Abstract

Usually the test detector of a standard ghost imaging scheme is a bucket detector; here the test detector in the scheme of multiple-input ghost imaging via sparsity constraints (MI-GISC) we proposed is characterized by some sparse-array single-pixel detectors, and the propagation process between the object plane and the test detection plane is also considered. Combining ghost imaging with the target’s sparsity constraints, the theory and reconstruction of MI-GISC are investigated. The property and differences between MI-GISC and compressive ghost imaging (CGI) are studied theoretically and backed up by numerical simulations. MI-GISC can be applied in a remote imaging system with a small receiving numerical aperture, improving the reconstruction’s quality of the target.

© 2012 Optical Society of America

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  1. A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
    [CrossRef]
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    [CrossRef]
  3. R. S. Bennink, S. J. Bentley, and R. W. Boyd, “Two-photon coincidence imaging with a classical source,” Phys. Rev. Lett. 89, 113601 (2002).
    [CrossRef]
  4. J. Cheng and S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. 92, 093903 (2004).
    [CrossRef]
  5. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classical correlation,” Phys. Rev. Lett. 93, 093602 (2004).
    [CrossRef]
  6. F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
    [CrossRef]
  7. D. Zhang, Y-H. Zhai, L-A. Wu, and X-H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30, 2354–2356 (2005).
    [CrossRef]
  8. M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
    [CrossRef]
  9. W. Gong, P. Zhang, X. Shen, and S. Han, “Ghost ‘pinhole’ imaging in Fraunhofer region,” Appl. Phys. Lett. 95, 071110 (2009).
    [CrossRef]
  10. W. Gong and S. Han, “Lens ghost imaging with thermal light: From the far field to the near field,” Phys. Lett. A 374, 3723–3725 (2010).
    [CrossRef]
  11. W. Gong and S. Han, “Correlated imaging in scattering media,” Opt. Lett. 36, 394–396 (2011).
    [CrossRef]
  12. W. Gong and S. Han, “A method to improve the visibility of ghost images obtained by thermal light,” Phys. Lett. A 374, 1005–1008 (2010).
    [CrossRef]
  13. F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 104, 253603 (2010).
    [CrossRef]
  14. H. Liu, J. Cheng, and S. Han, “Ghost imaging in Fourier space,” J. Appl. Phys. 102, 103102 (2007).
    [CrossRef]
  15. M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging schemes: fast and broadband,” Opt. Express 12, 6067–6081 (2004).
    [CrossRef]
  16. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79, 053840 (2009).
    [CrossRef]
  17. E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008) and references therein.
    [CrossRef]
  18. E. J. Candès, “Compressive sampling,” in Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006, Vol. III (European Mathematical Society, 2006), pp. 1433–1452.
  19. D. L. Donoho and Y. Tsaig, “Fast solution of ℓ1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54, 4789–4812 (2008).
    [CrossRef]
  20. J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 14–20 (2008).
    [CrossRef]
  21. O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
    [CrossRef]
  22. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  23. W. Gong and S. Han, “Super-resolution far-field ghost imaging via compressive sampling,” e-print arXiv: 0911.4750 [Quant-ph].
  24. J. Du, W. Gong, and S. Han, “The influence of sparsity property of images on ghost imaging with thermal light,” Opt. Lett. 37, 1067–1069 (2012).
    [CrossRef]
  25. M. A. T. 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, 586–597 (2007).
    [CrossRef]
  26. I. Yamaguchi and T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22, 1268–1270 (1997).
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  27. M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging using homodyne detection,” Phys. Rev. A 70, 023823 (2004).
    [CrossRef]
  28. J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802 (2008).
    [CrossRef]
  29. H. Wang and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98, 24003 (2012).
    [CrossRef]
  30. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
    [CrossRef]
  31. D. Graham-Rowe, “Digital cameras: pixel power,” Nature Photon. 1, 211–212 (2007).
  32. M. Lu, X. Shen, and S. S. Han, “Ghost imaging via compressive sampling based on digital micromirror device,” Acta Optica Sinica 31, 0711002 (2011).
    [CrossRef]

2012

H. Wang and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98, 24003 (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, 1067–1069 (2012).
[CrossRef]

2011

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

M. Lu, X. Shen, and S. S. Han, “Ghost imaging via compressive sampling based on digital micromirror device,” Acta Optica Sinica 31, 0711002 (2011).
[CrossRef]

2010

W. Gong and S. Han, “Lens ghost imaging with thermal light: From the far field to the near field,” Phys. Lett. A 374, 3723–3725 (2010).
[CrossRef]

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

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

2009

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

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

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

2008

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

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

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008) and references therein.
[CrossRef]

D. L. Donoho and Y. Tsaig, “Fast solution of ℓ1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54, 4789–4812 (2008).
[CrossRef]

J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 14–20 (2008).
[CrossRef]

2007

H. Liu, J. Cheng, and S. Han, “Ghost imaging in Fourier space,” J. Appl. Phys. 102, 103102 (2007).
[CrossRef]

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

M. A. T. 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, 586–597 (2007).
[CrossRef]

D. Graham-Rowe, “Digital cameras: pixel power,” Nature Photon. 1, 211–212 (2007).

2006

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

2005

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

D. Zhang, Y-H. Zhai, L-A. Wu, and X-H. Chen, “Correlated two-photon imaging with true thermal light,” Opt. Lett. 30, 2354–2356 (2005).
[CrossRef]

2004

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging using homodyne detection,” Phys. Rev. A 70, 023823 (2004).
[CrossRef]

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

J. Cheng and S. Han, “Incoherent coincidence imaging and its applicability in X-ray diffraction,” Phys. Rev. Lett. 92, 093903 (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, 093602 (2004).
[CrossRef]

2002

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

1997

1995

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, R3429 (1995).
[CrossRef]

Bache, M.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging schemes: fast and broadband,” Opt. Express 12, 6067–6081 (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, 093602 (2004).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging using homodyne detection,” Phys. Rev. A 70, 023823 (2004).
[CrossRef]

Baraniuk, R. G.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[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, 113601 (2002).
[CrossRef]

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, 113601 (2002).
[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, 113601 (2002).
[CrossRef]

Brambilla, E.

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging schemes: fast and broadband,” Opt. Express 12, 6067–6081 (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, 093602 (2004).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging using homodyne detection,” Phys. Rev. A 70, 023823 (2004).
[CrossRef]

Bromberg, Y.

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

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

Candès, E. J.

E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25, 21–30 (2008) and references therein.
[CrossRef]

E. J. Candès, “Compressive sampling,” in Proceedings of the International Congress of Mathematicians, Madrid, Spain, 2006, Vol. III (European Mathematical Society, 2006), pp. 1433–1452.

Chen, X-H.

Cheng, J.

H. Liu, J. Cheng, and S. Han, “Ghost imaging in Fourier space,” J. Appl. Phys. 102, 103102 (2007).
[CrossRef]

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

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

Davenport, M. A.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

Donoho, D. L.

D. L. Donoho and Y. Tsaig, “Fast solution of ℓ1-norm minimization problems when the solution may be sparse,” IEEE Trans. Inf. Theory 54, 4789–4812 (2008).
[CrossRef]

Du, J.

Duarte, M. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

Ferri, F.

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

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

Figueiredo, M. A. T.

M. A. T. 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, 586–597 (2007).
[CrossRef]

Gatti, A.

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

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging schemes: fast and broadband,” Opt. Express 12, 6067–6081 (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, 093602 (2004).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging using homodyne detection,” Phys. Rev. A 70, 023823 (2004).
[CrossRef]

Gong, W.

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

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

W. Gong and S. Han, “Lens ghost imaging with thermal light: From the far field to the near field,” Phys. Lett. A 374, 3723–3725 (2010).
[CrossRef]

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

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

W. Gong and S. Han, “Super-resolution far-field ghost imaging via compressive sampling,” e-print arXiv: 0911.4750 [Quant-ph].

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Graham-Rowe, D.

D. Graham-Rowe, “Digital cameras: pixel power,” Nature Photon. 1, 211–212 (2007).

Han, S.

H. Wang and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98, 24003 (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, 1067–1069 (2012).
[CrossRef]

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

W. Gong and S. Han, “Lens ghost imaging with thermal light: From the far field to the near field,” Phys. Lett. A 374, 3723–3725 (2010).
[CrossRef]

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

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

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

H. Liu, J. Cheng, and S. Han, “Ghost imaging in Fourier space,” J. Appl. Phys. 102, 103102 (2007).
[CrossRef]

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

W. Gong and S. Han, “Super-resolution far-field ghost imaging via compressive sampling,” e-print arXiv: 0911.4750 [Quant-ph].

Han, S. S.

M. Lu, X. Shen, and S. S. Han, “Ghost imaging via compressive sampling based on digital micromirror device,” Acta Optica Sinica 31, 0711002 (2011).
[CrossRef]

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 79, 053840 (2009).
[CrossRef]

Kelly, K. F.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

Laska, J. N.

M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

Liu, H.

H. Liu, J. Cheng, and S. Han, “Ghost imaging in Fourier space,” J. Appl. Phys. 102, 103102 (2007).
[CrossRef]

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Liu, Y.

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Lu, M.

M. Lu, X. Shen, and S. S. Han, “Ghost imaging via compressive sampling based on digital micromirror device,” Acta Optica Sinica 31, 0711002 (2011).
[CrossRef]

Lugiato, L. A.

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

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging schemes: fast and broadband,” Opt. Express 12, 6067–6081 (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, 093602 (2004).
[CrossRef]

M. Bache, E. Brambilla, A. Gatti, and L. A. Lugiato, “Ghost imaging using homodyne detection,” Phys. Rev. A 70, 023823 (2004).
[CrossRef]

Magatti, D.

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

A. Gatti, M. Bache, D. Magatti, E. Brambilla, F. Ferri, and L. A. Lugiato, “Coherent imaging with pseudo-thermal incoherent light,” J. Mod. Opt. 53, 739–760 (2006).
[CrossRef]

F. Ferri, D. Magatti, A. Gatti, M. Bache, E. Brambilla, and L. A. Lugiato, “High-resolution ghost image and ghost diffraction experiment with thermal light,” Phys. Rev. Lett. 94, 183602 (2005).
[CrossRef]

Nowak, R. D.

M. A. T. 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, 586–597 (2007).
[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, R3429 (1995).
[CrossRef]

Romberg, J.

J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 14–20 (2008).
[CrossRef]

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, R3429 (1995).
[CrossRef]

Shapiro, J. H.

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

Shen, X.

M. Lu, X. Shen, and S. S. Han, “Ghost imaging via compressive sampling based on digital micromirror device,” Acta Optica Sinica 31, 0711002 (2011).
[CrossRef]

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

M. Zhang, Q. Wei, X. Shen, Y. Liu, H. Liu, J. Cheng, and S. Han, “Lensless Fourier-transform ghost imaging with classical incoherent light,” Phys. Rev. A 75, 021803 (2007).
[CrossRef]

Shih, Y. H.

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[CrossRef]

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[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

The principle schematic of MI-GISC; the photons passing through the object are measured by some sparse-array single-pixel detectors.

Fig. 2.
Fig. 2.

Optical setup of MI-GISC, where the distances z1, z2, and f obey the Gaussian thin-lens equation: 1/z1+1/z2=1/f. Likewise, 1/z3+1/z4=1/f1, but the transmission aperture L1 of the lens f1 is very small.

Fig. 3.
Fig. 3.

GI and CGI with pseudothermal light in different N.A. when the test detector is a bucket detector, using M=200 measurements (70% Nyquist rate). Red solid curves in (a1-c1), respectively, are the intensity distribution on the detection plane Dt recorded by a camera, GI and CGI reconstruction results, with N.A.=0.001 (namely L1=1.0mm); (a2-c2) and (a3-c3) have the same description as (a1-c1), with N.A.=0.02 (namely L1=20.0mm) and N.A.=0.05 (namely L1=50.0mm), respectively. Blue solid curves are the object’s original function.

Fig. 4.
Fig. 4.

Results reconstructed by GI, CGI, and MI-GISC methods with N.A.=0.001 of the lens f1. (a) The original function of the object; (b) the intensity distribution on the detection plane Dt recorded by a camera (blue solid curve) and the detection positions of the sparse-array single-pixel detectors (red square points); (c) the PSF between the object plane and the detection plane Dt. Red solid curves in (d), (e), and (f) are the results recovered by GI (a bucket detector, M=600), CGI (a bucket detector, M=600), and MI-GISC (three sparse-array single-pixel detectors, M=200) methods, respectively. Compared with the results in (d), (e), and (f), red solid curves in (g), (h), and (i) are the results recovered by GI (a bucket detector, M=1800), CGI (a bucket detector, M=1800), and MI-GISC (three sparse-array single-pixel detectors, M=600) methods, respectively.

Fig. 5.
Fig. 5.

Influence of the number m of sparse-array single-pixel detectors in the test path to MI-GISC (M=600). (a) m=2 (the center-to-center separation of the sparse-array single-pixel detectors on the detection plane Dt is Δxs=340μm); (b) m=3 (Δxs=250μm); (c) m=7 (Δxs=100μm).

Fig. 6.
Fig. 6.

Effect of inaccurate knowledge of the impulse response function between the object plane and the detection plane Dt on the reconstruction results of MI-GISC (M=600). (a) Accurate knowledge of the impulse response function; (b) and (c) are corresponding to the phase distortion range at [π10, π10] and [π2, π2] between the object plane and the detection plane Dt, obeying Gaussian statistical distribution, respectively.

Fig. 7.
Fig. 7.

Influence of inaccurate knowledge of the phase of the light field located on the object plane on the reconstruction results of MI-GISC, using M=600 measurements. (a) Accurate knowledge of the phase of the light field; (b) and (c) are corresponding to the phase distortion range at [π10, π10] and [π2, π2] of the light field on the object plane, obeying Gaussian statistical distribution, respectively.

Fig. 8.
Fig. 8.

Results of recovering a complex-valued object (M=600); the conditions are the same as Fig. 4. Blue solid curves in (a)–(d) are the original function of the object, red solid curves illustrate the images reconstructed by GI reconstruction (a) and CGI reconstruction (b), and red solid curves in (c) and (d) are the object’s amplitude-dependent part and its complex-valued distribution reconstructed by the MI-GISC method, respectively.

Fig. 9.
Fig. 9.

Results reconstructed by GI, CGI, and MI-GISC methods with N.A.=0.001 of the lens f1, using M=100 measurements (35% Nyquist rate). (a) The original function of the object; (b) the intensity distribution on the detection plane Dt recorded by a camera (blue solid curve) and the detection positions of the sparse-array single-pixel detectors (red square points); (c) PSF between the object plane and the detection plane Dt Red solid curves in (d), (e), and (f) are the results recovered by GI (a bucket detector), CGI (a bucket detector), and MI-GISC (six sparse-array single-pixel detectors) methods, respectively.

Fig. 10.
Fig. 10.

Results reconstructed by MI-GISC in different M and ms (while M×ms=600). (a), (c), and (e) are different PSF between the object plane and the detection plane Dt by increasing the transmission aperture L1 of the lens f1 (where L1=1.0, 2.0, and 4.0 mm, respectively; then ms=6, 12, and 24, correspondingly). (b), (d), and (f) are the corresponding MI-GISC results (M=100, 50, and 25, respectively).

Equations (21)

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Y=AX,
minx1,subject to:Y=AX,
Eis(xi)=dx0E0s(x0)hi(xi,x0),i=r,t,
Its(xi)=[Ets(xi)]*Ets(xi),i=1m;=dx0dxdxdx[E0s(x0)]*E0s(x0)[ht(x,x0)]*ht(x,x0)[T(x)]*T(x)[ht(xi,x)]*ht(xi,x)=dxdx[Exs(x)]*Exs(x)[T(x)]*T(x)[ht(xi,x)]*ht(xi,x),
Irs(xr)=[Ers(xr)]*Ers(xr)[Exs(x)]*Exs(x),
Its(xi)dxdx[Ers(x)]*Ers(x)[T(x)]*T(x)[ht(xi,x)]*ht(xi,x).
|TGI|=ΔG(2,2)(xr)=1Ms=1MIrs(xr)Bs1M2s=1MIrs(xr)s=1MBs,
|TCGI|=|T|;which minimizes:12BsdxIrs(x)|T(x)|222+τΨ{|T(x)|2}1,s=1M,
Bsdxi|dxErs(x)T(x)ht(xi,x)|2,s=1M.
|TCGI|=|T|;which minimizes:Ψ{|T(x)|2}1,subject to: Bs=dxIrs(x)|T(x)|2,s=1M.
T MI - GISC = T ; which minimizes: Ψ { T ( x ) } 1 , subject to: I t s ( x i ) = d x d x [ E r s ( x ) ] * × E r s ( x ) [ T ( x ) ] * T ( x ) [ h t ( x i , x ) ] * h t ( x i , x ) , s = 1 M ; i = 1 m .
Minimizes:Ψ{TM}1,subject to:Its(xi)=|dxErs(x)T(x)ht(xi,x)|2,s=1M;i=1m,
TM=[T*(x1)T(x1)2Real{T*(x1)T(x2)}2Real{T*(x1)T(xN)}2Imag{T*(x2)T(x1)}T*(x2)T(x2)2Real{T*(x2)T(xN)}2Imag{T*(x3)T(x1)}2Imag{T*(x3)T(x2)}2Real{T*(x3)T(xN)}2Imag{T*(xN)T(x1)}2Imag{T*(xN)T(x2)}T*(xN)T(xN)].
Ts=[T*(x1){T(x1)T(x2)T(x3)T(xN)}T*(x2){T(x1)T(x2)T(x3)T(xN)}T*(x3){T(x1)T(x2)T(x3)T(xN)}T*(xN){T(x1)T(x2)T(x3)T(xN)}].
TMI-GISC(xi)=SQRT{Ts(i,i)},i=1N,
FindingT(xi)0:thenTMI-GISC=i=1NTs(i,:)/T*(xi)max{i=1NTs(i,:)/T*(xi)},
msNΔx.
MSE=1Ni(TGI/CGI/MI-GISC(xi)T0(xi))2,
BsdxidxIrs(x)|T(x)|2|ht(xi,x)|2dxIrs(x)|T(x)|2,s=1M,
|TCGI|=|T|;which minimizes:Ψ{|T(x)|2}1,subject to:Bs=dxIrs(x)|T(x)|2,s=1M.
|TMI-GISC|=|T|;which minimizes:Ψ{|T(x)|2}1,subject to:Its(xi)=dxIrs(x)|T(x)|2|ht(xi,x)|2,s=1M;i=1m.

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