Abstract

We experimentally demonstrate that the sensitivity of photon-counting imaging can be improved by 2 orders of magnitude with the compressed sensing (CS) theory. The maximum sensitivity of CS imaging under the quantum limit, which is approximately 1 photon in each pixel during one measurement, is quantitatively obtained through theoretical derivation and proved experimentally. The influences of dark noise and shot noise on photon-counting imaging are also studied to confirm the fundamental constrains on the imaging sensitivity of different imaging methods, which can guide the effort for further enhancing the ultra-weak light imaging ability.

© 2017 Optical Society of America

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References

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  1. W. Becker, A. Bergmann, M. A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63, 58–66 (2004).
    [Crossref]
  2. J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
    [Crossref]
  3. M. A. Albota, R. M. Heinrichs, D. G. Kocher, D. G. Fouche, B. E. Player, M. E. O’Brien, B. F. Aull, J. J. Zayhowski, J. Mooney, and B. C. Willard, “Three-dimensional imaging laser radar with a photon-counting avalanche photodiode array and microchip laser,” Appl. Opt. 41, 7671–7678 (2002).
    [Crossref]
  4. H. M. Qu, Y. F. Zhang Z, J. Ji, and Q. Chen, “The performance of photon counting imaging with a Geiger mode silicon avalanche photodiode,” Laser Phys. Lett. 10, 105201 (2013).
    [Crossref]
  5. A. Kirmani, D. Venkatraman, D. Shin, A. Colaco, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-Photon Imaging,” Science 343, 58–61 (2014).
    [Crossref]
  6. P. A. Morris, R. S. Aspden, J. E. C. Bell, R. W. Boyd, and M J Padgett, “ Imaging with a small number of photons,” Nat. Commun. 6, 5913 (2015).
    [Crossref] [PubMed]
  7. L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
    [Crossref]
  8. D. U. Li, J. Arlt, J. Richardson, R. Walker, A. Buts, D. Stoppa, E. Charbon, and R. Henderson, “Real-time fluorescence lifetime imaging system with a 32 × 32 0.13 μm CMOS low dark-count single-photon avalanche diode array,” Opt. Express 18, 10257–10269 (2010).
    [Crossref] [PubMed]
  9. 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 Sign. Process. Mag. 25, 83–91 (2008).
    [Crossref]
  10. R. M. Willett, M. F. Duarte, M. A. Davenport, and R. G. Baraniuk, “Sparsity and structure in hyperspectral imaging,” IEEE Sign. Process. Mag. 31, 116–126 (2014).
    [Crossref]
  11. G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Sign. Process. Mag. 31, 105–115 (2014).
    [Crossref]
  12. 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]
  13. G. A. Howland, P. B. Dixon, and J. C. Howell, “Photon-counting compressive sensing laser radar for 3D imaging,” Appl. Opt. 50, 5917–5920 (2011).
    [Crossref] [PubMed]
  14. C. Q. Zhao, W. L. Gong, M. L. Chen, E. R. Li, H. Wang, W. D. Xu, and S. S. Han, “Ghost imaging lidar via sparsity constraints,” Appl. Phys. Lett. 101, 141123 (2012).
    [Crossref]
  15. W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).
    [PubMed]
  16. X. F. Liu, W. K. Yu, X. R. Yao, B. Dai, L. Z. Li, C. Wang, and G. J. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
    [Crossref]
  17. W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, G. J. Zhai, and Q. Zhao, “Single-photon compressive imaging with some performance benefits over raster scanning,” Phys. Lett. A 378, 3406–3411 (2014).
    [Crossref]
  18. E. J. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
    [Crossref]
  19. D. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory 52, 1289–1306 (2006).
    [Crossref]
  20. E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
    [Crossref]
  21. E. J. Candès and M. B. Wakin, “An introduction to compressive sampling,” IEEE Sign. Process. Mag. 25, 21–30 (2008).
    [Crossref]
  22. R.M. Willett, R.F. Marcia, and J.M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial, ” Opt. Eng. 50, 072601 (2011)
    [Crossref]

2016 (1)

X. F. Liu, W. K. Yu, X. R. Yao, B. Dai, L. Z. Li, C. Wang, and G. J. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

2015 (2)

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[Crossref]

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

2014 (5)

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, G. J. Zhai, and Q. Zhao, “Single-photon compressive imaging with some performance benefits over raster scanning,” Phys. Lett. A 378, 3406–3411 (2014).
[Crossref]

A. Kirmani, D. Venkatraman, D. Shin, A. Colaco, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-Photon Imaging,” Science 343, 58–61 (2014).
[Crossref]

R. M. Willett, M. F. Duarte, M. A. Davenport, and R. G. Baraniuk, “Sparsity and structure in hyperspectral imaging,” IEEE Sign. Process. Mag. 31, 116–126 (2014).
[Crossref]

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Sign. Process. Mag. 31, 105–115 (2014).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).
[PubMed]

2013 (2)

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]

H. M. Qu, Y. F. Zhang Z, J. Ji, and Q. Chen, “The performance of photon counting imaging with a Geiger mode silicon avalanche photodiode,” Laser Phys. Lett. 10, 105201 (2013).
[Crossref]

2012 (1)

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

2011 (2)

G. A. Howland, P. B. Dixon, and J. C. Howell, “Photon-counting compressive sensing laser radar for 3D imaging,” Appl. Opt. 50, 5917–5920 (2011).
[Crossref] [PubMed]

R.M. Willett, R.F. Marcia, and J.M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial, ” Opt. Eng. 50, 072601 (2011)
[Crossref]

2010 (2)

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

D. U. Li, J. Arlt, J. Richardson, R. Walker, A. Buts, D. Stoppa, E. Charbon, and R. Henderson, “Real-time fluorescence lifetime imaging system with a 32 × 32 0.13 μm CMOS low dark-count single-photon avalanche diode array,” Opt. Express 18, 10257–10269 (2010).
[Crossref] [PubMed]

2008 (2)

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 Sign. Process. Mag. 25, 83–91 (2008).
[Crossref]

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

2006 (2)

D. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory 52, 1289–1306 (2006).
[Crossref]

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
[Crossref]

2005 (1)

E. J. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[Crossref]

2004 (1)

W. Becker, A. Bergmann, M. A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63, 58–66 (2004).
[Crossref]

2002 (1)

Albota, M. A.

Andersen, M. F.

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[Crossref]

Andersen, M. I.

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[Crossref]

Arce, G. R.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Sign. Process. Mag. 31, 105–115 (2014).
[Crossref]

Arguello, H.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Sign. Process. Mag. 31, 105–115 (2014).
[Crossref]

Arlt, J.

Aspden, R. S.

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

Aull, B. F.

Baraniuk, R. G.

R. M. Willett, M. F. Duarte, M. A. Davenport, and R. G. Baraniuk, “Sparsity and structure in hyperspectral imaging,” IEEE Sign. Process. Mag. 31, 116–126 (2014).
[Crossref]

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 Sign. Process. Mag. 25, 83–91 (2008).
[Crossref]

Becker, W.

W. Becker, A. Bergmann, M. A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63, 58–66 (2004).
[Crossref]

Bell, J. E. C.

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

Benndorf, K.

W. Becker, A. Bergmann, M. A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63, 58–66 (2004).
[Crossref]

Bergmann, A.

W. Becker, A. Bergmann, M. A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63, 58–66 (2004).
[Crossref]

Biskup, C.

W. Becker, A. Bergmann, M. A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63, 58–66 (2004).
[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.

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

Brady, D. J.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Sign. Process. Mag. 31, 105–115 (2014).
[Crossref]

Bramich, D. M.

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[Crossref]

Buts, A.

Candès, E. J.

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

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
[Crossref]

E. J. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[Crossref]

Carin, L.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Sign. Process. Mag. 31, 105–115 (2014).
[Crossref]

Charbon, E.

Chen, M. L.

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

Chen, Q.

H. M. Qu, Y. F. Zhang Z, J. Ji, and Q. Chen, “The performance of photon counting imaging with a Geiger mode silicon avalanche photodiode,” Laser Phys. Lett. 10, 105201 (2013).
[Crossref]

Colaco, A.

A. Kirmani, D. Venkatraman, D. Shin, A. Colaco, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-Photon Imaging,” Science 343, 58–61 (2014).
[Crossref]

Condorelli, G.

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

Dai, B.

X. F. Liu, W. K. Yu, X. R. Yao, B. Dai, L. Z. Li, C. Wang, and G. J. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

Davenport, M. A.

R. M. Willett, M. F. Duarte, M. A. Davenport, and R. G. Baraniuk, “Sparsity and structure in hyperspectral imaging,” IEEE Sign. Process. Mag. 31, 116–126 (2014).
[Crossref]

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 Sign. Process. Mag. 25, 83–91 (2008).
[Crossref]

Dixon, P. B.

Donoho, D.

D. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory 52, 1289–1306 (2006).
[Crossref]

Duarte, M. F.

R. M. Willett, M. F. Duarte, M. A. Davenport, and R. G. Baraniuk, “Sparsity and structure in hyperspectral imaging,” IEEE Sign. Process. Mag. 31, 116–126 (2014).
[Crossref]

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 Sign. Process. Mag. 25, 83–91 (2008).
[Crossref]

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]

Fallica, G.

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

Fouche, D. G.

Gong, W. L.

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

Goyal, V. K.

A. Kirmani, D. Venkatraman, D. Shin, A. Colaco, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-Photon Imaging,” Science 343, 58–61 (2014).
[Crossref]

Han, S. S.

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

Heinrichs, R. M.

Henderson, R.

Hink, M. A.

W. Becker, A. Bergmann, M. A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63, 58–66 (2004).
[Crossref]

Howell, J. C.

Howland, G. A.

Hundertmark, M.

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[Crossref]

Ji, J.

H. M. Qu, Y. F. Zhang Z, J. Ji, and Q. Chen, “The performance of photon counting imaging with a Geiger mode silicon avalanche photodiode,” Laser Phys. Lett. 10, 105201 (2013).
[Crossref]

Jorgensen, U. G.

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[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 Sign. Process. Mag. 25, 83–91 (2008).
[Crossref]

Kirmani, A.

A. Kirmani, D. Venkatraman, D. Shin, A. Colaco, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-Photon Imaging,” Science 343, 58–61 (2014).
[Crossref]

Kittle, D. S.

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Sign. Process. Mag. 31, 105–115 (2014).
[Crossref]

Kjaergaard, P.

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[Crossref]

Kocher, D. G.

Konig, K.

W. Becker, A. Bergmann, M. A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63, 58–66 (2004).
[Crossref]

Lanzan, L.

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[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 Sign. Process. Mag. 25, 83–91 (2008).
[Crossref]

Li, D. U.

Li, E. R.

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

Li, L. Z.

X. F. Liu, W. K. Yu, X. R. Yao, B. Dai, L. Z. Li, C. Wang, and G. J. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

Liu, X. F.

X. F. Liu, W. K. Yu, X. R. Yao, B. Dai, L. Z. Li, C. Wang, and G. J. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).
[PubMed]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, G. J. Zhai, and Q. Zhao, “Single-photon compressive imaging with some performance benefits over raster scanning,” Phys. Lett. A 378, 3406–3411 (2014).
[Crossref]

Marcia, R.F.

R.M. Willett, R.F. Marcia, and J.M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial, ” Opt. Eng. 50, 072601 (2011)
[Crossref]

Mazzillo, M.

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

Michaelsen, N.

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[Crossref]

Mooney, J.

Morris, P. A.

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

Musumeci, F.

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

Neri, L.

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

Nichols, J.M.

R.M. Willett, R.F. Marcia, and J.M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial, ” Opt. Eng. 50, 072601 (2011)
[Crossref]

O’Brien, M. E.

Padgett, M J

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

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]

Player, B. E.

Privitera, S.

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

Qu, H. M.

H. M. Qu, Y. F. Zhang Z, J. Ji, and Q. Chen, “The performance of photon counting imaging with a Geiger mode silicon avalanche photodiode,” Laser Phys. Lett. 10, 105201 (2013).
[Crossref]

Richardson, J.

Romberg, J. K.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
[Crossref]

Sanfilippo, D.

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

Scordino, A.

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

Shapiro, J. H.

A. Kirmani, D. Venkatraman, D. Shin, A. Colaco, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-Photon Imaging,” Science 343, 58–61 (2014).
[Crossref]

Shin, D.

A. Kirmani, D. Venkatraman, D. Shin, A. Colaco, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-Photon Imaging,” Science 343, 58–61 (2014).
[Crossref]

Skottfelt, J.

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[Crossref]

Sorensen, A. N.

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[Crossref]

Southworth, J.

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[Crossref]

Stoppa, D.

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]

Sun, T.

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 Sign. Process. Mag. 25, 83–91 (2008).
[Crossref]

Takhar, D.

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 Sign. Process. Mag. 25, 83–91 (2008).
[Crossref]

Tao, T.

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
[Crossref]

E. J. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[Crossref]

Tudisco, S.

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

Valvo, G.

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

Venkatraman, D.

A. Kirmani, D. Venkatraman, D. Shin, A. Colaco, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-Photon Imaging,” Science 343, 58–61 (2014).
[Crossref]

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]

Wakin, M. B.

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

Walker, R.

Wang, C.

X. F. Liu, W. K. Yu, X. R. Yao, B. Dai, L. Z. Li, C. Wang, and G. J. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).
[PubMed]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, G. J. Zhai, and Q. Zhao, “Single-photon compressive imaging with some performance benefits over raster scanning,” Phys. Lett. A 378, 3406–3411 (2014).
[Crossref]

Wang, H.

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

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]

Willard, B. C.

Willett, R. M.

R. M. Willett, M. F. Duarte, M. A. Davenport, and R. G. Baraniuk, “Sparsity and structure in hyperspectral imaging,” IEEE Sign. Process. Mag. 31, 116–126 (2014).
[Crossref]

Willett, R.M.

R.M. Willett, R.F. Marcia, and J.M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial, ” Opt. Eng. 50, 072601 (2011)
[Crossref]

Wong, F. N. C.

A. Kirmani, D. Venkatraman, D. Shin, A. Colaco, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-Photon Imaging,” Science 343, 58–61 (2014).
[Crossref]

Xu, W. D.

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

Yao, X. R.

X. F. Liu, W. K. Yu, X. R. Yao, B. Dai, L. Z. Li, C. Wang, and G. J. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, G. J. Zhai, and Q. Zhao, “Single-photon compressive imaging with some performance benefits over raster scanning,” Phys. Lett. A 378, 3406–3411 (2014).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).
[PubMed]

Yu, W. K.

X. F. Liu, W. K. Yu, X. R. Yao, B. Dai, L. Z. Li, C. Wang, and G. J. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).
[PubMed]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, G. J. Zhai, and Q. Zhao, “Single-photon compressive imaging with some performance benefits over raster scanning,” Phys. Lett. A 378, 3406–3411 (2014).
[Crossref]

Zayhowski, J. J.

Zhai, G. J.

X. F. Liu, W. K. Yu, X. R. Yao, B. Dai, L. Z. Li, C. Wang, and G. J. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).
[PubMed]

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, G. J. Zhai, and Q. Zhao, “Single-photon compressive imaging with some performance benefits over raster scanning,” Phys. Lett. A 378, 3406–3411 (2014).
[Crossref]

Zhai, Y.

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).
[PubMed]

Zhang Z, Y. F.

H. M. Qu, Y. F. Zhang Z, J. Ji, and Q. Chen, “The performance of photon counting imaging with a Geiger mode silicon avalanche photodiode,” Laser Phys. Lett. 10, 105201 (2013).
[Crossref]

Zhao, C. Q.

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

Zhao, Q.

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, G. J. Zhai, and Q. Zhao, “Single-photon compressive imaging with some performance benefits over raster scanning,” Phys. Lett. A 378, 3406–3411 (2014).
[Crossref]

Appl. Opt. (2)

Appl. Phys. Lett. (1)

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

Astron. Astrophys. (1)

J. Skottfelt, D. M. Bramich, M. Hundertmark, U. G. Jorgensen, N. Michaelsen, P. Kjaergaard, J. Southworth, A. N. Sorensen, M. F. Andersen, and M. I. Andersen, “The two-colour EMCCD instrument for the Danish 1.54 m telescope and SONG,” Astron. Astrophys. 574, A54 (2015).
[Crossref]

Commun. Pure Appl. Math. (1)

E. J. Candès, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
[Crossref]

IEEE Sign. Process. Mag. (4)

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

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 Sign. Process. Mag. 25, 83–91 (2008).
[Crossref]

R. M. Willett, M. F. Duarte, M. A. Davenport, and R. G. Baraniuk, “Sparsity and structure in hyperspectral imaging,” IEEE Sign. Process. Mag. 31, 116–126 (2014).
[Crossref]

G. R. Arce, D. J. Brady, L. Carin, H. Arguello, and D. S. Kittle, “Compressive coded aperture spectral imaging,” IEEE Sign. Process. Mag. 31, 105–115 (2014).
[Crossref]

IEEE Trans. Inf. Theory (1)

E. J. Candès and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005).
[Crossref]

IEEE Trans. Inform. Theory (1)

D. Donoho, “Compressed sensing,” IEEE Trans. Inform. Theory 52, 1289–1306 (2006).
[Crossref]

Laser Phys. Lett. (1)

H. M. Qu, Y. F. Zhang Z, J. Ji, and Q. Chen, “The performance of photon counting imaging with a Geiger mode silicon avalanche photodiode,” Laser Phys. Lett. 10, 105201 (2013).
[Crossref]

Microsc. Res. Tech. (1)

W. Becker, A. Bergmann, M. A. Hink, K. Konig, K. Benndorf, and C. Biskup, “Fluorescence lifetime imaging by time-correlated single-photon counting,” Microsc. Res. Tech. 63, 58–66 (2004).
[Crossref]

Nat. Commun. (1)

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

Nucl. Instrum. Method A (1)

L. Neri, S. Tudisco, L. Lanzan, F. Musumeci, S. Privitera, A. Scordino, G. Condorelli, G. Fallica, M. Mazzillo, D. Sanfilippo, and G. Valvo, “Design and characterization of single photon avalanche diodes arrays,” Nucl. Instrum. Method A 617, 432–433 (2010).
[Crossref]

Opt. Commun. (1)

X. F. Liu, W. K. Yu, X. R. Yao, B. Dai, L. Z. Li, C. Wang, and G. J. Zhai, “Measurement dimensions compressed spectral imaging with a single point detector,” Opt. Commun. 365, 173–179 (2016).
[Crossref]

Opt. Eng. (1)

R.M. Willett, R.F. Marcia, and J.M. Nichols, “Compressed sensing for practical optical imaging systems: a tutorial, ” Opt. Eng. 50, 072601 (2011)
[Crossref]

Opt. Express (1)

Phys. Lett. A (1)

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, G. J. Zhai, and Q. Zhao, “Single-photon compressive imaging with some performance benefits over raster scanning,” Phys. Lett. A 378, 3406–3411 (2014).
[Crossref]

Sci. Rep. (1)

W. K. Yu, X. F. Liu, X. R. Yao, C. Wang, Y. Zhai, and G. J. Zhai, “Complementary compressive imaging for the telescopic system,” Sci. Rep. 4, 5834 (2014).
[PubMed]

Science (2)

A. Kirmani, D. Venkatraman, D. Shin, A. Colaco, F. N. C. Wong, J. H. Shapiro, and V. K. Goyal, “First-Photon Imaging,” Science 343, 58–61 (2014).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D Computational Imaging with Single-Pixel Detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

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Figures (7)

Fig. 1
Fig. 1 Principle of CS-based imaging.
Fig. 2
Fig. 2 Experimental setup for photon-counting imaging.
Fig. 3
Fig. 3 Experimental results of photon-counting imaging.
Fig. 4
Fig. 4 Imaging SNRs as functions of effective photon number. Squares, circles, and crosses are the experimental results; curves are mathematical fits. The sampling numbers are all 4096.
Fig. 5
Fig. 5 Simulation results of grayscale-object photon-counting imaging. (a) The grayscale and pseudo-color images of original object. (b) Imaging results of photon-counting imaging with three methods under different effective photon numbers Pn. The images are 64 × 64 pixels and the modulation numbers are all 4096. (c) Imaging SNRs as functions of Pn. Squares, circles, and crosses are the simulation results; curves are mathematical fits.
Fig. 6
Fig. 6 Effect of dark noise on sensitivity of photon-counting imaging. Pn is the effective photon number in one pixel, and η is the ratio of SNRs of photon-counting imaging without and with dark noise.
Fig. 7
Fig. 7 Effect of shot noise on sensitivity of photon-counting imaging. Pn is the effective photon number in one pixel, and η is the ratio of SNRs of photon-counting imaging without and with shot noise.

Equations (15)

Equations on this page are rendered with MathJax. Learn more.

y = A x ,
x ^ x 2 > C N ε ,
ε 2 = 1 M y ^ y 2 2 = σ y 2 ,
y 1 = A x y 2 = ( 1 A ) x ,
y 1 y 2 = ( 2 A 1 ) x .
y 1 = y 2 = ( N k P 2 + P d ) T 2 M .
σ y 1 2 = σ y 2 2 = ( N k P 2 + P d ) T 2 M .
σ y 2 = ( N k P 2 + P d ) T 2 M 2 = ( N k P 2 + P d ) T M .
Signal = P τ = P T 2 M .
noise = 1 N x ^ x 2 2 < 1 N C N 2 σ y 2 .
SNR 1 = signal noise = 1 C N P T 2 M 1 ( N k N + 2 P d N P ) .
SNR 1 = signal noise = 1 C N P n 1 k .
y 1 = ( P + P d ) T N , y 2 = P d T N ,
σ y 1 2 = ( P + P d ) T N , σ y 2 2 = P d T N .
SNR 2 = y 1 y 2 σ y 2 = P T N 1 ( N k N + P d P ) = P n 2 k 1 ( 1 + 1 k P d P ) .

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