models,” in IEEE/CVF Winter Conference on Applications of Computer Vision, pp. 3434-3443, 2023.
[112] R. Nieuwenhuizen, J. Dijk, and K. Schutte, “Dynamic turbulence mitigation for long-range imaging in the presence of large moving objects,” EURASIP Journal on Image and Video Processing, vol. 2, no. 2, 2019. doi: 10.1186/s13640-018-0380-9. · doi:10.1186/s13640-018-0380-9
[113] R. Nieuwenhuizen and K. Schutte, “Deep learning for software-based turbulence mitigation in long-range imaging,” in Artificial Intelligence and Machine Learning in Defense Applications, Proc. SPIE 11169, 2019. doi: 10.1117/12.2532603. · doi:10.1117/12.2532603
[114] R. J. Noll, “Zernike polynomials and atmospheric turbulence,” Journal of the Optical Society of America, vol. 66, no. 3, pp. 207-211, Mar. 1976. doi: 10.1364/JOSA.66.000207. · doi:10.1364/JOSA.66.000207
[115] K. Novak and A. T. Watnik, “Imaging through deconvolution with a spatially variant point spread function,” in Computational Imaging VI, p. 1 173 105, Proc. SPIE 11731, 2021. doi: 10.1117/ 12.2585632. · doi:10.1117/12.2585632
[116] A. M. Obukhov, “On the distribution of energy in the sprectrum of turbulent flow,” Doklady Akademii Nauk SSSR, vol. 32, pp. 22-24, 1941.
[117] A. M. Obukhov, “Spectral energy distribution in a turbulent flow,” Izv. Akad. Nauk S.S.S.R, Ser. Georgr. Geofiz., vol. 5, pp. 453-466, 1941.
[118] A. M. Obukhov, “Effect of weak inhomogeneities in the atmo-sphere on sound and light propagation,” Izv. Akad. Nauk S.S.S.R, Ser. Geofiz., vol. 2, pp. 155-165, 1953.
[119] A. V. Oppenheim, A. S. Willsky, and S. H. Nawab, Signals & Systems. USA: Prentice-Hall, Inc., 1996.
[120] O. Oreifej, X. Li, and M. Shah, “Simultaneous video stabilization and moving object detection in turbulence,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 2, pp. 450-462, Feb. 2013. doi: 10.1109/TPAMI.2012.97. · doi:10.1109/TPAMI.2012.97
[121] R. R. Parenti and R. J. Sasiela, “Laser-guide-star systems for astronomical applications,” Journal of the Optical Society of America A, vol. 11, no. 1, pp. 288-309, Jan. 1994. doi: 10.1364/ JOSAA.11.000288. · doi:10.1364/JOSAA.11.000288
[122] C. J. Pellizzari, M. T. Banet, M. F. Spencer, and C. A. Bouman, “Demonstration of single-shot digital holography using a bayesian framework,” Journal of the Optical Society of America A, vol. 35, no. 1, pp. 103-107, Jan. 2018. doi: 10.1364/JOSAA.35.000103. · doi:10.1364/JOSAA.35.000103
[123] C. J. Pellizzari, M. F. Spencer, and C. A. Bouman, “Imaging through distributed-volume aberrations using single-shot digital holography,” Journal of the Optical Society of America A, vol. 36, no. 2, A20-A33, Feb. 2019. doi: 10.1364/JOSAA.36.000A20. · doi:10.1364/JOSAA.36.000A20
[124] C. J. Pellizzari, R. Trahan, H. Zhou, S. Williams, S. E. Williams, B. Nemati, M. Shao, and C. A. Bouman, “Optically coherent image formation and denoising using a plug and play inversion framework,” Applied Optics, vol. 56, no. 16, pp. 4735-4744, Jun. 2017. doi: 10.1364/AO.56.004735. · doi:10.1364/AO.56.004735
[125] J. R. Peterson, J. G. Jernigan, S. M. Kahn, A. P. Rasmussen, E. Peng, Z. Ahmad, J. Bankert, C. Chang, C. Claver, D. K. Gilmore, E. Grace, M. Hannel, M. Hodge, S. Lorenz, A. Lupu, A. Meert, S. Nagarajan, N. Todd, A. Winans, and M. Young, “Simulation of astronomical images from optical survey telescopes using a comprehensive photon monte carlo approach,” The Astrophysical Journal Supplement Series, vol. 218, no. 1, p. 14, May 2015. doi: 10.1088/0067-0049/218/1/14. · doi:10.1088/0067-0049/218/1/14
[126] J. D. Phillips, M. E. Goda, and J. Schmidt, “Atmospheric turbu-lence simulation using liquid crystal spatial light modulators,” in Advanced Wavefront Control: Methods, Devices, and Applications III, International Society for Optics and Photonics, vol. 5894, p. 589 406, SPIE, 2005. doi: 10.1117/12.620407. · doi:10.1117/12.620407
[127] G. Potvin, J. L. Forand, and D. Dion, “A simple physical model for simulating turbulent imaging,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXII, G. C. Holst and K. A. Krapels, Eds., International Society for Optics and Pho-tonics, vol. 8014, 80140Y, SPIE, 2011. doi: 10.1117/12.884989. · doi:10.1117/12.884989
[128] R. Ramamoorthi, “Precomputation-based rendering,” Founda-tions and Trends ® in Computer Graphics and Vision, vol. 3, no. 4, pp. 281-369, 2009. doi: 10.1561/0600000021. · Zbl 1200.68264 · doi:10.1561/0600000021
[129] A. Ranjan and M. J. Black, “Optical flow estimation using a spatial pyramid network,” in IEEE Conference on Computer Vision and Pattern Recognition, pp. 4161-4170, 2017. doi: 10. 1109/CVPR.2017.291. · doi:10.1109/CVPR.2017.291
[130] R. Raskar, A. Agrawal, and J. Tumblin, “Coded exposure photog-raphy: Motion deblurring using fluttered shutter,” ACM Trans-actions on Graphics, vol. 25, no. 3, pp. 795-804, Jul. 2006. doi: 10.1145/1141911.1141957. · doi:10.1145/1141911.1141957
[131] E. Repasi and R. Weiss, “Analysis of image distortions by at-mospheric turbulence and computer simulation of turbulence effects,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XIX, Proc. SPIE 6941, 2008. doi: 10.1117/12.775600. · doi:10.1117/12.775600
[132] E. Repasi and R. Weiss, “Computer simulation of image degrada-tions by atmospheric turbulence for horizontal views,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXII, Proc. SPIE 8014, 2011. doi: 10.1117/12.883805. · doi:10.1117/12.883805
[133] E. Repasi and R. Weiss, “Computer simulation of image degrada-tions by atmospheric turbulence for horizontal views,” in Infrared Imaging Systems: Design, Analysis, Modeling, and Testing XXII, International Society for Optics and Photonics, vol. 8014, 80140U, 2011. doi: 10.1117/12.883805. · doi:10.1117/12.883805
[134] F. Roddier, Adaptive Optics in Astronomy. Cambridge University Press, 1999. doi: 10.1017/CBO9780511525179. References · doi:10.1017/CBO9780511525179
[135] N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” Optical Engineering, vol. 29, no. 10, pp. 1174-1180, 1990. doi: 10.1117/12.55712. · doi:10.1117/12.55712
[136] B. Rodenburg, M. Mirhosseini, M. Malik, O. S. Magaña-Loaiza, M. Yanakas, L. Maher, N. K. Steinhoff, G. A. Tyler, and R. W. Boyd, “Simulating thick atmospheric turbulence in the lab with application to orbital angular momentum communication,” New Journal of Physics, vol. 16, no. 3, p. 033 020, Mar. 2014. doi: 10.1088/1367-2630/16/3/033020. · doi:10.1088/1367-2630/16/3/033020
[137] M. C. Roggemann and B. M. Welsh, Imaging Through Atmo-spheric Turbulence. Taylor & Francis, 1996.
[138] M. C. Roggemann, C. A. Stoudt, and B. M. Welsh, “Image-spectrum signal-to-noise-ratio improvements by statistical frame selection for adaptive-optics imaging through atmospheric tur-bulence,” Optical Engineering, vol. 33, no. 10, pp. 3254-3264, 1994. doi: 10.1117/12.181250. · doi:10.1117/12.181250
[139] M. C. Roggemann, B. M. Welsh, D. Montera, and T. A. Rhoad-armer, “Method for simulating atmospheric turbulence phase effects for multiple time slices and anisoplanatic conditions,” Applied Optics, vol. 34, no. 20, pp. 4037-4051, Jul. 1995. doi: 10.1364/AO.34.004037. · doi:10.1364/AO.34.004037
[140] Y. Romano, M. Elad, and P. Milanfar, “The little engine that could: Regularization by denoising (RED),” SIAM Journal on Imaging Sciences, vol. 10, no. 4, pp. 1804-1844, 2017. doi: 10. 1137/16M1102884. · Zbl 1401.62101 · doi:10.1137/16M1102884
[141] M. A. Rucci, R. C. Hardie, and R. K. Martin, “Simulation of anisoplanatic lucky look imaging and statistics through optical turbulence using numerical wave propagation,” Applied Optics, vol. 60, no. 25, G19-G29, Sep. 2021. doi: 10.1364/AO.427716. · doi:10.1364/AO.427716
[142] A. S. S. Gepshtein and B. Fishbain, “Restoration of atmospheric turbulent video containing real motion using rank filtering and elastic image registration,” in European Signal Processing Con-ference, pp. 477-480, Sep. 2004.
[143] S. M. Safdarnejad, X. Liu, L. Udpa, B. Andrus, J. Wood, and D. Craven, “Sports videos in the wild (svw): A video dataset for sports analysis,” in 2015 11th IEEE International Conference and Workshops on Automatic Face and Gesture Recognition, IEEE, vol. 1, pp. 1-7, 2015. doi: 10.1109/FG.2015.7163105. · doi:10.1109/FG.2015.7163105
[144] J. D. Schmidt, Numerical Simulation of Optical Wave Propaga-tion: With Examples in MATLAB. SPIE Press, 2010, pp. 1-197. doi: 10.1117/3.866274. · doi:10.1117/3.866274
[145] M. Shimizu, S. Yoshimura, M. Tanaka, and M. Okutomi, “Super-resolution from image sequence under influence of hot-air optical turbulence,” in IEEE Conference on Computer Vision and Pat-tern Recognition, pp. 1-8, 2008.
[146] M. Spivack and B. Uscinski, “The split-step solution in ran-dom wave propagation,” Journal of Computational and Applied Mathematics, vol. 27, no. 3, pp. 349-361, 1989. doi: 10.1016/ 0377-0427(89)90022-8. · Zbl 0683.65122 · doi:10.1016/0377-0427(89)90022-8
[147] N. Takato and I. Yamaguchi, “Spatial correlation of Zernike phase-expansion coefficients for atmospheric turbulence with finite outer scale,” Journal of the Optical Society of America A, vol. 12, no. 5, pp. 958-963, May 1995. doi: 10.1364/JOSAA.12. 000958. · doi:10.1364/JOSAA.12.000958
[148] V. I. Tatarskii, Wave Propagation in a Turbulent Medium. New York: Dover Publications, 1961. doi: 10.1063/1.3057286. · Zbl 0206.12203 · doi:10.1063/1.3057286
[149] V. Tatarskii, A. Ishimaru, and V. Zavorotny, Wave Propagation in Random Media (Scintillation): Proceedings of the Conference Held 3-7 August, 1992 at the University of Washington, USA, ser. SPIE press monographs. Taylor & Francis, 1993.
[150] V. Tatarskii and V. Zavorotnyi, “Strong fluctuations in light propagation in a randomly inhomogeneous medium,” Progress in Optics, vol. 18, pp. 204-256, 1980. doi: 10.1016/S0079-6638(08) 70214-2. · doi:10.1016/S0079-6638(08)70214-2
[151] C. Tian, Y. Xu, and W. Zuo, “Image denoising using deep cnn with batch renormalization,” Neural Networks, vol. 121, pp. 461-473, 2020. doi: 10.1016/j.neunet.2019.08.022. References · doi:10.1016/j.neunet.2019.08.022
[152] Y. Tian and S. G. Narasimhan, “Seeing through water: Image restoration using model-based tracking,” in IEEE International Conference on Computer Vision, pp. 2303-2310, 2009. doi: 10. 1109/ICCV.2009.5459440. · doi:10.1109/ICCV.2009.5459440
[153] Y. Tian, S. G. Narasimhan, and A. J. Vannevel, “Depth from optical turbulence,” in IEEE Conference on Computer Vision and Pattern Recognition, pp. 246-253, 2012. doi: 10.1109/CVPR. 2012.6247682. · doi:10.1109/CVPR.2012.6247682
[154] D. H. Tofsted, D. Quintis, S. G. O’Brien, J. Yarbrough, M. D. Bustillos, and G. M. T. Vaucher, Tech. Rep.
[155] D. Tofsted, S. O’Brien, J. Yarbrough, D. Quintis, and M. Bustil-los, “Characterization of atmospheric turbulence during the nato rtg-40 land field trials,” in Atmospheric Propagation IV, Proc. SPIE 6551, 2007. doi: 10.1117/12.720696. · doi:10.1117/12.720696
[156] R. Tyson, Principles of Adaptive Optics. CRC Press, 2010. doi: 10.1201/EBK1439808580. · doi:10.1201/EBK1439808580
[157] R. K. Tyson, “Adaptive optics and ground-to-space laser com-munications,” Applied Optics, vol. 35, no. 19, pp. 3640-3646, Jul. 1996. doi: 10.1364/AO.35.003640. · doi:10.1364/AO.35.003640
[158] G. C. Valley, “Isoplanatic degradation of tilt correction and short-term imaging systems,” Applied Optics, vol. 19, no. 4, pp. 574-577, Feb. 1980. doi: 10.1364/AO.19.000574. · doi:10.1364/AO.19.000574
[159] S. van Haver, “The extended Nijboer-Zernike diffraction theory and its applications,” Ph.D. dissertation, Delft University of Technology, 2010, 2010.
[160] A. Veeraraghavan, R. Raskar, A. Agrawal, A. Mohan, and J. Tumblin, “Dappled photography: Mask enhanced cameras for heterodyned light fields and coded aperture refocusing,” ACM Transactions on Graphics, vol. 26, no. 3, 69-es, 2007. doi: 10. 1145/1276377.1276463. · doi:10.1145/1276377.1276463
[161] M. T. Velluet, C. Bell, J. F. Daigle, J. Dijk, S. Gladysz, A. Kanaev, A. Lambert, D. Lemaster, G. Potvin, and M. Vorontsov, “Data collection and preliminary results on turbulence charac-terisation and mitigation techniques,” in Electro-Optical and Infrared Systems: Technology and Applications XVI, Proc. SPIE 11159, 2019. doi: 10.1117/12.2533821. · doi:10.1117/12.2533821
[162] S. V. Venkatakrishnan, C. A. Bouman, and B. Wohlberg, “Plug-and-play priors for model based reconstruction,” in IEEE Global Conference on Signal and Information Processing, IEEE, pp. 945-948, 2013. doi: 10.1109/GlobalSIP.2013.6737048. · doi:10.1109/GlobalSIP.2013.6737048
[163] D. Vint, G. D. Caterina, J. Soraghan, R. Lamb, and D. Humph-reys, “Analysis of deep learning architectures for turbulence mitigation in long-range imagery,” in Artificial Intelligence and Machine Learning in Defense Applications II, Proc. SPIE 11543, 2020. doi: 10.1117/12.2573927. · doi:10.1117/12.2573927
[164] D. G. Voelz, Computational Fourier Optics: A MATLAB Tutorial. SPIE Press, 2011. doi: 10.1117/3.858456. · doi:10.1117/3.858456
[165] D. G. Voelz, E. Wijerathna, A. Muschinski, and X. Xiao, “Com-puter simulations of optical turbulence in the weak-and strong-scattering regime: Angle-of-arrival fluctuations obtained from ray optics and wave optics,” Optical Engineering, vol. 57, no. 10, p. 104 102, 2018. doi: 10.1117/1.OE.57.10.104102. · doi:10.1117/1.OE.57.10.104102
[166] M. A. Vorontsov and G. W. Carhart, “Anisoplanatic imaging through turbulent media: Image recovery by local information fusion from a set of short-exposure images,” Journal of the Optical Society of America A, vol. 18, no. 6, pp. 1312-1324, Jun. 2001. doi: 10.1364/JOSAA.18.001312. · doi:10.1364/JOSAA.18.001312
[167] M. A. Vorontsov and V. Kolosov, “Target-in-the-loop beam control: Basic considerations for analysis and wave-front sensing,” Journal of the Optical Society of America A, vol. 22, no. 1, pp. 126-141, Jan. 2005. doi: 10.1364/JOSAA.22.000126. · doi:10.1364/JOSAA.22.000126
[168] F. Wang, I. Toselli, and O. Korotkova, “Two spatial light modula-tor system for laboratory simulation of random beam propagation in random media,” Applied Optics, vol. 55, no. 5, pp. 1112-1117, Feb. 2016. doi: 10.1364/AO.55.001112. · doi:10.1364/AO.55.001112
[169] J. Y. Wang and J. K. Markey, “Modal compensation of at-mospheric turbulence phase distortion,” Journal of the Optical Society of America, vol. 68, no. 1, pp. 78-87, Jan. 1978. doi: 10.1364/JOSA.68.000078. · doi:10.1364/JOSA.68.000078
[170] A. T. Watnik and D. F. Gardner, “Wavefront sensing in deep turbulence,” Optics and Photonics News, vol. 29, no. 10, pp. 38-45, Oct. 2018. doi: 10.1364/OPN.29.10.000038. References · doi:10.1364/OPN.29.10.000038
[171] B. M. Welsh, “Fourier-series-based atmospheric phase screen generator for simulating anisoplanatic geometries and temporal evolution,” in Propagation and Imaging through the Atmosphere, Proc. SPIE 3125, 1997. doi: 10.1117/12.279029. · doi:10.1117/12.279029
[172] M. R. Whiteley, M. C. Roggemann, and B. M. Welsh, “Temporal properties of the zernike expansion coefficients of turbulence-induced phase aberrations for aperture and source motion,” Jour-nal of the Optical Society of America A, vol. 15, no. 4, pp. 993-1005, Apr. 1998. doi: 10.1364/JOSAA.15.000993. · doi:10.1364/JOSAA.15.000993
[173] Y. Xie, W. Zhang, D. Tao, W. Hu, Y. Qu, and H. Wang, “Remov-ing turbulence effect via hybrid total variation and deformation-guided kernel regression,” IEEE Transactions on Image Process-ing, vol. 25, no. 10, pp. 4943-4958, Oct. 2016. doi: 10.1109/ TIP.2016.2598638. · Zbl 1408.94732 · doi:10.1109/TIP.2016.2598638
[174] B. Xue, Y. Liu, L. Cui, X. Bai, X. Cao, and F. Zhou, “Video sta-bilization in atmosphere turbulent conditions based on the Lapla-cian-Riesz pyramid,” Optics Express, vol. 24, no. 24, pp. 28 092-28 103, Nov. 2016. doi: 10.1364/OE.24.028092. · doi:10.1364/OE.24.028092
[175] R. Yasarla and V. M. Patel, “CNN-Based restoration of a single face image degraded by atmospheric turbulence,” IEEE Trans-actions on Biometrics, Behavior, and Identity Science, vol. 4, no. 2, pp. 222-233, 2022. doi: 10.1109/TBIOM.2022.3169697. · doi:10.1109/TBIOM.2022.3169697
[176] S. W. Zamir, A. Arora, S. Khan, M. Hayat, F. S. Khan, and M.-H. Yang, “Restormer: Efficient transformer for high-resolution image restoration,” in IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 5728-5739, 2022. doi: 10.1109/ CVPR52688.2022.00564. · doi:10.1109/CVPR52688.2022.00564
[177] V. U. Zavorotnyi, V. I. Kliatskin, and V. I. Tatarskii, “Strong fluctuations of electromagnetic-wave intensity in randomly inho-mogeneous media,” Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, vol. 73, pp. 481-497, Aug. 1977.
[178] K. Zhang, W. Zuo, Y. Chen, D. Meng, and L. Zhang, “Beyond a gaussian denoiser: Residual learning of deep CNN for image denoising,” IEEE Transactions on Image Processing, vol. 26, no. 7, pp. 3142-3155, 2017. doi: 10.1109/TIP.2017.2662206. · Zbl 1409.94754 · doi:10.1109/TIP.2017.2662206
[179] X. Zhang, Z. Mao, N. Chimitt, and S. H. Chan, “Imaging through the atmosphere using turbulence mitigation transformer,” url: https://arxiv.org/abs/2207.06465.
[180] Y. Zhang, K. Li, K. Li, L. Wang, B. Zhong, and Y. Fu, “Image super-resolution using very deep residual channel attention net-works,” in European Conference on Computer Vision, pp. 294-310, 2018. doi: 10.1007/978-3-030-01234-2_18. · doi:10.1007/978-3-030-01234-2_18
[181] Y. Zhang, Y. Tian, Y. Kong, B. Zhong, and Y. Fu, “Resid-ual dense network for image restoration,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 43, no. 7, pp. 2480-2495, 2021. doi: 10.1109/TPAMI.2020.2968521. · doi:10.1109/TPAMI.2020.2968521
[182] B. Zhou, A. Lapedriza, A. Khosla, A. Oliva, and A. Torralba, “Places: A 10 million image database for scene recognition,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017. doi: 10.1109/TPAMI.2017.2723009. · doi:10.1109/TPAMI.2017.2723009
[183] X. Zhu and P. Milanfar, “Removing atmospheric turbulence via space-invariant deconvolution,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 1, pp. 157-170, Jan. 2013. doi: 10.1109/TPAMI.2012.82. tilt correlation (approximation), 394 · doi:10.1109/TPAMI.2012.82
[184] Zernike-based simulation, 401 pseudo-code, 412 short summary, 409 WSS approximation, 403
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.