Abstract

Quantum imaging (QI) has some unique advantages, such as nonlocal imaging and enhanced space resolution. However, the quality of the reconstructed images and the time of data acquisition leave much to be desired. Based on the framework of compressive sensing, we propose an optimization criterion for high-quality QI whereby total variation restriction is specifically utilized for noise suppression. The corresponding reported algorithm uses a combination of a greedy strategy and the interactive reweight least-squares method. The simulation and the actual imaging experiment both show a significant improvement of the proposed algorithm the over previous imaging method.

© 2010 Optical Society of America

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  1. T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
    [CrossRef] [PubMed]
  2. A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
    [CrossRef] [PubMed]
  3. A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
    [CrossRef]
  4. Y. Zhai, X. Chen, D. Zhang, and L.-A. Wu, Phys. Rev. A 72, 043805 (2005).
    [CrossRef]
  5. J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, Phys. Rev. Lett. 94, 173601 (2005).
    [CrossRef] [PubMed]
  6. Y. Bai, and S. Han, Phys. Rev. A 76, 043828 (2007).
    [CrossRef]
  7. Y. J. Cai and S. Y. Zhu, Phys. Rev. E 71, 056607 (2005).
    [CrossRef]
  8. R. Hanbury-Brown and R. Q. Twiss, Nature 177, 27 (1956).
    [CrossRef]
  9. Y. H. Shih, IEEE J. Sel. Top. Quantum Electron. 13, 1016 (2007).
    [CrossRef]
  10. O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
    [CrossRef]
  11. W. Gong and S. Han, arXiv.org, arXiv:0910.4823v1 [quant-ph] (2009).
  12. E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
    [CrossRef]
  13. E. Candes, J. Romberg, and T. Tao, Commun. Pure Appl. Math. 59, 1207 (2006).
    [CrossRef]
  14. E. Candes and T. Tao, IEEE Trans. Inf. Theory 52, 5406 (2006).
    [CrossRef]
  15. D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
    [CrossRef]
  16. T. Chan, S. Esedoglu, F. Park, and A. Yip, in The Handbook of Mathematical Models in Computer Vision, (Springer, 2005), pp. 17–32.
  17. D. Needell and J. A. Tropp, Appl. Comput. Harmon. Anal. 26, 301 (2008).
    [CrossRef]
  18. B. Wohlberg, and P. Rodriguez, IEEE Signal Process. Lett. 14, 12 (2007).
  19. Y. Shih, SPIE Newsroom (July 28, 2009).
  20. R. E. Meyers, K. S. Deacon, Vacuum 83, 244 (2009).
    [CrossRef]

2009 (4)

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

W. Gong and S. Han, arXiv.org, arXiv:0910.4823v1 [quant-ph] (2009).

Y. Shih, SPIE Newsroom (July 28, 2009).

R. E. Meyers, K. S. Deacon, Vacuum 83, 244 (2009).
[CrossRef]

2008 (1)

D. Needell and J. A. Tropp, Appl. Comput. Harmon. Anal. 26, 301 (2008).
[CrossRef]

2007 (3)

B. Wohlberg, and P. Rodriguez, IEEE Signal Process. Lett. 14, 12 (2007).

Y. Bai, and S. Han, Phys. Rev. A 76, 043828 (2007).
[CrossRef]

Y. H. Shih, IEEE J. Sel. Top. Quantum Electron. 13, 1016 (2007).
[CrossRef]

2006 (4)

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

E. Candes and T. Tao, IEEE Trans. Inf. Theory 52, 5406 (2006).
[CrossRef]

D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

2005 (4)

T. Chan, S. Esedoglu, F. Park, and A. Yip, in The Handbook of Mathematical Models in Computer Vision, (Springer, 2005), pp. 17–32.

Y. J. Cai and S. Y. Zhu, Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Y. Zhai, X. Chen, D. Zhang, and L.-A. Wu, Phys. Rev. A 72, 043805 (2005).
[CrossRef]

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef] [PubMed]

2004 (1)

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

2000 (1)

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

1995 (1)

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

1956 (1)

R. Hanbury-Brown and R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

Abrams, D. S.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Bache, M.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Bai, Y.

Y. Bai, and S. Han, Phys. Rev. A 76, 043828 (2007).
[CrossRef]

Boto, A. N.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Brambilla, E.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Braunstein, S. L.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Bromberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Cai, Y. J.

Y. J. Cai and S. Y. Zhu, Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Candes, E.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

E. Candes and T. Tao, IEEE Trans. Inf. Theory 52, 5406 (2006).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

Cao, D.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef] [PubMed]

Chan, T.

T. Chan, S. Esedoglu, F. Park, and A. Yip, in The Handbook of Mathematical Models in Computer Vision, (Springer, 2005), pp. 17–32.

Chen, X.

Y. Zhai, X. Chen, D. Zhang, and L.-A. Wu, Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Deacon, K. S.

R. E. Meyers, K. S. Deacon, Vacuum 83, 244 (2009).
[CrossRef]

Donoho, D. L.

D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

Dowling, J. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Esedoglu, S.

T. Chan, S. Esedoglu, F. Park, and A. Yip, in The Handbook of Mathematical Models in Computer Vision, (Springer, 2005), pp. 17–32.

Gatti, A.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Gong, W.

W. Gong and S. Han, arXiv.org, arXiv:0910.4823v1 [quant-ph] (2009).

Han, S.

W. Gong and S. Han, arXiv.org, arXiv:0910.4823v1 [quant-ph] (2009).

Y. Bai, and S. Han, Phys. Rev. A 76, 043828 (2007).
[CrossRef]

Hanbury-Brown, R.

R. Hanbury-Brown and R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

Huang, F.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef] [PubMed]

Katz, O.

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Kok, P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Li, H.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef] [PubMed]

Lugiato, L. A.

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Meyers, R. E.

R. E. Meyers, K. S. Deacon, Vacuum 83, 244 (2009).
[CrossRef]

Needell, D.

D. Needell and J. A. Tropp, Appl. Comput. Harmon. Anal. 26, 301 (2008).
[CrossRef]

Park, F.

T. Chan, S. Esedoglu, F. Park, and A. Yip, in The Handbook of Mathematical Models in Computer Vision, (Springer, 2005), pp. 17–32.

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

Rodriguez, P.

B. Wohlberg, and P. Rodriguez, IEEE Signal Process. Lett. 14, 12 (2007).

Romberg, J.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

Sergienko, A. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

Shih, Y.

Y. Shih, SPIE Newsroom (July 28, 2009).

Shih, Y. H.

Y. H. Shih, IEEE J. Sel. Top. Quantum Electron. 13, 1016 (2007).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

Silberberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Strekalov, D. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

Sun, X.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef] [PubMed]

Tao, T.

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

E. Candes and T. Tao, IEEE Trans. Inf. Theory 52, 5406 (2006).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

Tropp, J. A.

D. Needell and J. A. Tropp, Appl. Comput. Harmon. Anal. 26, 301 (2008).
[CrossRef]

Twiss, R. Q.

R. Hanbury-Brown and R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

Wang, K.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef] [PubMed]

Williams, C. P.

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Wohlberg, B.

B. Wohlberg, and P. Rodriguez, IEEE Signal Process. Lett. 14, 12 (2007).

Wu, L.-A.

Y. Zhai, X. Chen, D. Zhang, and L.-A. Wu, Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Xiong, J.

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef] [PubMed]

Yip, A.

T. Chan, S. Esedoglu, F. Park, and A. Yip, in The Handbook of Mathematical Models in Computer Vision, (Springer, 2005), pp. 17–32.

Zhai, Y.

Y. Zhai, X. Chen, D. Zhang, and L.-A. Wu, Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Zhang, D.

Y. Zhai, X. Chen, D. Zhang, and L.-A. Wu, Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Zhu, S. Y.

Y. J. Cai and S. Y. Zhu, Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Appl. Comput. Harmon. Anal. (1)

D. Needell and J. A. Tropp, Appl. Comput. Harmon. Anal. 26, 301 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

O. Katz, Y. Bromberg, and Y. Silberberg, Appl. Phys. Lett. 95, 131110 (2009).
[CrossRef]

Commun. Pure Appl. Math. (1)

E. Candes, J. Romberg, and T. Tao, Commun. Pure Appl. Math. 59, 1207 (2006).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

Y. H. Shih, IEEE J. Sel. Top. Quantum Electron. 13, 1016 (2007).
[CrossRef]

IEEE Signal Process. Lett. (1)

B. Wohlberg, and P. Rodriguez, IEEE Signal Process. Lett. 14, 12 (2007).

IEEE Trans. Inf. Theory (3)

E. Candes and T. Tao, IEEE Trans. Inf. Theory 52, 5406 (2006).
[CrossRef]

D. L. Donoho, IEEE Trans. Inf. Theory 52, 1289 (2006).
[CrossRef]

E. Candes, J. Romberg, and T. Tao, IEEE Trans. Inf. Theory 52, 489 (2006).
[CrossRef]

Nature (1)

R. Hanbury-Brown and R. Q. Twiss, Nature 177, 27 (1956).
[CrossRef]

Phys. Rev. A (4)

Y. Bai, and S. Han, Phys. Rev. A 76, 043828 (2007).
[CrossRef]

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, Phys. Rev. A 52, R3429 (1995).
[CrossRef] [PubMed]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, Phys. Rev. A 70, 013802 (2004).
[CrossRef]

Y. Zhai, X. Chen, D. Zhang, and L.-A. Wu, Phys. Rev. A 72, 043805 (2005).
[CrossRef]

Phys. Rev. E (1)

Y. J. Cai and S. Y. Zhu, Phys. Rev. E 71, 056607 (2005).
[CrossRef]

Phys. Rev. Lett. (2)

J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, Phys. Rev. Lett. 94, 173601 (2005).
[CrossRef] [PubMed]

A. N. Boto, P. Kok, D. S. Abrams, S. L. Braunstein, C. P. Williams, and J. P. Dowling, Phys. Rev. Lett. 85, 2733 (2000).
[CrossRef] [PubMed]

Vacuum (1)

R. E. Meyers, K. S. Deacon, Vacuum 83, 244 (2009).
[CrossRef]

Other (3)

T. Chan, S. Esedoglu, F. Park, and A. Yip, in The Handbook of Mathematical Models in Computer Vision, (Springer, 2005), pp. 17–32.

Y. Shih, SPIE Newsroom (July 28, 2009).

W. Gong and S. Han, arXiv.org, arXiv:0910.4823v1 [quant-ph] (2009).

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Figures (5)

Fig. 1
Fig. 1

Schematic of chaotic thermal light QI.

Fig. 2
Fig. 2

Results of semireal experiments. (a) Numerical dual-slit image; (b), (c), (d) reconstructed images via conventional method, sparse recovery algorithm without and with TV restriction, respectively, when SNR = 15 dB ; (e), (f), (g) corresponding results when SNR = 40 dB .

Fig. 3
Fig. 3

RMSE curves of sparse recovery without and with TV.

Fig. 4
Fig. 4

Snapshot of our QI experiment system.

Fig. 5
Fig. 5

Reconstructed images from the chaotic pseudothermal light QI experiment. (a) Object mask; (b), (c) images calculated by using the conventional method and algorithm .

Tables (1)

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Table 1 Algorithm 1

Equations (4)

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I c = j ( a j M j ) ( j a j j M j ) ,
a = M x .
α s = arg min { a M D α 2 2 + λ α 1 } , x s = D α s ,
α s g = arg min { a M D α 2 2 + λ α 1 + γ G D α 1 } , x s g = D α s g ,

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