Abstract

Correlation is widely used to reconstruct the object image in ghost imaging (GI). But it only offers a linear proportion of the signal-to-noise ratios (SNR) to the number of measurements. We develop a Gerchberg-Saxton-like technique for GI image reconstruction in this manuscript. The proposed technique takes the advantage of the integral property of the Fourier transform, and treat the captured data as constraints for image reconstruction. We numerically and experimentally demonstrate the technique, and observe a nonlinear growth of the SNR value with respect to the number of measurements in the simulation. The proposed technique provides a different perspective of image reconstruction of GI, and will be beneficial to further explore its potential.

© 2015 Optical Society of America

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References

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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, 3429 (1995).
    [Crossref]
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    [Crossref]
  3. W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ’pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett 95, 071110 (2009).
    [Crossref]
  4. K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett 34, 213343 (2009).
    [Crossref]
  5. X. F. Liu, X. H. Chen, X. R. Yao, W. K. Yu, G. J. Zhai, and L. A. Wu, “Lensless ghost imaging with sunlight,” Opt. Lett 39, 002314 (2014).
    [Crossref]
  6. J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802R (2008).
    [Crossref]
  7. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 78, 053840 (2009).
    [Crossref]
  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, 844–847 (2013).
    [Crossref] [PubMed]
  9. C. Zhao, W. Gong, M. Che, E. Li, H. Wang, W. Xu, and S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett 101, 141123 (2012).
    [Crossref]
  10. P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett 35, 2391–2393 (2010).
    [Crossref] [PubMed]
  11. F. Ferri, D. Magatti, L. A Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett 104, 253603 (2010).
    [Crossref] [PubMed]
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    [Crossref]
  13. W. Wang, Y. P. Wang, Y. Wu, X. X. Yang, and Y. Wu, “Optical eigenmode imaging with a sparse constraint,” Opt. Lett 39, 092614 (2014).
  14. X. M. Hu, J. L. Suo, T. Yue, L. H. Bian, and Q. H. Dai, “Patch-primitive driven compressive ghost imaging,” Opt. Express 23, 011092 (2015).
    [Crossref]
  15. W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep 5, 9280 (2015).
    [Crossref] [PubMed]
  16. W. Wang, Y. P. Wang, J. H. Li, X. X. Yang, and Y. Wu, “Iterative ghost imaging,” Opt. Lett 39, 175150 (2014).
  17. X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 024268 (2014).
    [Crossref]
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    [Crossref]
  21. S. Y. Dong, P. Nanda, R. Shiradkar, K. K. Guo, and G. A. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express. 22, 020856 (2014).
    [Crossref]
  22. Y. S. G. Nashed, D. J. Vine, T. Peterka, J. J. Deng, R. Ross, and C. Jacobsen, “Parallel ptychographic reconstruction,” Opt. Express 22, 32082–32097 (2014).
    [Crossref]
  23. S. M. M. Khamoushi, Y. Nosrati, and S. H. Tavassoli, “Sinusoidal ghost imaging,” Opt. Lett 40, 003452 (2015).
    [Crossref]
  24. M. Guizar-Sicairos and J. R. Fienup, “Phase retrieval with transverse translation diversity: a nonlinear optimization approach,” Opt. Express 16, 7264–7278 (2008).
    [Crossref] [PubMed]
  25. L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5, 2376 – 2389 (2014).
    [Crossref] [PubMed]
  26. F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
    [Crossref] [PubMed]
  27. A. Alpers, G. T. Herman, H. F. Poulsen, and S. Schmidt, “Phase retrieval for superposed signals from multiple binary objects,” J. Opt. Soc. Am. A 27, 1927–1937 (2010).
    [Crossref]

2015 (3)

X. M. Hu, J. L. Suo, T. Yue, L. H. Bian, and Q. H. Dai, “Patch-primitive driven compressive ghost imaging,” Opt. Express 23, 011092 (2015).
[Crossref]

W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep 5, 9280 (2015).
[Crossref] [PubMed]

S. M. M. Khamoushi, Y. Nosrati, and S. H. Tavassoli, “Sinusoidal ghost imaging,” Opt. Lett 40, 003452 (2015).
[Crossref]

2014 (7)

S. Y. Dong, P. Nanda, R. Shiradkar, K. K. Guo, and G. A. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express. 22, 020856 (2014).
[Crossref]

Y. S. G. Nashed, D. J. Vine, T. Peterka, J. J. Deng, R. Ross, and C. Jacobsen, “Parallel ptychographic reconstruction,” Opt. Express 22, 32082–32097 (2014).
[Crossref]

L. Tian, X. Li, K. Ramchandran, and L. Waller, “Multiplexed coded illumination for Fourier Ptychography with an LED array microscope,” Biomed. Opt. Express 5, 2376 – 2389 (2014).
[Crossref] [PubMed]

W. Wang, Y. P. Wang, J. H. Li, X. X. Yang, and Y. Wu, “Iterative ghost imaging,” Opt. Lett 39, 175150 (2014).

X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 024268 (2014).
[Crossref]

X. F. Liu, X. H. Chen, X. R. Yao, W. K. Yu, G. J. Zhai, and L. A. Wu, “Lensless ghost imaging with sunlight,” Opt. Lett 39, 002314 (2014).
[Crossref]

W. Wang, Y. P. Wang, Y. Wu, X. X. Yang, and Y. Wu, “Optical eigenmode imaging with a sparse constraint,” Opt. Lett 39, 092614 (2014).

2013 (3)

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, 844–847 (2013).
[Crossref] [PubMed]

F. Zhang, I. Peterson, J. Vila-Comamala, A. Diaz, F. Berenguer, R. Bean, B. Chen, A. Menzel, I. K. Robinson, and J. M. Rodenburg, “Translation position determination in ptychographic coherent diffraction imaging,” Opt. Express 21, 13592–13606 (2013).
[Crossref] [PubMed]

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

2012 (1)

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

2010 (3)

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

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

A. Alpers, G. T. Herman, H. F. Poulsen, and S. Schmidt, “Phase retrieval for superposed signals from multiple binary objects,” J. Opt. Soc. Am. A 27, 1927–1937 (2010).
[Crossref]

2009 (4)

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

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ’pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett 95, 071110 (2009).
[Crossref]

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett 34, 213343 (2009).
[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 78, 053840 (2009).
[Crossref]

2008 (2)

2005 (1)

A. Valencia, G. Scarcelli, M. DAngelo, and Y. Shih, “Two-photon ghost imaging with thermal light,” Phys. Rev. Lett 94, 063601 (2005).
[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, 3429 (1995).
[Crossref]

1971 (1)

R. Gerchberg and W. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Alpers, A.

Bean, R.

Berenguer, F.

Bian, L. H.

X. M. Hu, J. L. Suo, T. Yue, L. H. Bian, and Q. H. Dai, “Patch-primitive driven compressive ghost imaging,” Opt. Express 23, 011092 (2015).
[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, 844–847 (2013).
[Crossref] [PubMed]

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, 844–847 (2013).
[Crossref] [PubMed]

Boyd, R. W.

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett 34, 213343 (2009).
[Crossref]

Bromberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 78, 053840 (2009).
[Crossref]

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

Chan, K. W. C.

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett 34, 213343 (2009).
[Crossref]

Che, M.

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

Chen, B.

Chen, X. H.

X. F. Liu, X. H. Chen, X. R. Yao, W. K. Yu, G. J. Zhai, and L. A. Wu, “Lensless ghost imaging with sunlight,” Opt. Lett 39, 002314 (2014).
[Crossref]

Clemente, P.

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

Dai, Q. H.

X. M. Hu, J. L. Suo, T. Yue, L. H. Bian, and Q. H. Dai, “Patch-primitive driven compressive ghost imaging,” Opt. Express 23, 011092 (2015).
[Crossref]

DAngelo, M.

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

Deng, J. J.

Diaz, A.

Dong, S. Y.

S. Y. Dong, P. Nanda, R. Shiradkar, K. K. Guo, and G. A. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express. 22, 020856 (2014).
[Crossref]

Durán, V.

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

Edgar, M. P.

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, 844–847 (2013).
[Crossref] [PubMed]

Ferri, F.

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

Fienup, J. R.

Gatti, A.

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

Gerchberg, R.

R. Gerchberg and W. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Gong, W.

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

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ’pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett 95, 071110 (2009).
[Crossref]

Gong, W. L.

W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep 5, 9280 (2015).
[Crossref] [PubMed]

Guizar-Sicairos, M.

Guo, K. K.

S. Y. Dong, P. Nanda, R. Shiradkar, K. K. Guo, and G. A. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express. 22, 020856 (2014).
[Crossref]

Han, S.

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

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ’pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett 95, 071110 (2009).
[Crossref]

Han, S. S.

W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep 5, 9280 (2015).
[Crossref] [PubMed]

Herman, G. T.

Horstmeyer, R.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Hu, X. M.

X. M. Hu, J. L. Suo, T. Yue, L. H. Bian, and Q. H. Dai, “Patch-primitive driven compressive ghost imaging,” Opt. Express 23, 011092 (2015).
[Crossref]

Jacobsen, C.

Katz, O.

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

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 78, 053840 (2009).
[Crossref]

Khamoushi, S. M. M.

S. M. M. Khamoushi, Y. Nosrati, and S. H. Tavassoli, “Sinusoidal ghost imaging,” Opt. Lett 40, 003452 (2015).
[Crossref]

Lancis, J.

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

Li, E.

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

Li, J. H.

W. Wang, Y. P. Wang, J. H. Li, X. X. Yang, and Y. Wu, “Iterative ghost imaging,” Opt. Lett 39, 175150 (2014).

Li, L. Z.

X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 024268 (2014).
[Crossref]

Li, X.

Liu, X. F.

X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 024268 (2014).
[Crossref]

X. F. Liu, X. H. Chen, X. R. Yao, W. K. Yu, G. J. Zhai, and L. A. Wu, “Lensless ghost imaging with sunlight,” Opt. Lett 39, 002314 (2014).
[Crossref]

Lugiato, L. A

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

Magatti, D.

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

Marks, R. J.

R. J. Marks, Handbook of Fourier Analysis and Its Applications (Oxford University Press, 2009).

Menzel, A.

Nanda, P.

S. Y. Dong, P. Nanda, R. Shiradkar, K. K. Guo, and G. A. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express. 22, 020856 (2014).
[Crossref]

Nashed, Y. S. G.

Nosrati, Y.

S. M. M. Khamoushi, Y. Nosrati, and S. H. Tavassoli, “Sinusoidal ghost imaging,” Opt. Lett 40, 003452 (2015).
[Crossref]

O’Sullivan, M. N.

K. W. C. Chan, M. N. O’Sullivan, and R. W. Boyd, “High-order thermal ghost imaging,” Opt. Lett 34, 213343 (2009).
[Crossref]

Padgett, M. J.

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, 844–847 (2013).
[Crossref] [PubMed]

Peterka, T.

Peterson, I.

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, 3429 (1995).
[Crossref]

Poulsen, H. F.

Ramchandran, K.

Robinson, I. K.

Rodenburg, J. M.

Ross, R.

Saxton, W.

R. Gerchberg and W. Saxton, “Phase determination for image and diffraction plane pictures in the electron microscope,” Optik 34, 275–284 (1971).

Scarcelli, G.

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

Schmidt, S.

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, 3429 (1995).
[Crossref]

Shapiro, J. H.

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

Shen, X.

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ’pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett 95, 071110 (2009).
[Crossref]

Shih, Y.

A. Valencia, G. Scarcelli, M. DAngelo, and Y. Shih, “Two-photon ghost imaging with thermal light,” Phys. Rev. Lett 94, 063601 (2005).
[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, 3429 (1995).
[Crossref]

Shiradkar, R.

S. Y. Dong, P. Nanda, R. Shiradkar, K. K. Guo, and G. A. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express. 22, 020856 (2014).
[Crossref]

Silberberg, Y.

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 78, 053840 (2009).
[Crossref]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett 95, 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, 3429 (1995).
[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, 844–847 (2013).
[Crossref] [PubMed]

Suo, J. L.

X. M. Hu, J. L. Suo, T. Yue, L. H. Bian, and Q. H. Dai, “Patch-primitive driven compressive ghost imaging,” Opt. Express 23, 011092 (2015).
[Crossref]

Tajahuerce, E.

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

Tavassoli, S. H.

S. M. M. Khamoushi, Y. Nosrati, and S. H. Tavassoli, “Sinusoidal ghost imaging,” Opt. Lett 40, 003452 (2015).
[Crossref]

Tian, L.

Torres-Company, V.

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

Valencia, A.

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

Vila-Comamala, J.

Vine, D. J.

Vittert, L. E.

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, 844–847 (2013).
[Crossref] [PubMed]

Waller, L.

Wang, H.

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

Wang, W.

W. Wang, Y. P. Wang, Y. Wu, X. X. Yang, and Y. Wu, “Optical eigenmode imaging with a sparse constraint,” Opt. Lett 39, 092614 (2014).

W. Wang, Y. P. Wang, J. H. Li, X. X. Yang, and Y. Wu, “Iterative ghost imaging,” Opt. Lett 39, 175150 (2014).

Wang, Y. P.

W. Wang, Y. P. Wang, J. H. Li, X. X. Yang, and Y. Wu, “Iterative ghost imaging,” Opt. Lett 39, 175150 (2014).

W. Wang, Y. P. Wang, Y. Wu, X. X. Yang, and Y. Wu, “Optical eigenmode imaging with a sparse constraint,” Opt. Lett 39, 092614 (2014).

Welsh, S.

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, 844–847 (2013).
[Crossref] [PubMed]

Wu, L. A.

X. F. Liu, X. H. Chen, X. R. Yao, W. K. Yu, G. J. Zhai, and L. A. Wu, “Lensless ghost imaging with sunlight,” Opt. Lett 39, 002314 (2014).
[Crossref]

X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 024268 (2014).
[Crossref]

Wu, Y.

W. Wang, Y. P. Wang, J. H. Li, X. X. Yang, and Y. Wu, “Iterative ghost imaging,” Opt. Lett 39, 175150 (2014).

W. Wang, Y. P. Wang, Y. Wu, X. X. Yang, and Y. Wu, “Optical eigenmode imaging with a sparse constraint,” Opt. Lett 39, 092614 (2014).

W. Wang, Y. P. Wang, Y. Wu, X. X. Yang, and Y. Wu, “Optical eigenmode imaging with a sparse constraint,” Opt. Lett 39, 092614 (2014).

Xu, W.

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

Yang, C.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Yang, X. X.

W. Wang, Y. P. Wang, Y. Wu, X. X. Yang, and Y. Wu, “Optical eigenmode imaging with a sparse constraint,” Opt. Lett 39, 092614 (2014).

W. Wang, Y. P. Wang, J. H. Li, X. X. Yang, and Y. Wu, “Iterative ghost imaging,” Opt. Lett 39, 175150 (2014).

Yao, X. R.

X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 024268 (2014).
[Crossref]

X. F. Liu, X. H. Chen, X. R. Yao, W. K. Yu, G. J. Zhai, and L. A. Wu, “Lensless ghost imaging with sunlight,” Opt. Lett 39, 002314 (2014).
[Crossref]

Yu, W. K.

X. F. Liu, X. H. Chen, X. R. Yao, W. K. Yu, G. J. Zhai, and L. A. Wu, “Lensless ghost imaging with sunlight,” Opt. Lett 39, 002314 (2014).
[Crossref]

X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 024268 (2014).
[Crossref]

Yue, T.

X. M. Hu, J. L. Suo, T. Yue, L. H. Bian, and Q. H. Dai, “Patch-primitive driven compressive ghost imaging,” Opt. Express 23, 011092 (2015).
[Crossref]

Zhai, G. J.

X. R. Yao, W. K. Yu, X. F. Liu, L. Z. Li, L. A. Wu, and G. J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22, 024268 (2014).
[Crossref]

X. F. Liu, X. H. Chen, X. R. Yao, W. K. Yu, G. J. Zhai, and L. A. Wu, “Lensless ghost imaging with sunlight,” Opt. Lett 39, 002314 (2014).
[Crossref]

Zhang, F.

Zhang, P.

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ’pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett 95, 071110 (2009).
[Crossref]

Zhao, C.

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

Zheng, G.

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Zheng, G. A.

S. Y. Dong, P. Nanda, R. Shiradkar, K. K. Guo, and G. A. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express. 22, 020856 (2014).
[Crossref]

Appl. Phys. Lett (3)

W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ’pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett 95, 071110 (2009).
[Crossref]

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

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

Biomed. Opt. Express (1)

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

Nat. Photonics (1)

G. Zheng, R. Horstmeyer, and C. Yang, “Wide-field, high-resolution Fourier Ptychographic microscopy,” Nat. Photonics 7, 739–745 (2013).
[Crossref]

Opt. Express (5)

Opt. Express. (1)

S. Y. Dong, P. Nanda, R. Shiradkar, K. K. Guo, and G. A. Zheng, “High-resolution fluorescence imaging via pattern-illuminated Fourier ptychography,” Opt. Express. 22, 020856 (2014).
[Crossref]

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S. M. M. Khamoushi, Y. Nosrati, and S. H. Tavassoli, “Sinusoidal ghost imaging,” Opt. Lett 40, 003452 (2015).
[Crossref]

W. Wang, Y. P. Wang, J. H. Li, X. X. Yang, and Y. Wu, “Iterative ghost imaging,” Opt. Lett 39, 175150 (2014).

W. Wang, Y. P. Wang, Y. Wu, X. X. Yang, and Y. Wu, “Optical eigenmode imaging with a sparse constraint,” Opt. Lett 39, 092614 (2014).

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

X. F. Liu, X. H. Chen, X. R. Yao, W. K. Yu, G. J. Zhai, and L. A. Wu, “Lensless ghost imaging with sunlight,” Opt. Lett 39, 002314 (2014).
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Optik (1)

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Phys. Rev. A (3)

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[Crossref]

Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 78, 053840 (2009).
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A. Valencia, G. Scarcelli, M. DAngelo, and Y. Shih, “Two-photon ghost imaging with thermal light,” Phys. Rev. Lett 94, 063601 (2005).
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Sci. Rep (1)

W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep 5, 9280 (2015).
[Crossref] [PubMed]

Science (1)

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, 844–847 (2013).
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Figures (5)

Fig. 1
Fig. 1 Experimental setup of ghost imaging. Lamp: Philips, 200W; DMD: digital micro devices (DLP Discovery-4100, TI).
Fig. 2
Fig. 2 Simulation results. Images recovered using GI (top row) and our method (bottom row) for different numbers of speckle patterns M. The original image is shown in the inset of the first image.
Fig. 3
Fig. 3 SNR values of the recovered images using GI (blue curve) and the proposed technique (dot) for different numbers of measurements. Exponential fit of the SNR using the proposed technique is illustrated in the red line.
Fig. 4
Fig. 4 (Color online) Experimental results. (a) The ‘ghost’ image under detection. (b) Experimentally reconstructed image using standard GI with an SNR value equal to 0.913, the number of speckle patterns is 64 × 64. (c) the recovered image using DGI, and (d) the recovered image using the proposed technique with an SNR value equal to 2.994.
Fig. 5
Fig. 5 Convergence of our proposed method using the SNR as the metric.

Equations (5)

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S m = I m ( x ) T ( x ) d x , ( m = 1 , , M ) .
O ( x ) = δ S m δ I m ,
{ I tm ( x ) } ( k ) | k = 0 = S m ,
O updated ( x ) = O + I m ( x ) max { I m 2 ( x ) } [ I tm updated ( x ) O ( x ) I m ( x ) ] .
SNR = [ T ( x ) T ¯ ] 2 [ O ( x ) T ( x ) ] 2 ,

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