Abstract

High-quality ghost imaging (GI) under low sampling is very important for scientific research and practical application. How to reconstruct high-quality image from low sampling has always been the focus of ghost imaging research. In this work, based on the hypothesis that the matrix stacked by the vectors of image’s nonlocal similar patches is of low rank and has sparse singular values, we both theoretically and experimentally demonstrate a method that applies the projected Landweber regularization and blocking matching low-rank denoising to obtain the excellent image under low sampling, which we call blocking matching low-rank ghost imaging (BLRGI). Comparing with these methods of "GI via sparsity constraint," "joint iteration GI" and "total variation based GI," both simulation and experiment show that the BLRGI can obtain better ghost imaging quality with low sampling in terms of peak signal-to-noise ratio, structural similarity index and visual observation.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
  3. J. H. Shapiro and B. I. Erkmen, “Ghost imaging: from quantum to classical to computational,” Adv. Opt. Photonics 2(4), 405–450 (2010).
    [Crossref]
  4. Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
    [Crossref]
  5. W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
    [Crossref]
  6. W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with "positive-negative" light modulation,” Opt. Commun. 371, 105–111 (2016).
    [Crossref]
  7. C. Luo, H. Xu, and J. Cheng, “High-resolution ghost imaging experiments with cosh-gaussian modulated incoherent sources,” J. Opt. Soc. Am. A 32(3), 482–485 (2015).
    [Crossref]
  8. C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
    [Crossref]
  9. C. Zhou, T. Tian, C. Gao, W. Gong, and L. Song, “Multi-resolution progressive computational ghost imaging,” J. Opt. 21(5), 055702 (2019).
    [Crossref]
  10. B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
    [Crossref]
  11. L. Shen, Y. Xu-Ri, Y. Wen-Kai, W. Ling-An, and Z. Guang-Jie, “High-speed secure key distribution over an optical network based on computational correlation imaging,” Opt. Lett. 38(12), 2144–2146 (2013).
    [Crossref]
  12. M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
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    [Crossref]
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    [Crossref]
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    [Crossref]
  17. A. Averbuch, S. Dekel, and S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. on Imaging Sci. 5(1), 57–89 (2012).
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  22. X.-R. Yao, W.-K. Yu, X.-F. Liu, L.-Z. Li, M.-F. Li, L.-A. Wu, and G.-J. Zhai, “Iterative denoising of ghost imaging,” Opt. Express 22(20), 24268–24275 (2014).
    [Crossref]
  23. X. Hu, J. Suo, T. Yue, L. Bian, and Q. Dai, “Patch-primitive driven compressive ghost imaging,” Opt. Express 23(9), 11092–11104 (2015).
    [Crossref]
  24. Y. Huo, H. He, and F. Chen, “Compressive adaptive ghost imaging via sharing mechanism and fellow relationship,” Appl. Opt. 55(12), 3356–3367 (2016).
    [Crossref]
  25. G. Wu, T. Li, J. Li, B. Luo, and H. Guo, “Ghost imaging under low-rank constraint,” Opt. Lett. 44(17), 4311–4314 (2019).
    [Crossref]
  26. J. F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. on Optim. 20(4), 1956–1982 (2010).
    [Crossref]
  27. K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans.Image Process. 16(8), 2080–2095 (2007).
    [Crossref]
  28. Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans.Image Process. 13(4), 600–612 (2004).
    [Crossref]
  29. A. Hore and D. Ziou, “Image quality metrics: Psnr vs. ssim,” in 2010 20th International Conference on Pattern Recognition, (IEEE, 2010), pp. 2366–2369.

2019 (4)

C. Zhou, T. Tian, C. Gao, W. Gong, and L. Song, “Multi-resolution progressive computational ghost imaging,” J. Opt. 21(5), 055702 (2019).
[Crossref]

A. M. Kingston, G. R. Myers, D. Pelliccia, I. D. Svalbe, and D. M. Paganin, “X-ray ghost-tomography: Artefacts, dose distribution, and mask considerations,” IEEE Trans. Comput. Imaging 5(1), 136–149 (2019).
[Crossref]

C. Zhou, G. Wang, H. Huang, L. Song, and K. Xue, “Edge detection based on joint iteration ghost imaging,” Opt. Express 27(19), 27295–27307 (2019).
[Crossref]

G. Wu, T. Li, J. Li, B. Luo, and H. Guo, “Ghost imaging under low-rank constraint,” Opt. Lett. 44(17), 4311–4314 (2019).
[Crossref]

2018 (2)

H. Huang, C. Zhou, T. Tian, D. Liu, and L. Song, “High-quality compressive ghost imaging,” Opt. Commun. 412, 60–65 (2018).
[Crossref]

D. Pelliccia, M. P. Olbinado, A. Rack, A. M. Kingston, G. R. Myers, and D. M. Paganin, “Towards a practical implementation of x-ray ghost imaging with synchrotron light,” IUCrJ 5(4), 428–438 (2018).
[Crossref]

2016 (3)

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with "positive-negative" light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Y. Huo, H. He, and F. Chen, “Compressive adaptive ghost imaging via sharing mechanism and fellow relationship,” Appl. Opt. 55(12), 3356–3367 (2016).
[Crossref]

2015 (5)

X. Hu, J. Suo, T. Yue, L. Bian, and Q. Dai, “Patch-primitive driven compressive ghost imaging,” Opt. Express 23(9), 11092–11104 (2015).
[Crossref]

C. Luo, H. Xu, and J. Cheng, “High-resolution ghost imaging experiments with cosh-gaussian modulated incoherent sources,” J. Opt. Soc. Am. A 32(3), 482–485 (2015).
[Crossref]

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

W. Gong and S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5(1), 9280 (2015).
[Crossref]

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
[Crossref]

2014 (1)

2013 (3)

M. Aßmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3(1), 1545 (2013).
[Crossref]

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

L. Shen, Y. Xu-Ri, Y. Wen-Kai, W. Ling-An, and Z. Guang-Jie, “High-speed secure key distribution over an optical network based on computational correlation imaging,” Opt. Lett. 38(12), 2144–2146 (2013).
[Crossref]

2012 (2)

W. Hui and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98(2), 24003 (2012).
[Crossref]

A. Averbuch, S. Dekel, and S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. on Imaging Sci. 5(1), 57–89 (2012).
[Crossref]

2010 (2)

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

J. F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. on Optim. 20(4), 1956–1982 (2010).
[Crossref]

2009 (1)

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

2007 (1)

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans.Image Process. 16(8), 2080–2095 (2007).
[Crossref]

2004 (2)

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans.Image Process. 13(4), 600–612 (2004).
[Crossref]

A. Gatti, E. Brambilla, M. Bache, and L. A. Lugiato, “Ghost imaging with thermal light: comparing entanglement and classicalcorrelation,” Phys. Rev. Lett. 93(9), 093602 (2004).
[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(5), R3429–R3432 (1995).
[Crossref]

Aßmann, M.

M. Aßmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3(1), 1545 (2013).
[Crossref]

Averbuch, A.

A. Averbuch, S. Dekel, and S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. on Imaging Sci. 5(1), 57–89 (2012).
[Crossref]

Bache, M.

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

Bayer, M.

M. Aßmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3(1), 1545 (2013).
[Crossref]

Bian, L.

Bovik, A. C.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans.Image Process. 13(4), 600–612 (2004).
[Crossref]

Bowman, A.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Bowman, R.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Bowman, R. W.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
[Crossref]

Brambilla, E.

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

Bromberg, Y.

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

Cai, J. F.

J. F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. on Optim. 20(4), 1956–1982 (2010).
[Crossref]

Candès, E. J.

J. F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. on Optim. 20(4), 1956–1982 (2010).
[Crossref]

Chen, A. X.

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

Chen, F.

Chen, M.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

Cheng, J.

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

C. Luo, H. Xu, and J. Cheng, “High-resolution ghost imaging experiments with cosh-gaussian modulated incoherent sources,” J. Opt. Soc. Am. A 32(3), 482–485 (2015).
[Crossref]

Dabov, K.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans.Image Process. 16(8), 2080–2095 (2007).
[Crossref]

Dai, Q.

Dekel, S.

A. Averbuch, S. Dekel, and S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. on Imaging Sci. 5(1), 57–89 (2012).
[Crossref]

Deutsch, S.

A. Averbuch, S. Dekel, and S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. on Imaging Sci. 5(1), 57–89 (2012).
[Crossref]

Edgar, M.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Edgar, M. P.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
[Crossref]

Egiazarian, K.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans.Image Process. 16(8), 2080–2095 (2007).
[Crossref]

Erkmen, B. I.

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

Foi, A.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans.Image Process. 16(8), 2080–2095 (2007).
[Crossref]

Gao, C.

C. Zhou, T. Tian, C. Gao, W. Gong, and L. Song, “Multi-resolution progressive computational ghost imaging,” J. Opt. 21(5), 055702 (2019).
[Crossref]

Gatti, A.

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

Gibson, G. M.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
[Crossref]

Gong, W.

C. Zhou, T. Tian, C. Gao, W. Gong, and L. Song, “Multi-resolution progressive computational ghost imaging,” J. Opt. 21(5), 055702 (2019).
[Crossref]

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

W. Gong and S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5(1), 9280 (2015).
[Crossref]

W. Gong and S. Han, “Super-resolution far-field ghost imaging via compressive sampling,” arXiv preprint arXiv:0911.4750 (2009).

Guang-Jie, Z.

Guo, H.

Han, S.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

W. Gong and S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5(1), 9280 (2015).
[Crossref]

W. Hui and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98(2), 24003 (2012).
[Crossref]

W. Gong and S. Han, “Super-resolution far-field ghost imaging via compressive sampling,” arXiv preprint arXiv:0911.4750 (2009).

He, H.

Hore, A.

A. Hore and D. Ziou, “Image quality metrics: Psnr vs. ssim,” in 2010 20th International Conference on Pattern Recognition, (IEEE, 2010), pp. 2366–2369.

Hu, X.

Huang, H.

C. Zhou, G. Wang, H. Huang, L. Song, and K. Xue, “Edge detection based on joint iteration ghost imaging,” Opt. Express 27(19), 27295–27307 (2019).
[Crossref]

H. Huang, C. Zhou, T. Tian, D. Liu, and L. Song, “High-quality compressive ghost imaging,” Opt. Commun. 412, 60–65 (2018).
[Crossref]

Hui, W.

W. Hui and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98(2), 24003 (2012).
[Crossref]

Huo, Y.

Katkovnik, V.

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans.Image Process. 16(8), 2080–2095 (2007).
[Crossref]

Katz, O.

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

Kingston, A. M.

A. M. Kingston, G. R. Myers, D. Pelliccia, I. D. Svalbe, and D. M. Paganin, “X-ray ghost-tomography: Artefacts, dose distribution, and mask considerations,” IEEE Trans. Comput. Imaging 5(1), 136–149 (2019).
[Crossref]

D. Pelliccia, M. P. Olbinado, A. Rack, A. M. Kingston, G. R. Myers, and D. M. Paganin, “Towards a practical implementation of x-ray ghost imaging with synchrotron light,” IUCrJ 5(4), 428–438 (2018).
[Crossref]

Lan, R. M.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with "positive-negative" light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Li, J.

Li, L.-Z.

Li, M.-F.

Li, T.

Ling-An, W.

Liu, D.

H. Huang, C. Zhou, T. Tian, D. Liu, and L. Song, “High-quality compressive ghost imaging,” Opt. Commun. 412, 60–65 (2018).
[Crossref]

Liu, X. F.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with "positive-negative" light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Liu, X.-F.

Liu, Z. M.

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

Lugiato, L. A.

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

Luo, B.

Luo, C.

Luo, C. L.

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

Mitchell, K. J.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
[Crossref]

Myers, G. R.

A. M. Kingston, G. R. Myers, D. Pelliccia, I. D. Svalbe, and D. M. Paganin, “X-ray ghost-tomography: Artefacts, dose distribution, and mask considerations,” IEEE Trans. Comput. Imaging 5(1), 136–149 (2019).
[Crossref]

D. Pelliccia, M. P. Olbinado, A. Rack, A. M. Kingston, G. R. Myers, and D. M. Paganin, “Towards a practical implementation of x-ray ghost imaging with synchrotron light,” IUCrJ 5(4), 428–438 (2018).
[Crossref]

Olbinado, M. P.

D. Pelliccia, M. P. Olbinado, A. Rack, A. M. Kingston, G. R. Myers, and D. M. Paganin, “Towards a practical implementation of x-ray ghost imaging with synchrotron light,” IUCrJ 5(4), 428–438 (2018).
[Crossref]

Padgett, M.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Padgett, M. J.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
[Crossref]

Paganin, D. M.

A. M. Kingston, G. R. Myers, D. Pelliccia, I. D. Svalbe, and D. M. Paganin, “X-ray ghost-tomography: Artefacts, dose distribution, and mask considerations,” IEEE Trans. Comput. Imaging 5(1), 136–149 (2019).
[Crossref]

D. Pelliccia, M. P. Olbinado, A. Rack, A. M. Kingston, G. R. Myers, and D. M. Paganin, “Towards a practical implementation of x-ray ghost imaging with synchrotron light,” IUCrJ 5(4), 428–438 (2018).
[Crossref]

Pelliccia, D.

A. M. Kingston, G. R. Myers, D. Pelliccia, I. D. Svalbe, and D. M. Paganin, “X-ray ghost-tomography: Artefacts, dose distribution, and mask considerations,” IEEE Trans. Comput. Imaging 5(1), 136–149 (2019).
[Crossref]

D. Pelliccia, M. P. Olbinado, A. Rack, A. M. Kingston, G. R. Myers, and D. M. Paganin, “Towards a practical implementation of x-ray ghost imaging with synchrotron light,” IUCrJ 5(4), 428–438 (2018).
[Crossref]

Pittman, T. B.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Rack, A.

D. Pelliccia, M. P. Olbinado, A. Rack, A. M. Kingston, G. R. Myers, and D. M. Paganin, “Towards a practical implementation of x-ray ghost imaging with synchrotron light,” IUCrJ 5(4), 428–438 (2018).
[Crossref]

Radwell, N.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
[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(5), R3429–R3432 (1995).
[Crossref]

Shapiro, J. H.

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

Sheikh, H. R.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans.Image Process. 13(4), 600–612 (2004).
[Crossref]

Shen, L.

Shen, Z.

J. F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. on Optim. 20(4), 1956–1982 (2010).
[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(5), R3429–R3432 (1995).
[Crossref]

Silberberg, Y.

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

Simoncelli, E. P.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans.Image Process. 13(4), 600–612 (2004).
[Crossref]

Song, L.

C. Zhou, T. Tian, C. Gao, W. Gong, and L. Song, “Multi-resolution progressive computational ghost imaging,” J. Opt. 21(5), 055702 (2019).
[Crossref]

C. Zhou, G. Wang, H. Huang, L. Song, and K. Xue, “Edge detection based on joint iteration ghost imaging,” Opt. Express 27(19), 27295–27307 (2019).
[Crossref]

H. Huang, C. Zhou, T. Tian, D. Liu, and L. Song, “High-quality compressive ghost imaging,” Opt. Commun. 412, 60–65 (2018).
[Crossref]

Strekalov, D. V.

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Sun, B.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
[Crossref]

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Suo, J.

Svalbe, I. D.

A. M. Kingston, G. R. Myers, D. Pelliccia, I. D. Svalbe, and D. M. Paganin, “X-ray ghost-tomography: Artefacts, dose distribution, and mask considerations,” IEEE Trans. Comput. Imaging 5(1), 136–149 (2019).
[Crossref]

Tian, T.

C. Zhou, T. Tian, C. Gao, W. Gong, and L. Song, “Multi-resolution progressive computational ghost imaging,” J. Opt. 21(5), 055702 (2019).
[Crossref]

H. Huang, C. Zhou, T. Tian, D. Liu, and L. Song, “High-quality compressive ghost imaging,” Opt. Commun. 412, 60–65 (2018).
[Crossref]

Vittert, L.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Wang, G.

Wang, Z.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans.Image Process. 13(4), 600–612 (2004).
[Crossref]

Welsh, S.

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

Welsh, S. S.

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
[Crossref]

Wen-Kai, Y.

Wu, G.

Wu, L. A.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with "positive-negative" light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Wu, L.-A.

Xu, H.

Xu, W.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

Xue, K.

Xu-Ri, Y.

Yao, X. R.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with "positive-negative" light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Yao, X.-R.

Yu, H.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

Yu, W. K.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with "positive-negative" light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Yu, W.-K.

Yue, T.

Zhai, G. J.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with "positive-negative" light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Zhai, G.-J.

Zhao, C.

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

Zhao, Q.

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with "positive-negative" light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

Zhou, C.

C. Zhou, T. Tian, C. Gao, W. Gong, and L. Song, “Multi-resolution progressive computational ghost imaging,” J. Opt. 21(5), 055702 (2019).
[Crossref]

C. Zhou, G. Wang, H. Huang, L. Song, and K. Xue, “Edge detection based on joint iteration ghost imaging,” Opt. Express 27(19), 27295–27307 (2019).
[Crossref]

H. Huang, C. Zhou, T. Tian, D. Liu, and L. Song, “High-quality compressive ghost imaging,” Opt. Commun. 412, 60–65 (2018).
[Crossref]

Ziou, D.

A. Hore and D. Ziou, “Image quality metrics: Psnr vs. ssim,” in 2010 20th International Conference on Pattern Recognition, (IEEE, 2010), pp. 2366–2369.

Adv. Opt. Photonics (1)

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

Appl. Opt. (1)

Europhys. Lett. (1)

W. Hui and S. Han, “Coherent ghost imaging based on sparsity constraint without phase-sensitive detection,” Europhys. Lett. 98(2), 24003 (2012).
[Crossref]

IEEE Trans. Comput. Imaging (1)

A. M. Kingston, G. R. Myers, D. Pelliccia, I. D. Svalbe, and D. M. Paganin, “X-ray ghost-tomography: Artefacts, dose distribution, and mask considerations,” IEEE Trans. Comput. Imaging 5(1), 136–149 (2019).
[Crossref]

IEEE Trans.Image Process. (2)

K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transform-domain collaborative filtering,” IEEE Trans.Image Process. 16(8), 2080–2095 (2007).
[Crossref]

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, “Image quality assessment: from error visibility to structural similarity,” IEEE Trans.Image Process. 13(4), 600–612 (2004).
[Crossref]

IUCrJ (1)

D. Pelliccia, M. P. Olbinado, A. Rack, A. M. Kingston, G. R. Myers, and D. M. Paganin, “Towards a practical implementation of x-ray ghost imaging with synchrotron light,” IUCrJ 5(4), 428–438 (2018).
[Crossref]

J. Opt. (1)

C. Zhou, T. Tian, C. Gao, W. Gong, and L. Song, “Multi-resolution progressive computational ghost imaging,” J. Opt. 21(5), 055702 (2019).
[Crossref]

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

Opt. Commun. (3)

W. K. Yu, X. R. Yao, X. F. Liu, R. M. Lan, L. A. Wu, G. J. Zhai, and Q. Zhao, “Compressive microscopic imaging with "positive-negative" light modulation,” Opt. Commun. 371, 105–111 (2016).
[Crossref]

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

H. Huang, C. Zhou, T. Tian, D. Liu, and L. Song, “High-quality compressive ghost imaging,” Opt. Commun. 412, 60–65 (2018).
[Crossref]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. A (2)

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

T. B. Pittman, Y. H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52(5), R3429–R3432 (1995).
[Crossref]

Phys. Rev. Lett. (1)

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

Sci. Rep. (4)

W. Gong, C. Zhao, H. Yu, M. Chen, W. Xu, and S. Han, “Three-dimensional ghost imaging lidar via sparsity constraint,” Sci. Rep. 6(1), 26133 (2016).
[Crossref]

W. Gong and S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5(1), 9280 (2015).
[Crossref]

M. P. Edgar, G. M. Gibson, R. W. Bowman, B. Sun, N. Radwell, K. J. Mitchell, S. S. Welsh, and M. J. Padgett, “Simultaneous real-time visible and infrared video with single-pixel detectors,” Sci. Rep. 5(1), 10669 (2015).
[Crossref]

M. Aßmann and M. Bayer, “Compressive adaptive computational ghost imaging,” Sci. Rep. 3(1), 1545 (2013).
[Crossref]

Science (1)

B. Sun, M. Edgar, R. Bowman, L. Vittert, S. Welsh, A. Bowman, and M. Padgett, “3d computational imaging with single-pixel detectors,” Science 340(6134), 844–847 (2013).
[Crossref]

SIAM J. on Imaging Sci. (1)

A. Averbuch, S. Dekel, and S. Deutsch, “Adaptive compressed image sensing using dictionaries,” SIAM J. on Imaging Sci. 5(1), 57–89 (2012).
[Crossref]

SIAM J. on Optim. (1)

J. F. Cai, E. J. Candès, and Z. Shen, “A singular value thresholding algorithm for matrix completion,” SIAM J. on Optim. 20(4), 1956–1982 (2010).
[Crossref]

Other (2)

W. Gong and S. Han, “Super-resolution far-field ghost imaging via compressive sampling,” arXiv preprint arXiv:0911.4750 (2009).

A. Hore and D. Ziou, “Image quality metrics: Psnr vs. ssim,” in 2010 20th International Conference on Pattern Recognition, (IEEE, 2010), pp. 2366–2369.

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Figures (9)

Fig. 1.
Fig. 1. The flowchart of BLRGI.
Fig. 2.
Fig. 2. Simulation results of "gong" image with TVAL3, GISC , JIGI and BLRGI under different sampling numbers $M$.
Fig. 3.
Fig. 3. Numerical curves of PSNR and SSIM under different $M$ with TVAL3, GISC, JIGI and BLRGI for "gong" image.
Fig. 4.
Fig. 4. Simulation results of "cameraman" image with TVAL3, GISC, JIGI and BLRGI under $M$ sampling.
Fig. 5.
Fig. 5. Numerical curves of PSNR and SSIM under different samples with TVAL3, GISC, JIGI and BLRGI for "cameraman" image.
Fig. 6.
Fig. 6. Regularized result, denoising result and residual image under different iteration numbers with 900 samples for "gong" image.
Fig. 7.
Fig. 7. The MSEs change curve of BLRGI reconstructed images under different iteration number for "gong" image with 900 samplings.
Fig. 8.
Fig. 8. Experiment schematic diagram of BLRGI.
Fig. 9.
Fig. 9. Experimental reconstructed results with different sampling numbers (3000, 4000, 5000) and the original object.

Equations (12)

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A = [ Ψ 1 Ψ 2 Ψ M ] = [ I 1 ( 1 , 1 ) I 1 ( 1 , 2 ) I 1 ( r , c ) I 2 ( 1 , 1 ) I 2 ( 1 , 2 ) I 2 ( r , c ) I M ( 1 , 1 ) I M ( 1 , 2 ) I M ( r , c ) ]
Y = [ B 1 , B 2 , , B M ] T
Y = [ B 1 B 2 B M ] = [ I 1 ( 1 , 1 ) I 1 ( 1 , 2 ) I 1 ( r , c ) I 2 ( 1 , 1 ) I 2 ( 1 , 2 ) I 2 ( r , c ) I M ( 1 , 1 ) I M ( 1 , 2 ) I M ( r , c ) ] [ x 1 x 2 x N ]
X ( k ) = X ( k 1 ) + D A T ( Y A X ( k 1 ) ) ,             k = 1 , 2 , , K
S ^ = arg min S S ,     s . t . X S 2 2 η 2
( U , Σ , V ) = arg min U , Σ , V X U Σ V 2 2 + i σ i ( S )
{ ( U , Σ , V ) = S V D ( X ) Σ ^ = S τ ( Σ )
d ( x p , x ¯ p ) = 1 b 2 x p x ¯ p 2 2
S p ^ = arg min S p S p ,       s . t . X p S p 2 2 η 2
{ ( U p , Σ p , V p ) = S V D ( X p ) Σ p ^ = S τ p ( Σ p )
PSNR = 10 × log 10 [ m a x V a l 2 MSE ] ,
SSIM ( u , x ) = ( 2 μ u μ x + C 1 ) ( 2 σ u x + C 2 ) ( μ u 2 + μ x 2 + C 1 ) ( σ u 2 + σ x 2 + C 2 ) ,

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