Abstract

At present, a large number of samplings are required to reconstruct an image of the objects in ghost imaging. When imaging moving objects, it will be hard to perform enough samplings during the moment when the objects can be taken as immobile, causing the reconstructed image of the objects deteriorating. In this paper, we propose a temporal intensity difference correlation ghost imaging scheme, in which a high-quality image of the moving objects within a complex scene can be extracted with much fewer samplings. The spatial sparsity of the moving objects is utilized, while only a linear algorithm is required. This method decreases the number of required samplings, thus relaxing the requirement on high refresh frequency of illumination source and high speed detector, to obtain the information of moving objects with ghost imaging.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  4. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005).
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  5. S. S. Hodgman, W. Bu, S. B. Mann, R. I. Khakimov, and A. G. Truscott, “Higher-Order Quantum Ghost Imaging with Ultracold Atoms,” Phys. Rev. Lett. 122(23), 233601 (2019).
    [Crossref]
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  7. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
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  8. B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J Padgett, “3D computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
    [Crossref]
  9. W. Gong, C. Zhang, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
    [Crossref]
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    [Crossref]
  11. 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]
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  13. Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361(6403), eaat2298 (2018).
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  15. W. Tan, X. Huang, S. Nan, Y. Bai, and X. Fu, “Effect of the collection range of a bucket detector on ghost imaging through turbulent atmosphere,” J. Opt. Soc. Am. A 36(7), 1261–1266 (2019).
    [Crossref]
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    [Crossref]
  22. K. W. Chan, M. N. O’Sullivan, and R. W. Boyd, “Optimization of thermal ghost imaging: high-order correlations vs. background subtraction,” Opt. Express 18(6), 5562–5573 (2010).
    [Crossref]
  23. J. Li, D. Yang, B. Luo, G. Wu, L. Yin, and H. Guo, “Image quality recovery in binary ghost imaging by adding random noise,” Opt. Lett. 42(8), 1640–1643 (2017).
    [Crossref]
  24. H. Li, J. Xiong, and G. H. Zeng, “Lensless ghost imaging for moving objects,” Opt. Eng. 50(12), 127005 (2011).
    [Crossref]
  25. E. R. Li, Z. W. Bo, M. L. Chen, W. L. Gong, and S. S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
    [Crossref]
  26. S. Jiao, M. Sun, Y. Gao, T. Lei, Z. Xie, and X. Yuan, “Motion estimation and quality enhancement for a single image in dynamic single-pixel imaging,” Opt. Express 27(9), 12841–12854 (2019).
    [Crossref]
  27. D. B. Phillips, M. J. Sun, M J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3(4), e1601782 (2017).
    [Crossref]
  28. N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowwan, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1(5), 285–289 (2014).
    [Crossref]
  29. W. T. Liu, T. Zhang, J. Y. Liu, P. X. Chen, and J. M. Yuan, “Experimental quantum state tomography via compressed sampling,” Phys. Rev. Lett. 108(17), 170403 (2012).
    [Crossref]
  30. O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
    [Crossref]
  31. I. Reed, “On a moment theorem for complex Gaussian processes,” IEEE Trans. Inf. Theory 8(3), 194–195 (1962).
    [Crossref]
  32. D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71(1), 013801 (2005).
    [Crossref]
  33. S. Sun, W. T. Liu, H. Z. Lin, E. F. Zhang, J. Y. Liu, Q. Li, and P. X. Chen, “Multi-scale adaptive computational ghost imaging,” Sci. Rep. 6(1), 37013 (2016).
    [Crossref]
  34. M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging schemes: fast and broadband,” Opt. Express 12(24), 6067–6081 (2004).
    [Crossref]
  35. 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]
  36. Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7(1), 45325 (2017).
    [Crossref]
  37. Z. H. Xu, W. Chen, J. Penuelas, M. Padgett, and M. J. Sun, “1000 fps computational ghost imaging using LED-based structured illumination,” Opt. Express 26(3), 2427–2434 (2018).
    [Crossref]
  38. M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
    [Crossref]

2019 (5)

S. S. Hodgman, W. Bu, S. B. Mann, R. I. Khakimov, and A. G. Truscott, “Higher-Order Quantum Ghost Imaging with Ultracold Atoms,” Phys. Rev. Lett. 122(23), 233601 (2019).
[Crossref]

J. P. Zhao, Y. W. E K. Williams, X. C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light: Sci. Appl. 8(1), 55 (2019).
[Crossref]

Y. Zhang, W. Li, H. Wu, Y. Chen, X. Su, Y. Xiao, and Y. Gu, “High-visibility underwater ghost imaging in low illumination,” Opt. Commun. 441, 45–48 (2019).
[Crossref]

S. Jiao, M. Sun, Y. Gao, T. Lei, Z. Xie, and X. Yuan, “Motion estimation and quality enhancement for a single image in dynamic single-pixel imaging,” Opt. Express 27(9), 12841–12854 (2019).
[Crossref]

W. Tan, X. Huang, S. Nan, Y. Bai, and X. Fu, “Effect of the collection range of a bucket detector on ghost imaging through turbulent atmosphere,” J. Opt. Soc. Am. A 36(7), 1261–1266 (2019).
[Crossref]

2018 (6)

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Deep-learning-based ghost imaging,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

S. Ota, R. Horisaki, Y. Kawamura, M. Ugawa, I. Sato, K. Hashimoto, and K. Waki, “Ghost cytometry,” Science 360(6394), 1246–1251 (2018).
[Crossref]

Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361(6403), eaat2298 (2018).
[Crossref]

Z. H. Xu, W. Chen, J. Penuelas, M. Padgett, and M. J. Sun, “1000 fps computational ghost imaging using LED-based structured illumination,” Opt. Express 26(3), 2427–2434 (2018).
[Crossref]

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

L. Li, Q. Li, S. Sun, H. Z. Lin, W. T. Liu, and P. X. Chen, “Imaging through scattering layers exceeding memory effect range with spatial-correlation-achieved point-spread-function,” Opt. Lett. 43(8), 1670–1673 (2018).
[Crossref]

2017 (4)

J. Li, D. Yang, B. Luo, G. Wu, L. Yin, and H. Guo, “Image quality recovery in binary ghost imaging by adding random noise,” Opt. Lett. 42(8), 1640–1643 (2017).
[Crossref]

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7(1), 45325 (2017).
[Crossref]

D. B. Phillips, M. J. Sun, M J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3(4), e1601782 (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]

2016 (4)

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]

W. Gong, C. Zhang, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

S. Sun, W. T. Liu, H. Z. Lin, E. F. Zhang, J. Y. Liu, Q. Li, and P. X. Chen, “Multi-scale adaptive computational ghost imaging,” Sci. Rep. 6(1), 37013 (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]

2015 (2)

Y. K. Xu, W. T. Liu, E. F. Zhang, Q. Li, H. Y. Dai, and P. X. Chen, “Is ghost imaging intrinsically more powerful against scattering?” Opt. Express 23(26), 32993–33000 (2015).
[Crossref]

P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

2014 (2)

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowwan, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1(5), 285–289 (2014).
[Crossref]

E. R. Li, Z. W. Bo, M. L. Chen, W. L. Gong, and S. S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
[Crossref]

2013 (2)

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
[Crossref]

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

2012 (1)

W. T. Liu, T. Zhang, J. Y. Liu, P. X. Chen, and J. M. Yuan, “Experimental quantum state tomography via compressed sampling,” Phys. Rev. Lett. 108(17), 170403 (2012).
[Crossref]

2011 (1)

H. Li, J. Xiong, and G. H. Zeng, “Lensless ghost imaging for moving objects,” Opt. Eng. 50(12), 127005 (2011).
[Crossref]

2010 (1)

2009 (1)

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

2008 (1)

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

2007 (1)

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

2005 (2)

D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71(1), 013801 (2005).
[Crossref]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref]

2004 (3)

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
[Crossref]

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref]

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging schemes: fast and broadband,” Opt. Express 12(24), 6067–6081 (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]

1962 (1)

I. Reed, “On a moment theorem for complex Gaussian processes,” IEEE Trans. Inf. Theory 8(3), 194–195 (1962).
[Crossref]

Altmann, Y.

Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361(6403), eaat2298 (2018).
[Crossref]

Aspden, R. S.

P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Bache, M.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
[Crossref]

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging schemes: fast and broadband,” Opt. Express 12(24), 6067–6081 (2004).
[Crossref]

Bai, Y.

Barnett, S. M.

D. B. Phillips, M. J. Sun, M J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3(4), e1601782 (2017).
[Crossref]

Bell, J. E.

P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref]

Bo, Z. W.

E. R. Li, Z. W. Bo, M. L. Chen, W. L. Gong, and S. S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
[Crossref]

Bowman, A.

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

Bowwan, R.

Boyd, R. W.

J. P. Zhao, Y. W. E K. Williams, X. C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light: Sci. Appl. 8(1), 55 (2019).
[Crossref]

P. A. Morris, R. S. Aspden, J. E. Bell, R. W. Boyd, and M. J Padgett, “Imaging with a small number of photons,” Nat. Commun. 6(1), 5913 (2015).
[Crossref]

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
[Crossref]

K. W. Chan, M. N. O’Sullivan, and R. W. Boyd, “Optimization of thermal ghost imaging: high-order correlations vs. background subtraction,” Opt. Express 18(6), 5562–5573 (2010).
[Crossref]

R. S. Bennink, S. J. Bentley, R. W. Boyd, and J. C. Howell, “Quantum and classical coincidence imaging,” Phys. Rev. Lett. 92(3), 033601 (2004).
[Crossref]

Brambilla, E.

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging schemes: fast and broadband,” Opt. Express 12(24), 6067–6081 (2004).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
[Crossref]

Bromberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

Bu, W.

S. S. Hodgman, W. Bu, S. B. Mann, R. I. Khakimov, and A. G. Truscott, “Higher-Order Quantum Ghost Imaging with Ultracold Atoms,” Phys. Rev. Lett. 122(23), 233601 (2019).
[Crossref]

Cao, D. Z.

D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71(1), 013801 (2005).
[Crossref]

Chan, K. W.

Chen, H.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Deep-learning-based ghost imaging,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Chen, L. M.

Chen, M.

W. Gong, C. Zhang, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

Chen, M. L.

E. R. Li, Z. W. Bo, M. L. Chen, W. L. Gong, and S. S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
[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]

Chen, P. X.

L. Li, Q. Li, S. Sun, H. Z. Lin, W. T. Liu, and P. X. Chen, “Imaging through scattering layers exceeding memory effect range with spatial-correlation-achieved point-spread-function,” Opt. Lett. 43(8), 1670–1673 (2018).
[Crossref]

S. Sun, W. T. Liu, H. Z. Lin, E. F. Zhang, J. Y. Liu, Q. Li, and P. X. Chen, “Multi-scale adaptive computational ghost imaging,” Sci. Rep. 6(1), 37013 (2016).
[Crossref]

Y. K. Xu, W. T. Liu, E. F. Zhang, Q. Li, H. Y. Dai, and P. X. Chen, “Is ghost imaging intrinsically more powerful against scattering?” Opt. Express 23(26), 32993–33000 (2015).
[Crossref]

W. T. Liu, T. Zhang, J. Y. Liu, P. X. Chen, and J. M. Yuan, “Experimental quantum state tomography via compressed sampling,” Phys. Rev. Lett. 108(17), 170403 (2012).
[Crossref]

Chen, W.

Chen, Y.

Y. Zhang, W. Li, H. Wu, Y. Chen, X. Su, Y. Xiao, and Y. Gu, “High-visibility underwater ghost imaging in low illumination,” Opt. Commun. 441, 45–48 (2019).
[Crossref]

D’Angelo, M.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref]

Dai, H. Y.

Dai, Q.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7(1), 45325 (2017).
[Crossref]

Dong, G.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Deep-learning-based ghost imaging,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Du T. Xiao, 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.

D. B. Phillips, M. J. Sun, M J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3(4), e1601782 (2017).
[Crossref]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowwan, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1(5), 285–289 (2014).
[Crossref]

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

Faccio, D.

Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361(6403), eaat2298 (2018).
[Crossref]

Figueiredo, M. A.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

Fu, X.

Gao, Y.

Gatti, A.

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E. R. Li, Z. W. Bo, M. L. Chen, W. L. Gong, and S. S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
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Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361(6403), eaat2298 (2018).
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Y. Zhang, W. Li, H. Wu, Y. Chen, X. Su, Y. Xiao, and Y. Gu, “High-visibility underwater ghost imaging in low illumination,” Opt. Commun. 441, 45–48 (2019).
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Guo, H.

Han, S.

W. Gong, C. Zhang, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
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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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E. R. Li, Z. W. Bo, M. L. Chen, W. L. Gong, and S. S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
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Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Deep-learning-based ghost imaging,” Sci. Rep. 8(1), 6469 (2018).
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He, Y. H.

Hero, A. O.

Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361(6403), eaat2298 (2018).
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S. S. Hodgman, W. Bu, S. B. Mann, R. I. Khakimov, and A. G. Truscott, “Higher-Order Quantum Ghost Imaging with Ultracold Atoms,” Phys. Rev. Lett. 122(23), 233601 (2019).
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J. M. Taylor, M

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K. Williams, Y. W. E

J. P. Zhao, Y. W. E K. Williams, X. C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light: Sci. Appl. 8(1), 55 (2019).
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Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
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S. Ota, R. Horisaki, Y. Kawamura, M. Ugawa, I. Sato, K. Hashimoto, and K. Waki, “Ghost cytometry,” Science 360(6394), 1246–1251 (2018).
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S. S. Hodgman, W. Bu, S. B. Mann, R. I. Khakimov, and A. G. Truscott, “Higher-Order Quantum Ghost Imaging with Ultracold Atoms,” Phys. Rev. Lett. 122(23), 233601 (2019).
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Li, E. R.

E. R. Li, Z. W. Bo, M. L. Chen, W. L. Gong, and S. S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
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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).
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Li, H.

H. Li, J. Xiong, and G. H. Zeng, “Lensless ghost imaging for moving objects,” Opt. Eng. 50(12), 127005 (2011).
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Li, L.

Li, Q.

Li, W.

Y. Zhang, W. Li, H. Wu, Y. Chen, X. Su, Y. Xiao, and Y. Gu, “High-visibility underwater ghost imaging in low illumination,” Opt. Commun. 441, 45–48 (2019).
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L. Li, Q. Li, S. Sun, H. Z. Lin, W. T. Liu, and P. X. Chen, “Imaging through scattering layers exceeding memory effect range with spatial-correlation-achieved point-spread-function,” Opt. Lett. 43(8), 1670–1673 (2018).
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Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7(1), 45325 (2017).
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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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A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Correlated imaging, quantum and classical,” Phys. Rev. A 70(1), 013802 (2004).
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M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging schemes: fast and broadband,” Opt. Express 12(24), 6067–6081 (2004).
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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).
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O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
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Malik, M.

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
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S. S. Hodgman, W. Bu, S. B. Mann, R. I. Khakimov, and A. G. Truscott, “Higher-Order Quantum Ghost Imaging with Ultracold Atoms,” Phys. Rev. Lett. 122(23), 233601 (2019).
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Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361(6403), eaat2298 (2018).
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Ota, S.

S. Ota, R. Horisaki, Y. Kawamura, M. Ugawa, I. Sato, K. Hashimoto, and K. Waki, “Ghost cytometry,” Science 360(6394), 1246–1251 (2018).
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Padgett, M. J

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Y. Altmann, S. McLaughlin, M. J. Padgett, V. K. Goyal, A. O. Hero, and D. Faccio, “Quantum-inspired computational imaging,” Science 361(6403), eaat2298 (2018).
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Phillips, D. B.

D. B. Phillips, M. J. Sun, M J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3(4), e1601782 (2017).
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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).
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Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7(1), 45325 (2017).
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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).
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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).
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Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
[Crossref]

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Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7(1), 45325 (2017).
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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]

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]

Su, X.

Y. Zhang, W. Li, H. Wu, Y. Chen, X. Su, Y. Xiao, and Y. Gu, “High-visibility underwater ghost imaging in low illumination,” Opt. Commun. 441, 45–48 (2019).
[Crossref]

Sun, B.

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

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D. B. Phillips, M. J. Sun, M J. M. Taylor, M. P. Edgar, S. M. Barnett, G. M. Gibson, and M. J. Padgett, “Adaptive foveated single-pixel imaging with dynamic supersampling,” Sci. Adv. 3(4), e1601782 (2017).
[Crossref]

Sun, S.

L. Li, Q. Li, S. Sun, H. Z. Lin, W. T. Liu, and P. X. Chen, “Imaging through scattering layers exceeding memory effect range with spatial-correlation-achieved point-spread-function,” Opt. Lett. 43(8), 1670–1673 (2018).
[Crossref]

S. Sun, W. T. Liu, H. Z. Lin, E. F. Zhang, J. Y. Liu, Q. Li, and P. X. Chen, “Multi-scale adaptive computational ghost imaging,” Sci. Rep. 6(1), 37013 (2016).
[Crossref]

Suo, J.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7(1), 45325 (2017).
[Crossref]

Tan, W.

Truscott, A. G.

S. S. Hodgman, W. Bu, S. B. Mann, R. I. Khakimov, and A. G. Truscott, “Higher-Order Quantum Ghost Imaging with Ultracold Atoms,” Phys. Rev. Lett. 122(23), 233601 (2019).
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S. Ota, R. Horisaki, Y. Kawamura, M. Ugawa, I. Sato, K. Hashimoto, and K. Waki, “Ghost cytometry,” Science 360(6394), 1246–1251 (2018).
[Crossref]

Valencia, A.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. H. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94(6), 063601 (2005).
[Crossref]

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

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S. Ota, R. Horisaki, Y. Kawamura, M. Ugawa, I. Sato, K. Hashimoto, and K. Waki, “Ghost cytometry,” Science 360(6394), 1246–1251 (2018).
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Wang, B.

Wang, G.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Deep-learning-based ghost imaging,” Sci. Rep. 8(1), 6469 (2018).
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Wang, H.

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).
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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).
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Wang, K. G.

D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71(1), 013801 (2005).
[Crossref]

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, 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, Y.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7(1), 45325 (2017).
[Crossref]

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

Wright, S. J.

M. A. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007).
[Crossref]

Wu, G.

Wu, H.

Y. Zhang, W. Li, H. Wu, Y. Chen, X. Su, Y. Xiao, and Y. Gu, “High-visibility underwater ghost imaging in low illumination,” Opt. Commun. 441, 45–48 (2019).
[Crossref]

Wu, L. A.

Xiao, Y.

Y. Zhang, W. Li, H. Wu, Y. Chen, X. Su, Y. Xiao, and Y. Gu, “High-visibility underwater ghost imaging in low illumination,” Opt. Commun. 441, 45–48 (2019).
[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]

Xie, Z.

Xiong, J.

H. Li, J. Xiong, and G. H. Zeng, “Lensless ghost imaging for moving objects,” Opt. Eng. 50(12), 127005 (2011).
[Crossref]

D. Z. Cao, J. Xiong, and K. G. Wang, “Geometrical optics in correlated imaging systems,” Phys. Rev. A 71(1), 013801 (2005).
[Crossref]

Xu, W.

W. Gong, C. Zhang, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

Xu, Y. K.

Xu, Z.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Deep-learning-based ghost imaging,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Xu, Z. H.

Yang, D.

Yin, L.

Yu, H.

W. Gong, C. Zhang, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (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]

Yuan, J. M.

W. T. Liu, T. Zhang, J. Y. Liu, P. X. Chen, and J. M. Yuan, “Experimental quantum state tomography via compressed sampling,” Phys. Rev. Lett. 108(17), 170403 (2012).
[Crossref]

Yuan, X.

Zeng, G. H.

H. Li, J. Xiong, and G. H. Zeng, “Lensless ghost imaging for moving objects,” Opt. Eng. 50(12), 127005 (2011).
[Crossref]

Zhang, A.

Y. He, G. Wang, G. Dong, S. Zhu, H. Chen, A. Zhang, and Z. Xu, “Deep-learning-based ghost imaging,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Zhang, A. X.

Zhang, C.

W. Gong, C. Zhang, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

Zhang, E. F.

S. Sun, W. T. Liu, H. Z. Lin, E. F. Zhang, J. Y. Liu, Q. Li, and P. X. Chen, “Multi-scale adaptive computational ghost imaging,” Sci. Rep. 6(1), 37013 (2016).
[Crossref]

Y. K. Xu, W. T. Liu, E. F. Zhang, Q. Li, H. Y. Dai, and P. X. Chen, “Is ghost imaging intrinsically more powerful against scattering?” Opt. Express 23(26), 32993–33000 (2015).
[Crossref]

Zhang, T.

W. T. Liu, T. Zhang, J. Y. Liu, P. X. Chen, and J. M. Yuan, “Experimental quantum state tomography via compressed sampling,” Phys. Rev. Lett. 108(17), 170403 (2012).
[Crossref]

Zhang, X. C.

J. P. Zhao, Y. W. E K. Williams, X. C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light: Sci. Appl. 8(1), 55 (2019).
[Crossref]

Zhang, Y.

Y. Zhang, W. Li, H. Wu, Y. Chen, X. Su, Y. Xiao, and Y. Gu, “High-visibility underwater ghost imaging in low illumination,” Opt. Commun. 441, 45–48 (2019).
[Crossref]

Zhao, J. P.

J. P. Zhao, Y. W. E K. Williams, X. C. Zhang, and R. W. Boyd, “Spatial sampling of terahertz fields with sub-wavelength accuracy via probe-beam encoding,” Light: Sci. Appl. 8(1), 55 (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]

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, “Deep-learning-based ghost imaging,” Sci. Rep. 8(1), 6469 (2018).
[Crossref]

Appl. Phys. Lett. (2)

E. R. Li, Z. W. Bo, M. L. Chen, W. L. Gong, and S. S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
[Crossref]

O. S. Magana-Loaiza, G. A. Howland, M. Malik, J. C. Howell, and R. W. Boyd, “Compressive object tracking using entangled photons,” Appl. Phys. Lett. 102(23), 231104 (2013).
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Figures (5)

Fig. 1.
Fig. 1. . Schematic Diagram of Experimental Setup. A laser beam is expanded by a 4-f system ($f1=5cm, f2=20cm$) and the expanded beam size is about 5mm, then is scattered by a RGG. An aperture, whose diameter is about 3mm is located in the focal plane of a 4-f system $f_3=f_4=20cm$. The scattering field is divided in two beams, each of which there is a 2-f system ($f_5=f_6=30cm$). The L7 is an imaging lens with $f7=20cm$. The scene to be imaged is displayed by the DMD and the image of the displayed scene is obtained by the CCD2, which also works as a bucket detector in GI.
Fig. 2.
Fig. 2. . Comparison between TDGI and TGI. (a) The first row are the discretized scene frames to be imaged. The second row are the results reconstructed by TGI, each of which is from with 500 samplings. The position of the moving object is marked by dashed box. The third row are the reconstructed images of moving objects, each of which is obtained by TDGI with 500 samplings. (b) The MSE of the reconstructed image in TDGI and that in TGI with different number of samplings.
Fig. 3.
Fig. 3. . Comparison between TDGI and TGI in the scene with multiple objects. The first row are the discretized scene frames to be imaged. The second row are the results reconstructed by TGI, each of which is from with 3000 samplings. The position of the moving object is marked by dashed box. The third row are the reconstructed images of moving objects, each of which is obtained by TDGI with 3000 samplings. (b) The MSE of the reconstructed image in TDGI and that in TGI with different number of samplings.
Fig. 4.
Fig. 4. . Comparison between TDGI and CS. (a) the first row is the reconstructed image in CS and the second row is the image reconstructed in TDGI. (b) the MSE of the images obtained in CS and that in TDGI. (c) the time consumption of the data processing in CS and in TDGI.
Fig. 5.
Fig. 5. . Comparison between TDGI and RCTDGI. The reconstructed imaged from TDGI and RCTDGI with N samplings, the upper row is from TDGI and the lower one is from RCTDGI.

Equations (14)

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E s ( r s , t ) = E 0 ( r s , t 0 ) h s ( r s , r s ; t , t 0 ) d r s , { s = o , r }
h s ( r s , r s ; t , t 0 ) = e j k z s j λ z s exp { j k 2 z s ( r s r s ) 2 } , { s = o , r }
E r ( r r , t ) E o ( r o , t ) = E 0 ( r r , t 0 ) E 0 ( r o , t 0 ) h r , ( r r , r r ; t , t 0 ) h o , ( r o , r o ; t , t 0 ) d r r d r r ,
E r ( r r , t ) E o ( r o , t ) = exp { j k 2 z ( | r r | 2 | r o | 2 ) } λ 2 z 2 | E 0 ( r ) | 2 exp { j k z ( r r r o ) r } d r ,
E r ( r r , t ) E o ( r o , t ) m = exp { j k 2 z ( | r r | 2 | r o | 2 ) } λ 2 z 2 | E 0 ( r ) | 2 exp { j k z ( r r r o ) r } d r + σ ( N ) ,
G ( r r , t ) = I ( r r , t ) B ( t ) I ( r r , t ) B ( t ) ,
G ( r r , t ) m = S ( r o , t ) | E r ( r r , t ) E o ( r o , t ) m | 2 d r o .
G ( r r , t ) m = S ( r o , t ) α | F { E 0 ~ ( r r r o λ z ) } | 2 + ϵ ( N ) ,
B D T ( t l n ) = S ( r o , t k ) I ( r o , t k n ) d r o S ( r o , t l ) I ( r o , t l n ) d r o , ( n = 1 , 2 N ) .
B T D ( t l n ) = Δ S ( r o , t l ) I ( r o , t l n ) d r o ,
Δ G ( r r , t l ) = I ( r r , t l ) B T D ( t l ) I ( r r , t l ) B T D ( t l ) ,
Δ G m ( r r , t l ) = Δ S ( r o , t l ) α | F { E 0 ~ ( r r r o λ z ) } | 2 + ϵ Δ ( N ) ,
Δ G m ( r r , t l ) = I ( r r , t l ) ) B ( t l ) I ( r r , t l ) ) B ( t l ) ( I ( r r , t k ) ) B ( t k ) I ( r r , t k ) ) B ( t k ) ) ,
Δ G m ( r r , t l ) = G m ( r r , t l ) G m ( r r , t k ) ,

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