Abstract

Ghost imaging incorporating deep learning technology has recently attracted much attention in the optical imaging field. However, deterministic illumination and multiple exposure are still essential in most scenarios. Here we propose a ghost imaging scheme based on a novel dynamic decoding deep learning framework (Y-net), which works well under both deterministic and indeterministic illumination. Benefited from the end-to-end characteristic of our network, the image of a sample can be achieved directly from the data collected by the detector. The sample is illuminated only once in the experiment, and the spatial distribution of the speckle encoding the sample in the experiment can be completely different from that of the simulation speckle in training, as long as the statistical characteristics of the speckle remain unchanged. This approach is particularly important to high-resolution x-ray ghost imaging applications due to its potential for improving image quality and reducing radiation damage.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (3)

2018 (15)

T. M. Quan, T. Nguyen-Duc, and W.-K. Jeong, “Compressed sensing mri reconstruction using a generative adversarial network with a cyclic loss,” IEEE Trans. Med. Imaging 37(6), 1488–1497 (2018).
[Crossref]

Y. Sun, Z. Xia, and U. S. Kamilov, “Efficient and accurate inversion of multiple scattering with deep learning,” Opt. Express 26(11), 14678–14688 (2018).
[Crossref]

S. Li, M. Deng, J. Lee, A. Sinha, and G. Barbastathis, “Imaging through glass diffusers using densely connected convolutional networks,” Optica 5(7), 803–813 (2018).
[Crossref]

Y. Li, Y. Xue, and L. Tian, “Deep speckle correlation: a deep learning approach toward scalable imaging through scattering media,” Optica 5(10), 1181–1190 (2018).
[Crossref]

T. Nguyen, Y. Xue, Y. Li, L. Tian, and G. Nehmetallah, “Deep learning approach for fourier ptychography microscopy,” Opt. Express 26(20), 26470–26484 (2018).
[Crossref]

E. Nehme, L. E. Weiss, T. Michaeli, and Y. Shechtman, “Deep-storm: super-resolution single-molecule microscopy by deep learning,” Optica 5(4), 458–464 (2018).
[Crossref]

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

T. Shimobaba, Y. Endo, T. Nishitsuji, T. Takahashi, Y. Nagahama, S. Hasegawa, M. Sano, R. Hirayama, T. Kakue, A. Shiraki, and T. Ito, “Computational ghost imaging using deep learning,” Opt. Commun. 413, 147–151 (2018).
[Crossref]

A. Goy, K. Arthur, S. Li, and G. Barbastathis, “Low photon count phase retrieval using deep learning,” Phys. Rev. Lett. 121(24), 243902 (2018).
[Crossref]

R. Zhu, H. Yu, R. Lu, Z. Tan, and S. Han, “Spatial multiplexing reconstruction for fourier-transform ghost imaging via sparsity constraints,” Opt. Express 26(3), 2181–2190 (2018).
[Crossref]

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

A.-X. Zhang, Y.-H. He, L.-A. Wu, L.-M. Chen, and B.-B. Wang, “Tabletop x-ray ghost imaging with ultra-low radiation,” Optica 5(4), 374–377 (2018).
[Crossref]

A. M. Kingston, D. Pelliccia, A. Rack, M. P. Olbinado, Y. Cheng, G. R. Myers, and D. M. Paganin, “Ghost tomography,” Optica 5(12), 1516–1520 (2018).
[Crossref]

S. Li, F. Cropp, K. Kabra, T. Lane, G. Wetzstein, P. Musumeci, and D. Ratner, “Electron ghost imaging,” Phys. Rev. Lett. 121(11), 114801 (2018).
[Crossref]

X. Liu, J. Shi, X. Wu, and G. Zeng, “Fast first-photon ghost imaging,” Sci. Rep. 8(1), 5012 (2018).
[Crossref]

2017 (3)

M. J. Padgett and R. W. Boyd, “An introduction to ghost imaging: quantum and classical,” Philos. Trans. R. Soc., A 375(2099), 20160233 (2017).
[Crossref]

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref]

A. Sinha, J. Lee, S. Li, and G. Barbastathis, “Lensless computational imaging through deep learning,” Optica 4(9), 1117–1125 (2017).
[Crossref]

2016 (5)

R. Horisaki, R. Takagi, and J. Tanida, “Learning-based imaging through scattering media,” Opt. Express 24(13), 13738–13743 (2016).
[Crossref]

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental x-ray ghost imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
[Crossref]

R. I. Khakimov, B. Henson, D. Shin, S. Hodgman, R. Dall, K. Baldwin, and A. Truscott, “Ghost imaging with atoms,” Nature 540(7631), 100–103 (2016).
[Crossref]

Z. Liu, S. Tan, J. Wu, E. Li, X. Shen, and S. Han, “Spectral camera based on ghost imaging via sparsity constraints,” Sci. Rep. 6(1), 25718 (2016).
[Crossref]

2015 (2)

H. Yu, E. Li, W. Gong, and S. Han, “Structured image reconstruction for three-dimensional ghost imaging lidar,” Opt. Express 23(11), 14541–14551 (2015).
[Crossref]

D.-J. Zhang, H.-G. Li, Q.-L. Zhao, S. Wang, H.-B. Wang, J. Xiong, and K. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

2014 (3)

W.-K. Yu, M.-F. Li, X.-R. Yao, X.-F. Liu, L.-A. Wu, and G.-J. Zhai, “Adaptive compressive ghost imaging based on wavelet trees and sparse representation,” Opt. Express 22(6), 7133–7144 (2014).
[Crossref]

O. Katz, P. Heidmann, M. Fink, and S. Gigan, “Non-invasive single-shot imaging through scattering layers and around corners via speckle correlations,” Nat. Photonics 8(10), 784–790 (2014).
[Crossref]

D. P. Kingma and M. Welling, “Auto-encoding variational bayes,” Stat 1050, 1 (2014).

2013 (3)

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref]

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87(2), 023820 (2013).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

2012 (2)

2011 (2)

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98(11), 111115 (2011).
[Crossref]

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84(6), 061804 (2011).
[Crossref]

2009 (1)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

2008 (2)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
[Crossref]

S. Suresh, N. Sundararajan, and P. Saratchandran, “Risk-sensitive loss functions for sparse multi-category classification problems,” Inf. Sci. 178(12), 2621–2638 (2008).
[Crossref]

2006 (1)

G. Scarcelli, V. Berardi, and Y. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006).
[Crossref]

2004 (2)

J. Cheng and S. Han, “Incoherent coincidence imaging and its applicability in x-ray diffraction,” Phys. Rev. Lett. 92(9), 093903 (2004).
[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process 13(4), 600–612 (2004).
[Crossref]

1988 (1)

I. Freund, M. Rosenbluh, and S. Feng, “Memory effects in propagation of optical waves through disordered media,” Phys. Rev. Lett. 61(20), 2328–2331 (1988).
[Crossref]

1982 (1)

Acosta, A.

C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, and W. Shi, “Photo-realistic single image super-resolution using a generative adversarial network,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2017), pp. 4681–4690.

Aitken, A.

C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, and W. Shi, “Photo-realistic single image super-resolution using a generative adversarial network,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2017), pp. 4681–4690.

Arthur, K.

A. Goy, K. Arthur, S. Li, and G. Barbastathis, “Low photon count phase retrieval using deep learning,” Phys. Rev. Lett. 121(24), 243902 (2018).
[Crossref]

Astola, J.

Baldwin, K.

R. I. Khakimov, B. Henson, D. Shin, S. Hodgman, R. Dall, K. Baldwin, and A. Truscott, “Ghost imaging with atoms,” Nature 540(7631), 100–103 (2016).
[Crossref]

Barbastathis, G.

Benz, A.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Berardi, V.

G. Scarcelli, V. Berardi, and Y. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006).
[Crossref]

Bhatti, D.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Bina, M.

M. Bina, D. Magatti, M. Molteni, A. Gatti, L. A. Lugiato, and F. Ferri, “Backscattering differential ghost imaging in turbid media,” Phys. Rev. Lett. 110(8), 083901 (2013).
[Crossref]

Bocklage, L.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Bora, A.

A. Bora, A. Jalal, E. Price, and A. G. Dimakis, “Compressed sensing using generative models,” in Proceedings of the 34th International Conference on Machine Learning - Volume 70 (JMLR.org, 2017), pp. 537–546.

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process 13(4), 600–612 (2004).
[Crossref]

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Bowman, R.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Boyd, R. W.

M. J. Padgett and R. W. Boyd, “An introduction to ghost imaging: quantum and classical,” Philos. Trans. R. Soc., A 375(2099), 20160233 (2017).
[Crossref]

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84(6), 061804 (2011).
[Crossref]

Brenner, G.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Bromberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Caballero, J.

C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, and W. Shi, “Photo-realistic single image super-resolution using a generative adversarial network,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2017), pp. 4681–4690.

Cantelli, V.

D. Pelliccia, A. Rack, M. Scheel, V. Cantelli, and D. M. Paganin, “Experimental x-ray ghost imaging,” Phys. Rev. Lett. 117(11), 113902 (2016).
[Crossref]

Chan, K. W. C.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84(6), 061804 (2011).
[Crossref]

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R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Shapiro, J. H.

N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87(2), 023820 (2013).
[Crossref]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
[Crossref]

Shechtman, Y.

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process 13(4), 600–612 (2004).
[Crossref]

Shen, X.

Z. Liu, S. Tan, J. Wu, E. Li, X. Shen, and S. Han, “Spectral camera based on ghost imaging via sparsity constraints,” Sci. Rep. 6(1), 25718 (2016).
[Crossref]

Shi, J.

Shi, W.

C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, and W. Shi, “Photo-realistic single image super-resolution using a generative adversarial network,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2017), pp. 4681–4690.

Shih, Y.

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98(11), 111115 (2011).
[Crossref]

G. Scarcelli, V. Berardi, and Y. Shih, “Can two-photon correlation of chaotic light be considered as correlation of intensity fluctuations?” Phys. Rev. Lett. 96(6), 063602 (2006).
[Crossref]

Shimobaba, T.

T. Shimobaba, Y. Endo, T. Nishitsuji, T. Takahashi, Y. Nagahama, S. Hasegawa, M. Sano, R. Hirayama, T. Kakue, A. Shiraki, and T. Ito, “Computational ghost imaging using deep learning,” Opt. Commun. 413, 147–151 (2018).
[Crossref]

Shin, D.

R. I. Khakimov, B. Henson, D. Shin, S. Hodgman, R. Dall, K. Baldwin, and A. Truscott, “Ghost imaging with atoms,” Nature 540(7631), 100–103 (2016).
[Crossref]

Shiraki, A.

T. Shimobaba, Y. Endo, T. Nishitsuji, T. Takahashi, Y. Nagahama, S. Hasegawa, M. Sano, R. Hirayama, T. Kakue, A. Shiraki, and T. Ito, “Computational ghost imaging using deep learning,” Opt. Commun. 413, 147–151 (2018).
[Crossref]

Silberberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process 13(4), 600–612 (2004).
[Crossref]

Sinha, A.

Situ, G.

Skopintsev, P.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Sun, B.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Sun, L.

Sun, Y.

Sundararajan, N.

S. Suresh, N. Sundararajan, and P. Saratchandran, “Risk-sensitive loss functions for sparse multi-category classification problems,” Inf. Sci. 178(12), 2621–2638 (2008).
[Crossref]

Suresh, S.

S. Suresh, N. Sundararajan, and P. Saratchandran, “Risk-sensitive loss functions for sparse multi-category classification problems,” Inf. Sci. 178(12), 2621–2638 (2008).
[Crossref]

Takagi, R.

Takahashi, T.

T. Shimobaba, Y. Endo, T. Nishitsuji, T. Takahashi, Y. Nagahama, S. Hasegawa, M. Sano, R. Hirayama, T. Kakue, A. Shiraki, and T. Ito, “Computational ghost imaging using deep learning,” Opt. Commun. 413, 147–151 (2018).
[Crossref]

Tan, S.

Z. Liu, S. Tan, J. Wu, E. Li, X. Shen, and S. Han, “Spectral camera based on ghost imaging via sparsity constraints,” Sci. Rep. 6(1), 25718 (2016).
[Crossref]

Tan, Z.

Tang, X.

C. Dong, C. C. Loy, K. He, and X. Tang, “Learning a deep convolutional network for image super-resolution,” in Computer Vision – ECCV 2014, D. Fleet, T. Pajdla, B. Schiele, and T. Tuytelaars, eds. (Springer, 2014), pp. 184–199.

Tanida, J.

Tejani, A.

C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, and W. Shi, “Photo-realistic single image super-resolution using a generative adversarial network,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2017), pp. 4681–4690.

Teng, D.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

Theis, L.

C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, and W. Shi, “Photo-realistic single image super-resolution using a generative adversarial network,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2017), pp. 4681–4690.

Tian, L.

Tong, Z.

Totz, J.

C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, and W. Shi, “Photo-realistic single image super-resolution using a generative adversarial network,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2017), pp. 4681–4690.

Truscott, A.

R. I. Khakimov, B. Henson, D. Shin, S. Hodgman, R. Dall, K. Baldwin, and A. Truscott, “Ghost imaging with atoms,” Nature 540(7631), 100–103 (2016).
[Crossref]

Vartanyants Ivan, R. A.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Vittert, L. E.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

von Zanthier Joachim, Röhlsberger

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Wagner, J.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Waldmann, F.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Wang, B.-B.

Wang, F.

Wang, H.

Wang, H.-B.

D.-J. Zhang, H.-G. Li, Q.-L. Zhao, S. Wang, H.-B. Wang, J. Xiong, and K. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Wang, J.

Wang, K.

D.-J. Zhang, H.-G. Li, Q.-L. Zhao, S. Wang, H.-B. Wang, J. Xiong, and K. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Wang, S.

D.-J. Zhang, H.-G. Li, Q.-L. Zhao, S. Wang, H.-B. Wang, J. Xiong, and K. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Wang, W.

M. Lyu, W. Wang, H. Wang, H. Wang, G. Li, N. Chen, and G. Situ, “Deep-learning-based ghost imaging,” Sci. Rep. 7(1), 17865 (2017).
[Crossref]

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process 13(4), 600–612 (2004).
[Crossref]

C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, and W. Shi, “Photo-realistic single image super-resolution using a generative adversarial network,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2017), pp. 4681–4690.

Weiss, L. E.

Welling, M.

D. P. Kingma and M. Welling, “Auto-encoding variational bayes,” Stat 1050, 1 (2014).

Welsh, S.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Wenthaus, L.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Wetzstein, G.

S. Li, F. Cropp, K. Kabra, T. Lane, G. Wetzstein, P. Musumeci, and D. Ratner, “Electron ghost imaging,” Phys. Rev. Lett. 121(11), 114801 (2018).
[Crossref]

Willing, S.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Wu, J.

Z. Liu, S. Tan, J. Wu, E. Li, X. Shen, and S. Han, “Spectral camera based on ghost imaging via sparsity constraints,” Sci. Rep. 6(1), 25718 (2016).
[Crossref]

Wu, L.-A.

Wu, X.

Wurth, W.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Xia, Z.

Xiao, T.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

Xie, H.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

Xiong, J.

D.-J. Zhang, H.-G. Li, Q.-L. Zhao, S. Wang, H.-B. Wang, J. Xiong, and K. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Xue, Y.

Yao, X.-R.

Yu, H.

Yu, W.-K.

Zakyzhnyy, I.

R. Schneider, T. Mehringer, G. Mercurio, L. Wenthaus, A. Classen, G. Brenner, O. Gorobtsov, A. Benz, D. Bhatti, L. Bocklage, B. Fishcher, S. Lazarev, Y. Obukhov, K. Scblage, P. Skopintsev, J. Wagner, F. Waldmann, S. Willing, I. Zakyzhnyy, W. Wurth, R. A. Vartanyants Ivan, and Röhlsberger von Zanthier Joachim, “Quantum imaging with incoherently scattered light from a free-electron laser,” Nat. Phys. 14(2), 126–129 (2018).
[Crossref]

Zeng, G.

Zerom, P.

P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84(6), 061804 (2011).
[Crossref]

Zhai, G.-J.

Zhang, A.-X.

Zhang, D.-J.

D.-J. Zhang, H.-G. Li, Q.-L. Zhao, S. Wang, H.-B. Wang, J. Xiong, and K. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Zhang, Y.

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
[Crossref]

Zhao, Q.-L.

D.-J. Zhang, H.-G. Li, Q.-L. Zhao, S. Wang, H.-B. Wang, J. Xiong, and K. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
[Crossref]

Zhu, D.

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
[Crossref]

Zhu, R.

Appl. Opt. (1)

Appl. Phys. Lett. (2)

R. E. Meyers, K. S. Deacon, and Y. Shih, “Turbulence-free ghost imaging,” Appl. Phys. Lett. 98(11), 111115 (2011).
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O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
[Crossref]

IEEE Trans. Image Process (1)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans. Image Process 13(4), 600–612 (2004).
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IEEE Trans. Med. Imaging (1)

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J. Opt. Soc. Am. A (2)

Light: Sci. Appl. (1)

Y. Rivenson, Y. Zhang, H. Günaydın, D. Teng, and A. Ozcan, “Phase recovery and holographic image reconstruction using deep learning in neural networks,” Light: Sci. Appl. 7(2), 17141 (2018).
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[Crossref]

Nature (1)

R. I. Khakimov, B. Henson, D. Shin, S. Hodgman, R. Dall, K. Baldwin, and A. Truscott, “Ghost imaging with atoms,” Nature 540(7631), 100–103 (2016).
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Opt. Commun. (1)

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D.-J. Zhang, H.-G. Li, Q.-L. Zhao, S. Wang, H.-B. Wang, J. Xiong, and K. Wang, “Wavelength-multiplexing ghost imaging,” Phys. Rev. A 92(1), 013823 (2015).
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P. Zerom, K. W. C. Chan, J. C. Howell, and R. W. Boyd, “Entangled-photon compressive ghost imaging,” Phys. Rev. A 84(6), 061804 (2011).
[Crossref]

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
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N. D. Hardy and J. H. Shapiro, “Computational ghost imaging versus imaging laser radar for three-dimensional imaging,” Phys. Rev. A 87(2), 023820 (2013).
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Phys. Rev. Lett. (8)

H. Yu, R. Lu, S. Han, H. Xie, G. Du, T. Xiao, and D. Zhu, “Fourier-transform ghost imaging with hard x rays,” Phys. Rev. Lett. 117(11), 113901 (2016).
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C. Ledig, L. Theis, F. Huszár, J. Caballero, A. Cunningham, A. Acosta, A. Aitken, A. Tejani, J. Totz, Z. Wang, and W. Shi, “Photo-realistic single image super-resolution using a generative adversarial network,” in Proceedings of the IEEE conference on computer vision and pattern recognition, (IEEE, 2017), pp. 4681–4690.

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Figures (10)

Fig. 1.
Fig. 1. Overview of our ghost imaging method based on deep learning. (a) is the optical setup of the ghost imaging system. (b) is the data flow illustration of the network.
Fig. 2.
Fig. 2. Architecture of the proposed Y-net. It consists of two encoders and one decoder. The input of the network is the speckle and intensity data collected by the detectors and the output of the network is the image of the sample.
Fig. 3.
Fig. 3. Comparison between the speckles collected in the experiment and generated by simulation. (a) and (c) are the speckle images recorded by ${\rm CCD_1}$ and generated by simulation, respectively. (b) and (d) are the corresponding second-order auto-correlation of the speckle images in (a) and (c), respectively.
Fig. 4.
Fig. 4. Experimental results. (a) is the original image of samples, (b) and (c) are the patterns recorded by the detectors in the reference beam and the test beam, (d) and (e) are the output of our network with sampling number ${\rm M} = 4096$ and ${\rm M} = 1024$, (f) is the results obtained by traditional ghost imaging method.
Fig. 5.
Fig. 5. Experimental results under dynamic illuminations. (a) is the original image of samples, (b)(c)(d) are the speckles collected by the detector at different times, (e)(f)(g) are the reconstructed images corresponding to (b)(c)(d), respectively.
Fig. 6.
Fig. 6. Network performance for the static system. (a) is the original images, (b) is the output of the network.
Fig. 7.
Fig. 7. Network performance with dynamic illumination. (a) is the original images, (b) is the network outputs, and (c) is the corresponding input speckles. For each digit sample, the simulation experiment was repeated 10 times.
Fig. 8.
Fig. 8. Simulation results with different sampling numbers. (a) is the original images, (b) is the network output when ${\rm M} = 650$, (c) is the network output when ${\rm M} = 50$.
Fig. 9.
Fig. 9. Image quality as a function of the sampling number. The SSIM and PSNR of the testing data set are shown with the red line and the blue line, respectively.
Fig. 10.
Fig. 10. Results when the light intensity is weak. (a) is the original images, (b) is the partial-form speckle distribution with $PPP =0.5$, (c) is the output of our network corresponding to (b), (d) is the well-form speckle distribution with $PPP=100$, (e) is the output of our network corresponding to (d).

Tables (1)

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Table 1. Quantitative evaluation of the image quality

Equations (14)

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min x Θ ( x ) y 2 + γ Φ ( x ) ,
I r ( x r ) = | σ s E 0 ( x 0 ) h d ( x 0 , x r ) d x 0 | 2 ,
I t ( x t ) = | σ s , o b j e c t E 0 ( x 0 ) h d 1 ( x 0 , x ) t ( x ) h d 2 ( x , x t ) d x 0 d x | 2 ,
h z ( x 1 , x 2 ) = e i k z i λ z exp { i k 2 z ( x 1 x 2 ) 2 } ,
Δ I r ( x r ) Δ I t ( x t ) | T ( x r x t λ d 2 ) | 2 ,
I t ( x t ) r e f I r ( x r ) | T ( x r x t λ d 2 ) | 2 d x r .
y = A b ,
min x Θ ( x ) y 2 + α Π ( Θ ) A 2 + γ Φ ( x ) ,
min Ω 1 Θ 1 ( y ) x 2 + α Π 1 ( A ) Θ 2 + γ Φ 1 .
L ( P , Q ) = 1 2 N i N [ Q i log ( P i ) + ( 1 Q i ) log ( 1 P i ) ] ,
S S I M ( U , V ) = ( 2 μ u μ v + C 1 ) ( 2 σ u v + C 2 ) ( μ u 2 + μ v 2 + C 1 ) ( σ u 2 + σ v 2 + C 2 ) ,
P S N R ( U , V ) = 10 log 10 M A X I 2 M S E ( U , V ) ,
M S E ( U , V ) = 1 N i N ( U i V i ) 2 ,
P P P = N p h N ,

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