Abstract

We propose a novel method for object reconstruction of ghost imaging based on Pseudo-Inverse, where the original objects are reconstructed by computing the pseudo-inverse of the matrix constituted by the row vectors of each speckle field. We conduct reconstructions for binary images and gray-scale images. With equal number of measurements, our method presents a satisfying performance on enhancing Peak Signal to Noise Ratio (PSNR) and reducing computing time. Being compared with the other existing methods, its PSNR distinctly exceeds that of the traditional Ghost Imaging (GI) and Differential Ghost Imaging (DGI). In comparison with the Compressive-sensing Ghost Imaging (CGI), the computing time is substantially shortened, and in regard to PSNR our method exceeds CGI on grayscale images and performs as well as CGI visually on binary images. The influence of both the detection noise and the accuracy of measurement matrix on PSNR are also presented.

© 2014 Optical Society of America

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  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).
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  5. 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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  6. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
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  7. J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
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  10. P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35(14), 2391–2393 (2010).
    [Crossref] [PubMed]
  11. W. Gong and S. Han, “A method to improve the visibility of ghost images obtained by thermal light,” Phys. Lett. A 374(8), 1005–1008 (2010).
    [Crossref]
  12. F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
    [Crossref] [PubMed]
  13. B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20(15), 16892–16901 (2012).
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  14. X. H. Chen, I. N. Agafonov, K. H. Luo, Q. Liu, R. Xian, M. V. Chekhova, and L. A. Wu, “High-visibility, high-order lensless ghost imaging with thermal light,” Opt. Lett. 35(8), 1166–1168 (2010).
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  15. B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Advances in Optics and Photonics 2(4), 405–450 (2010).
    [Crossref]
  16. B. I. Erkmen, “Computational ghost imaging for remote sensing,” J. Opt. Soc. Am. A 29(5), 782–789 (2012).
    [Crossref] [PubMed]
  17. P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82(3), 033817 (2010).
    [Crossref]
  18. J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17(10), 7916–7921 (2009).
    [Crossref] [PubMed]
  19. W. Gong and S. Han, “Correlated imaging in scattering media,” Opt. Lett. 36(3), 394–396 (2011).
    [Crossref] [PubMed]
  20. 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] [PubMed]
  21. C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
    [Crossref]
  22. O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95(13), 131110 (2009).
    [Crossref]
  23. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
    [Crossref]
  24. J. Du, W. Gong, and S. Han, “The influence of sparsity property of images on ghost imaging with thermal light,” Opt. Lett. 37(6), 1067–1069 (2012).
    [Crossref] [PubMed]
  25. 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).
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  26. E. Li, Z. Bo, M. Chen, W. Gong, and S. Han, “Ghost imaging of a moving target with an unknown constant speed,” Appl. Phys. Lett. 104(25), 251120 (2014).
    [Crossref]
  27. W. Chen and X. Chen, “Marked ghost imaging,” Appl. Phys. Lett. 104(25), 251109 (2014).
    [Crossref]
  28. W. Gong and S. Han, “The influence of axial correlation depth of light field on lensless ghost imaging,” JOSA B 27(4), 675–678 (2010).
    [Crossref]
  29. S. Chountasis, V. N. Katsikis, and D. Pappas, “Applications of the Moore-Penrose inverse in digital image restoration,” Math. Probl. Eng. 2009, 1–12 (2009).
    [Crossref]
  30. S. Chountasis, V. N. Katsikis, and D. Pappas, “Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse,” Math. Probl. Eng. 2010, 1–14 (2010).
    [Crossref]
  31. K. Manjunatha Prasad and R. B. Bapat, “The generalized Moore-Penrose inverse,” Linear Algebra Appl. 165, 59–69 (1992).
    [Crossref]
  32. E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” Signal Processing Magazine, IEEE 25(2), 21–30 (2008).
    [Crossref]

2014 (3)

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

W. Chen and X. Chen, “Marked ghost imaging,” Appl. Phys. Lett. 104(25), 251109 (2014).
[Crossref]

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] [PubMed]

2013 (1)

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] [PubMed]

2012 (5)

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

J. Du, W. Gong, and S. Han, “The influence of sparsity property of images on ghost imaging with thermal light,” Opt. Lett. 37(6), 1067–1069 (2012).
[Crossref] [PubMed]

B. I. Erkmen, “Computational ghost imaging for remote sensing,” J. Opt. Soc. Am. A 29(5), 782–789 (2012).
[Crossref] [PubMed]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20(15), 16892–16901 (2012).
[Crossref]

2011 (1)

2010 (8)

S. Chountasis, V. N. Katsikis, and D. Pappas, “Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse,” Math. Probl. Eng. 2010, 1–14 (2010).
[Crossref]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82(3), 033817 (2010).
[Crossref]

X. H. Chen, I. N. Agafonov, K. H. Luo, Q. Liu, R. Xian, M. V. Chekhova, and L. A. Wu, “High-visibility, high-order lensless ghost imaging with thermal light,” Opt. Lett. 35(8), 1166–1168 (2010).
[Crossref] [PubMed]

P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35(14), 2391–2393 (2010).
[Crossref] [PubMed]

W. Gong and S. Han, “A method to improve the visibility of ghost images obtained by thermal light,” Phys. Lett. A 374(8), 1005–1008 (2010).
[Crossref]

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref] [PubMed]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Advances in Optics and Photonics 2(4), 405–450 (2010).
[Crossref]

W. Gong and S. Han, “The influence of axial correlation depth of light field on lensless ghost imaging,” JOSA B 27(4), 675–678 (2010).
[Crossref]

2009 (4)

S. Chountasis, V. N. Katsikis, and D. Pappas, “Applications of the Moore-Penrose inverse in digital image restoration,” Math. Probl. Eng. 2009, 1–12 (2009).
[Crossref]

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

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

J. Cheng, “Ghost imaging through turbulent atmosphere,” Opt. Express 17(10), 7916–7921 (2009).
[Crossref] [PubMed]

2008 (2)

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

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” Signal Processing Magazine, IEEE 25(2), 21–30 (2008).
[Crossref]

2004 (2)

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

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref] [PubMed]

2002 (1)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-Photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref] [PubMed]

1995 (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] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
[Crossref] [PubMed]

1992 (1)

K. Manjunatha Prasad and R. B. Bapat, “The generalized Moore-Penrose inverse,” Linear Algebra Appl. 165, 59–69 (1992).
[Crossref]

Agafonov, I. N.

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]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref] [PubMed]

Bapat, R. B.

K. Manjunatha Prasad and R. B. Bapat, “The generalized Moore-Penrose inverse,” Linear Algebra Appl. 165, 59–69 (1992).
[Crossref]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-Photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref] [PubMed]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-Photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref] [PubMed]

Bertolotti, J.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

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] [PubMed]

Blum, C.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

Bo, Z.

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

Boyd, R. W.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-Photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref] [PubMed]

Brambilla, E.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref] [PubMed]

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]

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

Candès, E. J.

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” Signal Processing Magazine, IEEE 25(2), 21–30 (2008).
[Crossref]

Chekhova, M. V.

Chen, M.

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

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

Chen, W.

W. Chen and X. Chen, “Marked ghost imaging,” Appl. Phys. Lett. 104(25), 251109 (2014).
[Crossref]

Chen, X.

W. Chen and X. Chen, “Marked ghost imaging,” Appl. Phys. Lett. 104(25), 251109 (2014).
[Crossref]

Chen, X. H.

Cheng, J.

Chountasis, S.

S. Chountasis, V. N. Katsikis, and D. Pappas, “Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse,” Math. Probl. Eng. 2010, 1–14 (2010).
[Crossref]

S. Chountasis, V. N. Katsikis, and D. Pappas, “Applications of the Moore-Penrose inverse in digital image restoration,” Math. Probl. Eng. 2009, 1–12 (2009).
[Crossref]

Clemente, P.

Du, J.

Durán, V.

Edgar, M. P.

Erkmen, B. I.

B. I. Erkmen, “Computational ghost imaging for remote sensing,” J. Opt. Soc. Am. A 29(5), 782–789 (2012).
[Crossref] [PubMed]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Advances in Optics and Photonics 2(4), 405–450 (2010).
[Crossref]

Ferri, F.

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] [PubMed]

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref] [PubMed]

Gatti, A.

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] [PubMed]

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref] [PubMed]

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

Gong, W.

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

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

J. Du, W. Gong, and S. Han, “The influence of sparsity property of images on ghost imaging with thermal light,” Opt. Lett. 37(6), 1067–1069 (2012).
[Crossref] [PubMed]

W. Gong and S. Han, “Correlated imaging in scattering media,” Opt. Lett. 36(3), 394–396 (2011).
[Crossref] [PubMed]

W. Gong and S. Han, “The influence of axial correlation depth of light field on lensless ghost imaging,” JOSA B 27(4), 675–678 (2010).
[Crossref]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82(3), 033817 (2010).
[Crossref]

W. Gong and S. Han, “A method to improve the visibility of ghost images obtained by thermal light,” Phys. Lett. A 374(8), 1005–1008 (2010).
[Crossref]

Han, S.

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

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

J. Du, W. Gong, and S. Han, “The influence of sparsity property of images on ghost imaging with thermal light,” Opt. Lett. 37(6), 1067–1069 (2012).
[Crossref] [PubMed]

W. Gong and S. Han, “Correlated imaging in scattering media,” Opt. Lett. 36(3), 394–396 (2011).
[Crossref] [PubMed]

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82(3), 033817 (2010).
[Crossref]

W. Gong and S. Han, “The influence of axial correlation depth of light field on lensless ghost imaging,” JOSA B 27(4), 675–678 (2010).
[Crossref]

W. Gong and S. Han, “A method to improve the visibility of ghost images obtained by thermal light,” Phys. Lett. A 374(8), 1005–1008 (2010).
[Crossref]

Katsikis, V. N.

S. Chountasis, V. N. Katsikis, and D. Pappas, “Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse,” Math. Probl. Eng. 2010, 1–14 (2010).
[Crossref]

S. Chountasis, V. N. Katsikis, and D. Pappas, “Applications of the Moore-Penrose inverse in digital image restoration,” Math. Probl. Eng. 2009, 1–12 (2009).
[Crossref]

Katz, O.

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

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

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
[Crossref] [PubMed]

Lagendijk, A.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

Lancis, J.

Li, E.

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

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

Li, M. F.

Liu, Q.

Liu, X. F.

Lugiato, L. A.

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] [PubMed]

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref] [PubMed]

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

Luo, K. H.

Magatti, D.

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] [PubMed]

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref] [PubMed]

Manjunatha Prasad, K.

K. Manjunatha Prasad and R. B. Bapat, “The generalized Moore-Penrose inverse,” Linear Algebra Appl. 165, 59–69 (1992).
[Crossref]

Molteni, 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] [PubMed]

Mosk, A. P.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

Padgett, M. J.

Pappas, D.

S. Chountasis, V. N. Katsikis, and D. Pappas, “Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse,” Math. Probl. Eng. 2010, 1–14 (2010).
[Crossref]

S. Chountasis, V. N. Katsikis, and D. Pappas, “Applications of the Moore-Penrose inverse in digital image restoration,” Math. Probl. Eng. 2009, 1–12 (2009).
[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] [PubMed]

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] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
[Crossref] [PubMed]

Shapiro, J. H.

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20(15), 16892–16901 (2012).
[Crossref]

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Advances in Optics and Photonics 2(4), 405–450 (2010).
[Crossref]

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

Shen, X.

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82(3), 033817 (2010).
[Crossref]

Shih, Y. H.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
[Crossref] [PubMed]

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] [PubMed]

Silberberg, Y.

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

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

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
[Crossref] [PubMed]

Sun, B.

Tajahuerce, E.

Torres-Company, V.

van Putten, E. G.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

Vos, W. L.

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

Wakin, M. B.

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” Signal Processing Magazine, IEEE 25(2), 21–30 (2008).
[Crossref]

Wang, H.

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

Welsh, S. S.

Wu, L. A.

Xian, R.

Xu, W.

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

Yao, X. R.

Yu, W. K.

Zhai, G. J.

Zhang, P.

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82(3), 033817 (2010).
[Crossref]

Zhao, C.

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

Advances in Optics and Photonics (1)

B. I. Erkmen and J. H. Shapiro, “Ghost imaging: from quantum to classical to computational,” Advances in Optics and Photonics 2(4), 405–450 (2010).
[Crossref]

Appl. Phys. Lett. (4)

C. Zhao, W. Gong, M. Chen, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101(14), 141123 (2012).
[Crossref]

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

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

W. Chen and X. Chen, “Marked ghost imaging,” Appl. Phys. Lett. 104(25), 251109 (2014).
[Crossref]

J. Opt. Soc. Am. A (1)

JOSA B (1)

W. Gong and S. Han, “The influence of axial correlation depth of light field on lensless ghost imaging,” JOSA B 27(4), 675–678 (2010).
[Crossref]

Linear Algebra Appl. (1)

K. Manjunatha Prasad and R. B. Bapat, “The generalized Moore-Penrose inverse,” Linear Algebra Appl. 165, 59–69 (1992).
[Crossref]

Math. Probl. Eng. (2)

S. Chountasis, V. N. Katsikis, and D. Pappas, “Applications of the Moore-Penrose inverse in digital image restoration,” Math. Probl. Eng. 2009, 1–12 (2009).
[Crossref]

S. Chountasis, V. N. Katsikis, and D. Pappas, “Digital image reconstruction in the spectral domain utilizing the Moore-Penrose inverse,” Math. Probl. Eng. 2010, 1–14 (2010).
[Crossref]

Nature (1)

J. Bertolotti, E. G. van Putten, C. Blum, A. Lagendijk, W. L. Vos, and A. P. Mosk, “Non-invasive imaging through opaque scattering layers,” Nature 491(7423), 232–234 (2012).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (4)

Phys. Lett. A (1)

W. Gong and S. Han, “A method to improve the visibility of ghost images obtained by thermal light,” Phys. Lett. A 374(8), 1005–1008 (2010).
[Crossref]

Phys. Rev. A (5)

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] [PubMed]

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

P. Zhang, W. Gong, X. Shen, and S. Han, “Correlated imaging through atmospheric turbulence,” Phys. Rev. A 82(3), 033817 (2010).
[Crossref]

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

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

Phys. Rev. Lett. (5)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-Photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89(11), 113601 (2002).
[Crossref] [PubMed]

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] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[Crossref] [PubMed]

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74(18), 3600–3603 (1995).
[Crossref] [PubMed]

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104(25), 253603 (2010).
[Crossref] [PubMed]

Signal Processing Magazine, IEEE (1)

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” Signal Processing Magazine, IEEE 25(2), 21–30 (2008).
[Crossref]

Other (2)

R. E. Meyers and K. S. Deacon, “Quantum ghost imaging experiments at ARL,” in SPIE Optical Engineering + Applications, International Society for Optics and Photonics (2010), (pp. 78150I–78150I).

W. Gong, C. Zhao, J. Jiao, E. Li, M. Chen, H. Wang, and S. Han, “Three-dimensional ghost imaging ladar. ” arXiv preprint arXiv:1301.5767(2013).

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Figures (8)

Fig. 1
Fig. 1 Schematics of GI and PGI systems. (a) traditional GI method; (b) PGI method; OBJ: Object Arm; REF: Reference Arm z1: the distance between pseudo-thermal source and the object plane z2: the distance between pseudo-thermal source and the reference CCD plane
Fig. 2
Fig. 2 Comparison of Φ T Φ and Φ   Φ x: row coordinate of the matrixes y: column coordinate of the matrixes
Fig. 3
Fig. 3 Comparison of results by GI, DGI, CGI and PGI for grayscale images: (a) (f) original image; (b) (g) GI method; (c) (h) DGI method; (d) (i) CGI method; (e) (j) PGI method
Fig. 4
Fig. 4 Comparison of results from GI, DGI, CGI and PGI for binary images: (a) (f) original image; (b) (g) GI method; (c) (h) DGI method; (d) (i) CGI method; (e) (j) PGI method
Fig. 5
Fig. 5 The PSNR curves of the grayscale images: (a) lena; (b) cat
Fig. 6
Fig. 6 The PSNR curves of the binary images: (a) ’ji’; (b) dotarray
Fig. 7
Fig. 7 Comparison of the four methods’ reconstructions with deviation z2-z1 (a) The PSNRs of reconstructed images versus SNR of B (b) curves of the PSNRs versus z2-z1
Fig. 8
Fig. 8 The comparison of computing time by the four methods for grayscale and binary images: (a)lena; (b)’ji’

Equations (14)

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T GI ( x,y )= 1 N n=1 N ( B n B n ) I n ( x,y )
Φ=[ I 1 (1,1) I 1 (1,2) I 1 (p,p) I 2 (1,1) I 2 (p,p) I N (1,1) I N (1,2) I N (p,p) ]
BI B n =[ B 1 B 2 B N ]I B n =Φ[ T(1,1) T(1,2) T(p,p) ]I B n
T GI = 1 N [ I 1 ( 1,1 ) I 2 ( 1,1 ) I N ( 1,1 ) I 1 ( 1,2 ) I N ( 1,2 ) I 1 ( p,p ) I 2 ( p,p ) I N ( p,p ) ]( [ B 1 B 2 B N ][ B n B n B n ] )
T GI = 1 N Φ T Φ[ T(1,1) T(1,2) T(p,p) ] B n [ I n (1,1) I n (1,2) I n (p,p) ]
Φ T Φ=s+n
s=diag[ n=1 N I n 2 ( 1,1 ), n=1 N I n 2 ( 1,2 ) n=1 N I n 2 ( p,p )]
n=[ 0 n=1 N I n ( 1,1 ) I n ( 1,2 ) n=1 N I n ( 1,1 ) I n ( p,p ) n=1 N I n ( 1,2 ) I n ( 1,1 ) n=1 N I n ( p,p1 ) I n ( p,p ) n=1 N I n ( p,p ) I n ( 1,1 ) n=1 N I n ( p,p ) I n ( p,p1 ) 0 ]
T PGI = 1 N Φ   ( B 1 , B 2 B N ) T = 1 N Φ   Φ [ T(1,1),T(1,2)T(p,p) ] T
{ ΦXΦ=Φ XΦX=X (ΦX) H =ΦX (XΦ) H =XΦ
Φ=U( Σ 0 0 0 ) V H
Φ   =V( Σ 1 0 0 0 ) U H
Φ   Φ=s'+n'
PSNR=10× log 10 [ ( 2 m 1) 2 MSE ]

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