Abstract

We propose a deep learning computational ghost imaging (CGI) scheme to achieve sub-Nyquist and high-quality image reconstruction. Unlike the second-order-correlation CGI and compressive-sensing CGI, which use lots of illumination patterns and a one-dimensional (1-D) light intensity sequence (LIS) for image reconstruction, a deep neural network (DAttNet) is proposed to restore the target image only using the 1-D LIS. The DAttNet is trained with simulation data and retrieves the target image from experimental data. The experimental results indicate that the proposed scheme can provide high-quality images with a sub-Nyquist sampling ratio and performs better than the conventional and compressive-sensing CGI methods in sub-Nyquist sampling ratio conditions (e.g., 5.45%). The proposed scheme has potential practical applications in underwater, real-time and dynamic CGI.

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

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References

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H. Wu, R. Wang, C. Li, M. Chen, G. Zhao, Z. He, and L. Cheng, “Influence of intensity fluctuations on Hadamard-based computational ghost imaging,” Opt. Commun. 454, 124490 (2020).
[Crossref]

2019 (6)

S. Ma, Z. Liu, C. Wang, C. Hu, E. Li, W. Gong, Z. Tong, J. Wu, X. Shen, and S. Han, “Ghost imaging LiDAR via sparsity constraints using push-broom scanning,” Opt. Express 27(9), 13219–13228 (2019).
[Crossref]

M. Chen, H. Wu, R. Wang, Z. He, H. Li, J. Gan, and G. Zhao, “Computational ghost imaging with uncertain imaging distance,” Opt. Commun. 445, 106–110 (2019).
[Crossref]

M. Sun and J. Zhang, “Single-pixel imaging and its application in three-dimensional reconstruction: a brief review,” Sensors 19(3), 732 (2019).
[Crossref]

W. Yu, “Super Sub-Nyquist Single-Pixel Imaging by Means of Cake-Cutting Hadamard Basis Sort,” Sensors 19(19), 4122 (2019).
[Crossref]

S. Rizvi, J. Cao, K. Zhang, and Q. Hao, “Improving Imaging Quality of Real-time Fourier Single-pixel Imaging via Deep Learning,” Sensors 19(19), 4190 (2019).
[Crossref]

F. Wang, H. Wang, H. Wang, G. Li, and G. Situ, “Learning from simulation: An end-to-end deep-learning approach for computational ghost imaging,” Opt. Express 27(18), 25560–25572 (2019).
[Crossref]

2018 (3)

2017 (5)

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]

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[Crossref]

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
[Crossref]

J. Huang and D. Shi, “Multispectral computational ghost imaging with multiplexed illumination,” J. Opt. 19(7), 075701 (2017).
[Crossref]

M. Sun, L. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7(1), 3464 (2017).
[Crossref]

2016 (6)

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (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]

L. Wang and S. Zhao, “Fast reconstructed and high-quality ghost imaging with fast Walsh–Hadamard transform,” Photonics Res. 4(6), 240–244 (2016).
[Crossref]

C. Yang, C. Wang, J. Guan, C. Zhang, S. Guo, W. Gong, and F. Gao, “Scalar-matrix-structured ghost imaging,” Photonics Res. 4(6), 281–285 (2016).
[Crossref]

H. Wu, X. Zhang, J. Gan, C. Luo, and P. Ge, “High-quality correspondence imaging based on sorting and compressive sensing technique,” Laser Phys. Lett. 13(11), 115205 (2016).
[Crossref]

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8(12), 991 (2016).
[Crossref]

2015 (2)

2014 (2)

2012 (1)

R. E. Meyers, K. S. Deacon, and Y. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012).
[Crossref]

2008 (1)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
[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. on Image Process. 13(4), 600–612 (2004).
[Crossref]

1995 (1)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Ba, J.

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

Barbastathis, G.

Bo, Z.

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8(12), 991 (2016).
[Crossref]

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. on Image Process. 13(4), 600–612 (2004).
[Crossref]

Brox, T.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” In International Conference on Medical image computing and computer-assisted intervention, pp. 234–241, Springer, Cham, Oct 5, 2015.

Cao, J.

S. Rizvi, J. Cao, K. Zhang, and Q. Hao, “Improving Imaging Quality of Real-time Fourier Single-pixel Imaging via Deep Learning,” Sensors 19(19), 4190 (2019).
[Crossref]

Chen, H.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost Imaging Based on Deep Learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Chen, M.

H. Wu, R. Wang, C. Li, M. Chen, G. Zhao, Z. He, and L. Cheng, “Influence of intensity fluctuations on Hadamard-based computational ghost imaging,” Opt. Commun. 454, 124490 (2020).
[Crossref]

M. Chen, H. Wu, R. Wang, Z. He, H. Li, J. Gan, and G. Zhao, “Computational ghost imaging with uncertain imaging distance,” Opt. Commun. 445, 106–110 (2019).
[Crossref]

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8(12), 991 (2016).
[Crossref]

Chen, N.

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]

Cheng, J.

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

Cheng, L.

H. Wu, R. Wang, C. Li, M. Chen, G. Zhao, Z. He, and L. Cheng, “Influence of intensity fluctuations on Hadamard-based computational ghost imaging,” Opt. Commun. 454, 124490 (2020).
[Crossref]

Deacon, K. S.

R. E. Meyers, K. S. Deacon, and Y. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012).
[Crossref]

Deng, M.

Dong, G.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost Imaging Based on Deep Learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Du, G.

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]

Edgar, M. P.

M. Sun, L. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7(1), 3464 (2017).
[Crossref]

Fischer, P.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” In International Conference on Medical image computing and computer-assisted intervention, pp. 234–241, Springer, Cham, Oct 5, 2015.

Folgoc, L. L.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, and B. Kainz, “Attention u-net: Learning where to look for the pancreas,” arXiv preprint arXiv:1804.03999 (2018).

Fukatsu, S.

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
[Crossref]

Gan, J.

M. Chen, H. Wu, R. Wang, Z. He, H. Li, J. Gan, and G. Zhao, “Computational ghost imaging with uncertain imaging distance,” Opt. Commun. 445, 106–110 (2019).
[Crossref]

H. Wu, X. Zhang, J. Gan, C. Luo, and P. Ge, “High-quality correspondence imaging based on sorting and compressive sensing technique,” Laser Phys. Lett. 13(11), 115205 (2016).
[Crossref]

Gao, F.

C. Yang, C. Wang, J. Guan, C. Zhang, S. Guo, W. Gong, and F. Gao, “Scalar-matrix-structured ghost imaging,” Photonics Res. 4(6), 281–285 (2016).
[Crossref]

Ge, P.

H. Wu, X. Zhang, J. Gan, C. Luo, and P. Ge, “High-quality correspondence imaging based on sorting and compressive sensing technique,” Laser Phys. Lett. 13(11), 115205 (2016).
[Crossref]

Gibson, G. M.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

Gong, W.

S. Ma, Z. Liu, C. Wang, C. Hu, E. Li, W. Gong, Z. Tong, J. Wu, X. Shen, and S. Han, “Ghost imaging LiDAR via sparsity constraints using push-broom scanning,” Opt. Express 27(9), 13219–13228 (2019).
[Crossref]

C. Yang, C. Wang, J. Guan, C. Zhang, S. Guo, W. Gong, and F. Gao, “Scalar-matrix-structured ghost imaging,” Photonics Res. 4(6), 281–285 (2016).
[Crossref]

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8(12), 991 (2016).
[Crossref]

W. Gong, “High-resolution pseudo-inverse ghost imaging,” Photonics Res. 3(5), 234–237 (2015).
[Crossref]

Gu, S.

R. Timofte, S. Gu, J. Wu, and L. Van Gool, “Ntire 2018 challenge on single image super-resolution: Methods and results,” In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, pp. 852–863, June, (2018).

Guan, C.

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[Crossref]

Guan, J.

C. Yang, C. Wang, J. Guan, C. Zhang, S. Guo, W. Gong, and F. Gao, “Scalar-matrix-structured ghost imaging,” Photonics Res. 4(6), 281–285 (2016).
[Crossref]

Guo, H.

Guo, Q.

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[Crossref]

Guo, S.

C. Yang, C. Wang, J. Guan, C. Zhang, S. Guo, W. Gong, and F. Gao, “Scalar-matrix-structured ghost imaging,” Photonics Res. 4(6), 281–285 (2016).
[Crossref]

Hammerla, N. Y.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, and B. Kainz, “Attention u-net: Learning where to look for the pancreas,” arXiv preprint arXiv:1804.03999 (2018).

Han, S.

S. Ma, Z. Liu, C. Wang, C. Hu, E. Li, W. Gong, Z. Tong, J. Wu, X. Shen, and S. Han, “Ghost imaging LiDAR via sparsity constraints using push-broom scanning,” Opt. Express 27(9), 13219–13228 (2019).
[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]

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

Hao, Q.

S. Rizvi, J. Cao, K. Zhang, and Q. Hao, “Improving Imaging Quality of Real-time Fourier Single-pixel Imaging via Deep Learning,” Sensors 19(19), 4190 (2019).
[Crossref]

He, Y.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost Imaging Based on Deep Learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

He, Z.

H. Wu, R. Wang, C. Li, M. Chen, G. Zhao, Z. He, and L. Cheng, “Influence of intensity fluctuations on Hadamard-based computational ghost imaging,” Opt. Commun. 454, 124490 (2020).
[Crossref]

M. Chen, H. Wu, R. Wang, Z. He, H. Li, J. Gan, and G. Zhao, “Computational ghost imaging with uncertain imaging distance,” Opt. Commun. 445, 106–110 (2019).
[Crossref]

Heinrich, M.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, and B. Kainz, “Attention u-net: Learning where to look for the pancreas,” arXiv preprint arXiv:1804.03999 (2018).

Hendry, E.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

Hinton, G. E.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” Advances in neural information processing systems, 1097–1105 (2012).

Hobson, P. A.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

Hornett, S. M.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

Hu, C.

Huang, G.

G. Huang, Z. Liu, L. Van Der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4700–4708. 2017.

Huang, J.

J. Huang and D. Shi, “Multispectral computational ghost imaging with multiplexed illumination,” J. Opt. 19(7), 075701 (2017).
[Crossref]

Ioffe, S.

S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” arXiv preprint arXiv:1502.03167 (2015).

Kainz, B.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, and B. Kainz, “Attention u-net: Learning where to look for the pancreas,” arXiv preprint arXiv:1804.03999 (2018).

Kingma, D. P.

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

Krizhevsky, A.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” Advances in neural information processing systems, 1097–1105 (2012).

Lan, R.

Lee, J.

Lee, M.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, and B. Kainz, “Attention u-net: Learning where to look for the pancreas,” arXiv preprint arXiv:1804.03999 (2018).

Li, C.

H. Wu, R. Wang, C. Li, M. Chen, G. Zhao, Z. He, and L. Cheng, “Influence of intensity fluctuations on Hadamard-based computational ghost imaging,” Opt. Commun. 454, 124490 (2020).
[Crossref]

Li, E.

Li, G.

F. Wang, H. Wang, H. Wang, G. Li, and G. Situ, “Learning from simulation: An end-to-end deep-learning approach for computational ghost imaging,” Opt. Express 27(18), 25560–25572 (2019).
[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]

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[Crossref]

Li, H.

M. Chen, H. Wu, R. Wang, Z. He, H. Li, J. Gan, and G. Zhao, “Computational ghost imaging with uncertain imaging distance,” Opt. Commun. 445, 106–110 (2019).
[Crossref]

Li, L.

Li, M.

Li, S.

Liu, H.

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[Crossref]

Liu, X.

Liu, Z.

S. Ma, Z. Liu, C. Wang, C. Hu, E. Li, W. Gong, Z. Tong, J. Wu, X. Shen, and S. Han, “Ghost imaging LiDAR via sparsity constraints using push-broom scanning,” Opt. Express 27(9), 13219–13228 (2019).
[Crossref]

G. Huang, Z. Liu, L. Van Der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4700–4708. 2017.

Lu, R.

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]

Luo, B.

Luo, C.

H. Wu, X. Zhang, J. Gan, C. Luo, and P. Ge, “High-quality correspondence imaging based on sorting and compressive sensing technique,” Laser Phys. Lett. 13(11), 115205 (2016).
[Crossref]

Lyu, M.

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]

Ma, S.

McDonagh, S.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, and B. Kainz, “Attention u-net: Learning where to look for the pancreas,” arXiv preprint arXiv:1804.03999 (2018).

Meng, L.

M. Sun, L. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7(1), 3464 (2017).
[Crossref]

Meyers, R. E.

R. E. Meyers, K. S. Deacon, and Y. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012).
[Crossref]

Misawa, K.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, and B. Kainz, “Attention u-net: Learning where to look for the pancreas,” arXiv preprint arXiv:1804.03999 (2018).

Mori, K.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, and B. Kainz, “Attention u-net: Learning where to look for the pancreas,” arXiv preprint arXiv:1804.03999 (2018).

Mühlenbernd, H.

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[Crossref]

Oktay, O.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, and B. Kainz, “Attention u-net: Learning where to look for the pancreas,” arXiv preprint arXiv:1804.03999 (2018).

O-oka, Y.

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
[Crossref]

Padgett, M. J.

M. Sun, L. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7(1), 3464 (2017).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Radwell, N.

M. Sun, L. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7(1), 3464 (2017).
[Crossref]

Rizvi, S.

S. Rizvi, J. Cao, K. Zhang, and Q. Hao, “Improving Imaging Quality of Real-time Fourier Single-pixel Imaging via Deep Learning,” Sensors 19(19), 4190 (2019).
[Crossref]

Ronneberger, O.

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” In International Conference on Medical image computing and computer-assisted intervention, pp. 234–241, Springer, Cham, Oct 5, 2015.

Schlemper, J.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, and B. Kainz, “Attention u-net: Learning where to look for the pancreas,” arXiv preprint arXiv:1804.03999 (2018).

Sergienko, A. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Shapiro, J. H.

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

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. on Image Process. 13(4), 600–612 (2004).
[Crossref]

Shen, X.

Shi, D.

J. Huang and D. Shi, “Multispectral computational ghost imaging with multiplexed illumination,” J. Opt. 19(7), 075701 (2017).
[Crossref]

Shi, J.

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[Crossref]

Shih, Y.

R. E. Meyers, K. S. Deacon, and Y. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012).
[Crossref]

Shih, Y. H.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[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. on Image Process. 13(4), 600–612 (2004).
[Crossref]

Sinha, A.

Situ, G.

Stantchev, R. I.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

Strekalov, D. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Sun, B.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

Sun, M.

M. Sun and J. Zhang, “Single-pixel imaging and its application in three-dimensional reconstruction: a brief review,” Sensors 19(3), 732 (2019).
[Crossref]

M. Sun, L. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7(1), 3464 (2017).
[Crossref]

Sutskever, I.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” Advances in neural information processing systems, 1097–1105 (2012).

Szegedy, C.

S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” arXiv preprint arXiv:1502.03167 (2015).

Timofte, R.

R. Timofte, S. Gu, J. Wu, and L. Van Gool, “Ntire 2018 challenge on single image super-resolution: Methods and results,” In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, pp. 852–863, June, (2018).

Tong, Z.

Van Der Maaten, L.

G. Huang, Z. Liu, L. Van Der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4700–4708. 2017.

Van Gool, L.

R. Timofte, S. Gu, J. Wu, and L. Van Gool, “Ntire 2018 challenge on single image super-resolution: Methods and results,” In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, pp. 852–863, June, (2018).

Wang, C.

Wang, F.

Wang, G.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost Imaging Based on Deep Learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Wang, H.

Wang, L.

L. Wang and S. Zhao, “Fast reconstructed and high-quality ghost imaging with fast Walsh–Hadamard transform,” Photonics Res. 4(6), 240–244 (2016).
[Crossref]

Wang, R.

H. Wu, R. Wang, C. Li, M. Chen, G. Zhao, Z. He, and L. Cheng, “Influence of intensity fluctuations on Hadamard-based computational ghost imaging,” Opt. Commun. 454, 124490 (2020).
[Crossref]

M. Chen, H. Wu, R. Wang, Z. He, H. Li, J. Gan, and G. Zhao, “Computational ghost imaging with uncertain imaging distance,” Opt. Commun. 445, 106–110 (2019).
[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. on Image Process. 13(4), 600–612 (2004).
[Crossref]

Weinberger, K. Q.

G. Huang, Z. Liu, L. Van Der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4700–4708. 2017.

Wu, G.

Wu, H.

H. Wu, R. Wang, C. Li, M. Chen, G. Zhao, Z. He, and L. Cheng, “Influence of intensity fluctuations on Hadamard-based computational ghost imaging,” Opt. Commun. 454, 124490 (2020).
[Crossref]

M. Chen, H. Wu, R. Wang, Z. He, H. Li, J. Gan, and G. Zhao, “Computational ghost imaging with uncertain imaging distance,” Opt. Commun. 445, 106–110 (2019).
[Crossref]

H. Wu, X. Zhang, J. Gan, C. Luo, and P. Ge, “High-quality correspondence imaging based on sorting and compressive sensing technique,” Laser Phys. Lett. 13(11), 115205 (2016).
[Crossref]

Wu, J.

S. Ma, Z. Liu, C. Wang, C. Hu, E. Li, W. Gong, Z. Tong, J. Wu, X. Shen, and S. Han, “Ghost imaging LiDAR via sparsity constraints using push-broom scanning,” Opt. Express 27(9), 13219–13228 (2019).
[Crossref]

R. Timofte, S. Gu, J. Wu, and L. Van Gool, “Ntire 2018 challenge on single image super-resolution: Methods and results,” In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, pp. 852–863, June, (2018).

Wu, L.

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]

Xu, W.

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8(12), 991 (2016).
[Crossref]

Xu, Z.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost Imaging Based on Deep Learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Yang, B.

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[Crossref]

Yang, C.

C. Yang, C. Wang, J. Guan, C. Zhang, S. Guo, W. Gong, and F. Gao, “Scalar-matrix-structured ghost imaging,” Photonics Res. 4(6), 281–285 (2016).
[Crossref]

Yao, X.

Yin, L.

Yin, P.

Yu, H.

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8(12), 991 (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]

Yu, W.

Zentgraf, T.

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[Crossref]

Zhai, G.

Zhang, A.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost Imaging Based on Deep Learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Zhang, C.

C. Yang, C. Wang, J. Guan, C. Zhang, S. Guo, W. Gong, and F. Gao, “Scalar-matrix-structured ghost imaging,” Photonics Res. 4(6), 281–285 (2016).
[Crossref]

Zhang, J.

M. Sun and J. Zhang, “Single-pixel imaging and its application in three-dimensional reconstruction: a brief review,” Sensors 19(3), 732 (2019).
[Crossref]

Zhang, K.

S. Rizvi, J. Cao, K. Zhang, and Q. Hao, “Improving Imaging Quality of Real-time Fourier Single-pixel Imaging via Deep Learning,” Sensors 19(19), 4190 (2019).
[Crossref]

Zhang, S.

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[Crossref]

Zhang, X.

H. Wu, X. Zhang, J. Gan, C. Luo, and P. Ge, “High-quality correspondence imaging based on sorting and compressive sensing technique,” Laser Phys. Lett. 13(11), 115205 (2016).
[Crossref]

Zhao, C.

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8(12), 991 (2016).
[Crossref]

Zhao, G.

H. Wu, R. Wang, C. Li, M. Chen, G. Zhao, Z. He, and L. Cheng, “Influence of intensity fluctuations on Hadamard-based computational ghost imaging,” Opt. Commun. 454, 124490 (2020).
[Crossref]

M. Chen, H. Wu, R. Wang, Z. He, H. Li, J. Gan, and G. Zhao, “Computational ghost imaging with uncertain imaging distance,” Opt. Commun. 445, 106–110 (2019).
[Crossref]

Zhao, S.

L. Wang and S. Zhao, “Fast reconstructed and high-quality ghost imaging with fast Walsh–Hadamard transform,” Photonics Res. 4(6), 240–244 (2016).
[Crossref]

Zheng, G.

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[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, S.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost Imaging Based on Deep Learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Appl. Phys. Lett. (2)

Y. O-oka and S. Fukatsu, “Differential ghost imaging in time domain,” Appl. Phys. Lett. 111(6), 061106 (2017).
[Crossref]

R. E. Meyers, K. S. Deacon, and Y. Shih, “Positive-negative turbulence-free ghost imaging,” Appl. Phys. Lett. 100(13), 131114 (2012).
[Crossref]

IEEE Trans. on 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. on Image Process. 13(4), 600–612 (2004).
[Crossref]

J. Opt. (1)

J. Huang and D. Shi, “Multispectral computational ghost imaging with multiplexed illumination,” J. Opt. 19(7), 075701 (2017).
[Crossref]

Laser Phys. Lett. (1)

H. Wu, X. Zhang, J. Gan, C. Luo, and P. Ge, “High-quality correspondence imaging based on sorting and compressive sensing technique,” Laser Phys. Lett. 13(11), 115205 (2016).
[Crossref]

Opt. Commun. (2)

H. Wu, R. Wang, C. Li, M. Chen, G. Zhao, Z. He, and L. Cheng, “Influence of intensity fluctuations on Hadamard-based computational ghost imaging,” Opt. Commun. 454, 124490 (2020).
[Crossref]

M. Chen, H. Wu, R. Wang, Z. He, H. Li, J. Gan, and G. Zhao, “Computational ghost imaging with uncertain imaging distance,” Opt. Commun. 445, 106–110 (2019).
[Crossref]

Opt. Express (6)

Optica (1)

Photonics Res. (3)

W. Gong, “High-resolution pseudo-inverse ghost imaging,” Photonics Res. 3(5), 234–237 (2015).
[Crossref]

L. Wang and S. Zhao, “Fast reconstructed and high-quality ghost imaging with fast Walsh–Hadamard transform,” Photonics Res. 4(6), 240–244 (2016).
[Crossref]

C. Yang, C. Wang, J. Guan, C. Zhang, S. Guo, W. Gong, and F. Gao, “Scalar-matrix-structured ghost imaging,” Photonics Res. 4(6), 281–285 (2016).
[Crossref]

Phys. Rev. A (2)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

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

Phys. Rev. Lett. (2)

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

Remote Sens. (1)

W. Gong, H. Yu, C. Zhao, Z. Bo, M. Chen, and W. Xu, “Improving the imaging quality of ghost imaging lidar via sparsity constraint by time-resolved technique,” Remote Sens. 8(12), 991 (2016).
[Crossref]

Sci. Adv. (2)

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

H. Liu, B. Yang, Q. Guo, J. Shi, C. Guan, G. Zheng, H. Mühlenbernd, G. Li, T. Zentgraf, and S. Zhang, “Single-pixel computational ghost imaging with helicity-dependent metasurface hologram,” Sci. Adv. 3(9), e1701477 (2017).
[Crossref]

Sci. Rep. (3)

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]

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Ghost Imaging Based on Deep Learning,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

M. Sun, L. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A Russian Dolls ordering of the Hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7(1), 3464 (2017).
[Crossref]

Sensors (3)

W. Yu, “Super Sub-Nyquist Single-Pixel Imaging by Means of Cake-Cutting Hadamard Basis Sort,” Sensors 19(19), 4122 (2019).
[Crossref]

M. Sun and J. Zhang, “Single-pixel imaging and its application in three-dimensional reconstruction: a brief review,” Sensors 19(3), 732 (2019).
[Crossref]

S. Rizvi, J. Cao, K. Zhang, and Q. Hao, “Improving Imaging Quality of Real-time Fourier Single-pixel Imaging via Deep Learning,” Sensors 19(19), 4190 (2019).
[Crossref]

Other (8)

O. Ronneberger, P. Fischer, and T. Brox, “U-net: Convolutional networks for biomedical image segmentation,” In International Conference on Medical image computing and computer-assisted intervention, pp. 234–241, Springer, Cham, Oct 5, 2015.

O. Oktay, J. Schlemper, L. L. Folgoc, M. Lee, M. Heinrich, K. Misawa, K. Mori, S. McDonagh, N. Y. Hammerla, and B. Kainz, “Attention u-net: Learning where to look for the pancreas,” arXiv preprint arXiv:1804.03999 (2018).

G. Huang, Z. Liu, L. Van Der Maaten, and K. Q. Weinberger, “Densely connected convolutional networks,” In Proceedings of the IEEE conference on computer vision and pattern recognition, pp. 4700–4708. 2017.

A. Krizhevsky, I. Sutskever, and G. E. Hinton, “Imagenet classification with deep convolutional neural networks,” Advances in neural information processing systems, 1097–1105 (2012).

S. Ioffe and C. Szegedy, “Batch normalization: Accelerating deep network training by reducing internal covariate shift,” arXiv preprint arXiv:1502.03167 (2015).

R. Timofte, S. Gu, J. Wu, and L. Van Gool, “Ntire 2018 challenge on single image super-resolution: Methods and results,” In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, pp. 852–863, June, (2018).

http://cocodataset.org/#download .

D. P. Kingma and J. Ba, “Adam: A method for stochastic optimization,” arXiv preprint arXiv:1412.6980 (2014).

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Figures (6)

Fig. 1.
Fig. 1. Experimental setup. The target is printed on a white paper.
Fig. 2.
Fig. 2. The architecture of the proposed DAttNet. BN, batch normalization; DiConv, dilated convolution; Conv 3 × 3, convolution with filter size 3 × 3; Conv 1 × 1, convolution with filter size 1 × 1; Dropout, dropout rate is 0.05; ReLU, rectified linear unit; NLT, normalization and linear transformation; Average pooling and pooling, stride (2, 2); Upscale, factor 2.
Fig. 3.
Fig. 3. Test results of the trained model with the SRs of 2%, 5.45% and 6.75%.
Fig. 4.
Fig. 4. Comparison of experimental results obtained by FWHT, RD, CSRD, CC and DL with the SR at 2%, 5.45%, 6.75% and 8%, respectively.
Fig. 5.
Fig. 5. Comparison of PSNR and SSIM acquired by FWHT, RD, CSRD, CC and DL using different SRs. The horizontal axis is not plotted in ratio.
Fig. 6.
Fig. 6. Experimental results of a grayscale target reconstructed by FWHT, RD, CSRD, CC and DL with a SR of 5.45%.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

I k = T ( x , y ) P k ( x , y ) d x d y ,
O ( x , y ) = 1 K k = 1 K ( I k I ) P k ( x , y ) ,
T ^ = T ^ ( x , y ) = ( I ; Ψ ) ,
L ( Ψ ) = 1 2 N n = 1 N | | ( B n ; Ψ ) G n | | 2 ,

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