Abstract

In previous single-pixel imaging systems, the light source was generally idle with respect to time. Here, we propose a novel image fusion and visible watermarking scheme based on Fourier single-pixel imaging (FSPI) with a multiplexed time-varying (TV) signal, which is generated by the watermark pattern hidden in the light source. We call this scheme TV-FSPI. With TV-FSPI, we can realize high-quality visible image watermarking, encrypted image watermarking and full-color visible image watermarking. We also discuss the extension to invisible watermarking based on TV-FSPI. Furthermore, we don’t have to recode illumination patterns, because TV-FSPI can be extended to existing mainstream illumination patterns, such as random illumination mode and Hadamard illumination mode. Thus TV-FSPI has the potential to be used in single-pixel broadcasting system and multi-spectral single-pixel imaging system.

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

Full Article  |  PDF Article
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References

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2019 (4)

X. Hu, H. Zhang, Q. Zhao, P. Yu, Y. Li, and L. Gong, “Single-pixel phase imaging by Fourier spectrum sampling,” Appl. Phys. Lett. 114(5), 051102 (2019).
[Crossref]

R. Liu, S. Zhao, P. Zhang, H. Gao, and F. Li, “Complex wavefront reconstruction with single-pixel detector,” Appl. Phys. Lett. 114(16), 161901 (2019).
[Crossref]

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13(1), 13–20 (2019).
[Crossref]

C. Zhang, W. He, B. Han, M. Liao, D. Lu, X. Peng, and C. Xu, “Compressive optical steganography via single-pixel imaging,” Opt. Express 27(9), 13469–13478 (2019).
[Crossref]

2018 (8)

2017 (4)

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Efficient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7(1), 41435 (2017).
[Crossref]

M. J. Sun, L. T. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A russian dolls ordering of the hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7(1), 3464 (2017).
[Crossref]

Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Hadamard single-pixel imaging versus Fourier single-pixel imaging,” Opt. Express 25(16), 19619–19639 (2017).
[Crossref]

D. Shi, J. Huang, Y. Wang, K. Yuan, C. Xie, D. Liu, and W. Zhu, “Simultaneous fusion, imaging and encryption of multiple objects using a single-pixel detector,” Sci. Rep. 7(1), 13172 (2017).
[Crossref]

2016 (4)

M. J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24(10), 10476–10485 (2016).
[Crossref]

W.-H. Xu, H.-F. Xu, Y. Luo, T. Li, and Y.-S. Shi, “Optical watermarking based on single-shot-ptychography encoding,” Opt. Express 24(24), 27922–27936 (2016).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref]

2015 (3)

S. M. Khamoushi, Y. Nosrati, and S. H. Tavassoli, “Sinusoidal ghost imaging,” Opt. Lett. 40(15), 3452–3455 (2015).
[Crossref]

W. Gong, “High-resolution pseudo-inverse ghost imaging,” Photonics Res. 3(5), 234 (2015).
[Crossref]

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of fourier spectrum acquisition,” Nat. Commun. 6(1), 6225 (2015).
[Crossref]

2014 (3)

2013 (4)

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(6134), 844–847 (2013).
[Crossref]

M. F. Li, Y. R. Zhang, X. F. Liu, X. R. Yao, K. H. Luo, H. Fan, and L. A. Wu, “A double-threshold technique for fast time-correspondence imaging,” Appl. Phys. Lett. 103(21), 211119 (2013).
[Crossref]

M. Sun, J. Shi, H. Li, and G. Zeng, “A simple optical encryption based on shape merging technique in periodic diffraction correlation imaging,” Opt. Express 21(16), 19395–19400 (2013).
[Crossref]

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21(20), 23068–23074 (2013).
[Crossref]

2012 (2)

2010 (1)

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 105(21), 219902 (2010).
[Crossref]

2009 (3)

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

P. Sen and S. Darabi, “Compressive dual photography,” Computer Graphics Forum 28(2), 609–618, Oxford, UK: Blackwell Publishing Ltd (2009).
[Crossref]

P. Peers, D. K. Mahajan, B. Lamond, A. Ghosh, W. Matusik, R. Ramamoorthi, and P. Debevec, “Compressive light transport sensing,” ACM Trans. Graph. 28(1), 1–18 (2009).
[Crossref]

2008 (2)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (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 Signal Process. Mag. 25(2), 83–91 (2008).
[Crossref]

2007 (1)

D. M. Thodi and J. J. Rodríguez, “Expansion embedding techniques for reversible watermarking,” IEEE Trans. on Image Process. 16(3), 721–730 (2007).
[Crossref]

2006 (1)

Y. Hu, S. Kwong, and J. Huang, “An algorithm for removable visible watermarking,” IEEE Trans. Circuits Syst. Video Technol. 16(1), 129–133 (2006).
[Crossref]

1995 (1)

H. Li, B. S. Manjunath, and S. K. Mitra, “Multi-sensor image fusion using the wavelet transform,” Graphical Models and Image Processing 57(3), 235–245 (1995).
[Crossref]

Asundi, A. K.

L. Sui, Y. Cheng, A. Tian, and A. K. Asundi, “An optical watermarking scheme with two-layer framework based on computational ghost imaging,” Opt. Lasers Eng. 107, 38–45 (2018).
[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(2), 83–91 (2008).
[Crossref]

Bloom, J. A.

I. J. Cox, M. L. Miller, J. A. Bloom, and C. Honsinger, “Digital watermarking,” San Francisco: Morgan Kaufmann 53 (2002).

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(6134), 844–847 (2013).
[Crossref]

Bowman, R.

Bromberg, Y.

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

Cao, J.

Chen, W.

W. Chen and X. Chen, “Marked ghost imaging,” Appl. Phys. Lett. 104(25), 251109 (2014).
[Crossref]

Chen, X.

W. Chen and X. Chen, “Marked ghost imaging,” Appl. Phys. Lett. 104(25), 251109 (2014).
[Crossref]

Chen, Z.

Cheng, Y.

L. Sui, Y. Cheng, A. Tian, and A. K. Asundi, “An optical watermarking scheme with two-layer framework based on computational ghost imaging,” Opt. Lasers Eng. 107, 38–45 (2018).
[Crossref]

Clemente, P.

Cox, I. J.

I. J. Cox, M. L. Miller, J. A. Bloom, and C. Honsinger, “Digital watermarking,” San Francisco: Morgan Kaufmann 53 (2002).

Czajkowski, K. M.

Dai, Q.

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Efficient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7(1), 41435 (2017).
[Crossref]

Darabi, S.

P. Sen and S. Darabi, “Compressive dual photography,” Computer Graphics Forum 28(2), 609–618, Oxford, UK: Blackwell Publishing Ltd (2009).
[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(2), 83–91 (2008).
[Crossref]

Debevec, P.

P. Peers, D. K. Mahajan, B. Lamond, A. Ghosh, W. Matusik, R. Ramamoorthi, and P. Debevec, “Compressive light transport sensing,” ACM Trans. Graph. 28(1), 1–18 (2009).
[Crossref]

Deng, C.

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Efficient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7(1), 41435 (2017).
[Crossref]

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(2), 83–91 (2008).
[Crossref]

Durán, V.

Edgar, M. P.

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13(1), 13–20 (2019).
[Crossref]

M. J. Sun, L. T. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A russian dolls ordering of the hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7(1), 3464 (2017).
[Crossref]

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref]

M. J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24(10), 10476–10485 (2016).
[Crossref]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1(5), 285 (2014).
[Crossref]

S. S. Welsh, M. P. Edgar, R. Bowman, P. Jonathan, B. Sun, and M. J. Padgett, “Fast full-color computational imaging with single-pixel detectors,” Opt. Express 21(20), 23068–23074 (2013).
[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(6134), 844–847 (2013).
[Crossref]

B. Sun, S. S. Welsh, M. P. Edgar, J. H. Shapiro, and M. J. Padgett, “Normalized ghost imaging,” Opt. Express 20(15), 16892–16901 (2012).
[Crossref]

Fan, H.

M. F. Li, Y. R. Zhang, X. F. Liu, X. R. Yao, K. H. Luo, H. Fan, and L. A. Wu, “A double-threshold technique for fast time-correspondence imaging,” Appl. Phys. Lett. 103(21), 211119 (2013).
[Crossref]

Fan, J.

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Efficient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7(1), 41435 (2017).
[Crossref]

Ferri, F.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 105(21), 219902 (2010).
[Crossref]

Gao, F.

Gao, H.

R. Liu, S. Zhao, P. Zhang, H. Gao, and F. Li, “Complex wavefront reconstruction with single-pixel detector,” Appl. Phys. Lett. 114(16), 161901 (2019).
[Crossref]

Gao, Q.-K.

Gatti, A.

F. Ferri, D. Magatti, L. A. Lugiato, and A. Gatti, “Differential ghost imaging,” Phys. Rev. Lett. 105(21), 219902 (2010).
[Crossref]

Ghosh, A.

P. Peers, D. K. Mahajan, B. Lamond, A. Ghosh, W. Matusik, R. Ramamoorthi, and P. Debevec, “Compressive light transport sensing,” ACM Trans. Graph. 28(1), 1–18 (2009).
[Crossref]

Gibson, G. M.

M. P. Edgar, G. M. Gibson, and M. J. Padgett, “Principles and prospects for single-pixel imaging,” Nat. Photonics 13(1), 13–20 (2019).
[Crossref]

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
[Crossref]

M. J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24(10), 10476–10485 (2016).
[Crossref]

N. Radwell, K. J. Mitchell, G. M. Gibson, M. P. Edgar, R. Bowman, and M. J. Padgett, “Single-pixel infrared and visible microscope,” Optica 1(5), 285 (2014).
[Crossref]

Gong, L.

X. Hu, H. Zhang, Q. Zhao, P. Yu, Y. Li, and L. Gong, “Single-pixel phase imaging by Fourier spectrum sampling,” Appl. Phys. Lett. 114(5), 051102 (2019).
[Crossref]

Gong, W.

W. Gong, “High-resolution pseudo-inverse ghost imaging,” Photonics Res. 3(5), 234 (2015).
[Crossref]

Guan, J.

Guo, S.

Han, B.

He, W.

Hendry, E.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

Hobson, P. A.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

Honsinger, C.

I. J. Cox, M. L. Miller, J. A. Bloom, and C. Honsinger, “Digital watermarking,” San Francisco: Morgan Kaufmann 53 (2002).

Hore, A.

A. Hore and D. Ziou, “Image quality metrics: PSNR vs. SSIM,” 20th International Conference on Pattern Recognition, IEEE computer society, 2366–2369 (2010).

Hornett, S. M.

R. I. Stantchev, B. Sun, S. M. Hornett, P. A. Hobson, G. M. Gibson, M. J. Padgett, and E. Hendry, “Noninvasive, near-field terahertz imaging of hidden objects using a single-pixel detector,” Sci. Adv. 2(6), e1600190 (2016).
[Crossref]

Hu, S.

J. Huang, D. Shi, K. Yuan, S. Hu, and Y. Wang, “Computational-weighted Fourier single-pixel imaging via binary illumination,” Opt. Express 26(13), 16475–16559 (2018).
[Crossref]

Hu, X.

X. Hu, H. Zhang, Q. Zhao, P. Yu, Y. Li, and L. Gong, “Single-pixel phase imaging by Fourier spectrum sampling,” Appl. Phys. Lett. 114(5), 051102 (2019).
[Crossref]

Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Efficient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7(1), 41435 (2017).
[Crossref]

Hu, Y.

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Peers, P.

P. Peers, D. K. Mahajan, B. Lamond, A. Ghosh, W. Matusik, R. Ramamoorthi, and P. Debevec, “Compressive light transport sensing,” ACM Trans. Graph. 28(1), 1–18 (2009).
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Peng, X.

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M. J. Sun, L. T. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A russian dolls ordering of the hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7(1), 3464 (2017).
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M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
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Sun, M. J.

M. J. Sun, L. T. Meng, M. P. Edgar, M. J. Padgett, and N. Radwell, “A russian dolls ordering of the hadamard basis for compressive single-pixel imaging,” Sci. Rep. 7(1), 3464 (2017).
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M. J. Sun, M. P. Edgar, G. M. Gibson, B. Sun, N. Radwell, R. Lamb, and M. J. Padgett, “Single-pixel three-dimensional imaging with time-based depth resolution,” Nat. Commun. 7(1), 12010 (2016).
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M. J. Sun, M. P. Edgar, D. B. Phillips, G. M. Gibson, and M. J. Padgett, “Improving the signal-to-noise ratio of single-pixel imaging using digital microscanning,” Opt. Express 24(10), 10476–10485 (2016).
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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(2), 83–91 (2008).
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Z. Li, J. Suo, X. Hu, C. Deng, J. Fan, and Q. Dai, “Efficient single-pixel multispectral imaging via non-mechanical spatio-spectral modulation,” Sci. Rep. 7(1), 41435 (2017).
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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 Signal Process. Mag. 25(2), 83–91 (2008).
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D. M. Thodi and J. J. Rodríguez, “Expansion embedding techniques for reversible watermarking,” IEEE Trans. on Image Process. 16(3), 721–730 (2007).
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L. Sui, Y. Cheng, A. Tian, and A. K. Asundi, “An optical watermarking scheme with two-layer framework based on computational ghost imaging,” Opt. Lasers Eng. 107, 38–45 (2018).
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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(6134), 844–847 (2013).
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Wang, Y.

J. Huang, D. Shi, K. Yuan, S. Hu, and Y. Wang, “Computational-weighted Fourier single-pixel imaging via binary illumination,” Opt. Express 26(13), 16475–16559 (2018).
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D. Shi, J. Huang, Y. Wang, K. Yuan, C. Xie, D. Liu, and W. Zhu, “Simultaneous fusion, imaging and encryption of multiple objects using a single-pixel detector,” Sci. Rep. 7(1), 13172 (2017).
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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(6134), 844–847 (2013).
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Wu, L. A.

M. F. Li, Y. R. Zhang, X. F. Liu, X. R. Yao, K. H. Luo, H. Fan, and L. A. Wu, “A double-threshold technique for fast time-correspondence imaging,” Appl. Phys. Lett. 103(21), 211119 (2013).
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Xie, C.

D. Shi, J. Huang, Y. Wang, K. Yuan, C. Xie, D. Liu, and W. Zhu, “Simultaneous fusion, imaging and encryption of multiple objects using a single-pixel detector,” Sci. Rep. 7(1), 13172 (2017).
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R. Liu, S. Zhao, P. Zhang, H. Gao, and F. Li, “Complex wavefront reconstruction with single-pixel detector,” Appl. Phys. Lett. 114(16), 161901 (2019).
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M. F. Li, Y. R. Zhang, X. F. Liu, X. R. Yao, K. H. Luo, H. Fan, and L. A. Wu, “A double-threshold technique for fast time-correspondence imaging,” Appl. Phys. Lett. 103(21), 211119 (2013).
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H. Jiang, H. Liu, X. Li, and H. Zhao, “Efficient regional single-pixel imaging for multiple objects based on projective reconstruction theorem,” Opt. Lasers Eng. 110, 33–40 (2018).
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D. Shi, J. Huang, Y. Wang, K. Yuan, C. Xie, D. Liu, and W. Zhu, “Simultaneous fusion, imaging and encryption of multiple objects using a single-pixel detector,” Sci. Rep. 7(1), 13172 (2017).
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R. Liu, S. Zhao, P. Zhang, H. Gao, and F. Li, “Complex wavefront reconstruction with single-pixel detector,” Appl. Phys. Lett. 114(16), 161901 (2019).
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M. F. Li, Y. R. Zhang, X. F. Liu, X. R. Yao, K. H. Luo, H. Fan, and L. A. Wu, “A double-threshold technique for fast time-correspondence imaging,” Appl. Phys. Lett. 103(21), 211119 (2013).
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Computer Graphics Forum (1)

P. Sen and S. Darabi, “Compressive dual photography,” Computer Graphics Forum 28(2), 609–618, Oxford, UK: Blackwell Publishing Ltd (2009).
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Graphical Models and Image Processing (1)

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IEEE Signal Process. Mag. (1)

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IEEE Trans. Circuits Syst. Video Technol. (1)

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IEEE Trans. on Image Process. (1)

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Nat. Photonics (1)

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Opt. Express (13)

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Z. Zhang, X. Wang, G. Zheng, and J. Zhong, “Hadamard single-pixel imaging versus Fourier single-pixel imaging,” Opt. Express 25(16), 19619–19639 (2017).
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C. Zhang, S. Guo, J. Cao, J. Guan, and F. Gao, “Object reconstitution using pseudo-inverse for ghost imaging,” Opt. Express 22(24), 30063 (2014).
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J. Zhong, M. Yao, S. Jiao, L. Xiang, and Z. Zhang, “Secured single-pixel broadcast imaging,” Opt. Express 26(11), 14578–14591 (2018).
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K. M. Czajkowski, A. Pastuszczak, and R. Kotyński, “Real-time single-pixel video imaging with Fourier domain regularization,” Opt. Express 26(16), 20009–20022 (2018).
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N. Yang, Q.-K. Gao, and Y.-S. Shi, “Visual-cryptographic image hiding with holographic optical elements,” Opt. Express 26(24), 31995–32006 (2018).
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Opt. Lasers Eng. (2)

L. Sui, Y. Cheng, A. Tian, and A. K. Asundi, “An optical watermarking scheme with two-layer framework based on computational ghost imaging,” Opt. Lasers Eng. 107, 38–45 (2018).
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H. Jiang, H. Liu, X. Li, and H. Zhao, “Efficient regional single-pixel imaging for multiple objects based on projective reconstruction theorem,” Opt. Lasers Eng. 110, 33–40 (2018).
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Opt. Lett. (1)

Optica (3)

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Phys. Rev. A (2)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78(6), 061802 (2008).
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Y. Bromberg, O. Katz, and Y. Silberberg, “Ghost imaging with a single detector,” Phys. Rev. A 79(5), 053840 (2009).
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Figures (17)

Fig. 1.
Fig. 1. Schematic diagram of TV-FSPI scheme: (a) the watermark pattern $R_{W}$ (100 $\times$ 100 pixels); (b) the four-step normalized coefficients $W$ of the watermark pattern; (c) the four-step illumination patterns with the TV signals.
Fig. 2.
Fig. 2. Schematic diagram of the experimental setup.
Fig. 3.
Fig. 3. Numerical simulation results of FSPI-based visible watermarking: (a) host image of "peppers"; (b) watermark image of "bnu" logo; (c) FSPI-based watermarked images under different values of $Q$ (the yellow number in the upper right corner of the images)
Fig. 4.
Fig. 4. Experimental results of TV-FSPI-based image fusion or visible watermark: (a1) the Fourier spectrum of the scene obtained by FSPI technique and (a2) the reconstructed image; (b1), (c1) and (d1) the watermark images of "smile" at different DC; (e1), (f1) and (g1) the watermark images of "BNU" at different DC; (h1)-(k1) the watermark images of complex grayscale animals; (b2)-(k2) the Fourier spectrum acquired in the experiments; (b3)-(k3) experimental results of single-pixel fusion of each watermark image.
Fig. 5.
Fig. 5. Numerical simulations of compressive image watermarking using TV-FSPI scheme: (a) partially collected Fourier spectrum of the image, where the percentage of the yellow bold in the lower right corner is the sampling rate; (b) reconstructed image of (a); (c) image watermarking results when the watermark is compressively hidden in the low frequency region of the Fourier spectrum of the host image. The percentage of the yellow bold in the lower right corner is the ratio of the TV signal length to the number of samples.
Fig. 6.
Fig. 6. Experimental results of compressive image watermarking using TV-FSPI scheme: (a1)-(d1) partial Fourier spectrum of the scene, where the percentage of the top purple bold is the sampling rate; (a2)-(d2) reconstructed image of (a1)-(d1); (e1)-(g1) the spectrum information collected at a sampling rate of 200$\%$, where the percentage of the uppermost sky blue bold indicates the ratio of the length of the TV signal to the number of samples; (e2)-(g2) image watermarking when the watermark is compressively hidden in the low frequency region of the Fourier spectrum of the host image.
Fig. 7.
Fig. 7. Numerical quantitative analysis of the SSIM of the watermarked image with the sampling rate (a), and with the rate of the length of TV signal to the samples (b).
Fig. 8.
Fig. 8. Numerical simulation analysis of the noise immunity of TV-FSPI scheme: (a) the PSNR of the watermarked image with the change of the SNR of the system; (b) the SSIM of the watermarked image versus the SNR. The yellow number in the upper right corner of the images represents the corresponding SNR.
Fig. 9.
Fig. 9. Numerical simulation analysis of the noise immunity of the de-watermarking progress: (a) the PSNR of the watermarked image versus the SNR of the system; (b) the SSIM of the watermarked image versus the SNR. The yellow number in the upper right corner of the de-watermarked images represents the corresponding SNR.
Fig. 10.
Fig. 10. Experimental results of two de-watermarking schemes: (a) original de-watermarking at different DC values; (b) de-watermarking by digital filtering.
Fig. 11.
Fig. 11. Experimental results of encrypted FSPI-based single-pixel image watermarking: (a1) original watermark pattern; (a2) encrypted watermark pattern; (b1)-(d1) image watermarking under different background DC values; (b2)-(d2) watermark extraction.
Fig. 12.
Fig. 12. Experimental results of FSPI-based full-visible watermarking: (a) theed watermark; (b1) the red (R) channel, (c1) the green (G), and (d1) the blue (B) channel offul watermark pattern; (b2)-(d2) SPI watermarking of RGB channels; (e1)-(e3) full-ed image watermarking under different values of DC background.
Fig. 13.
Fig. 13. The schematic diagram of the steganography scheme based on the TV-FSPI scheme.
Fig. 14.
Fig. 14. A numerical simulation example using the steganography scheme: (a) watermark; (b) host scene; (c) mask of the Fourier frequency domain; (d) numerically simulated Fourier spectrum; (e) the reconstructed host scene; (f) the extracted watermark.
Fig. 15.
Fig. 15. The reconstructed images of the host scene using different regions in Fig.14(d): (a) ground truth; (b) reconstructed image of the host scene using all regions, $R_{1}$ and $R_{2}$; (c) reconstructed image using only region $R_{1}$.
Fig. 16.
Fig. 16. Numerical simulation analysis of the noise immunity of the TV-FSPI-based steganography scheme: (a) the PSNR of the reconstructed host scene and the extracted watermark with the change of the SNR of the system; (b) the SSIM of the reconstructed host scene and the extracted watermark versus the SNR; (c) the reconstructed images of host scene at different SNRs; (d) the images of extracted watermark at different SNRs.
Fig. 17.
Fig. 17. Simulation results of image watermarking in other illumination modes: (a) random illumination mode; (b) sinusoidal orthogonal illumination mode; (c) differential Hadamard orthogonal illumination mode.

Equations (19)

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Pφ(x,y;fx,fy)=a+bcos(2πfxx+2πfyy+φ),
Iφ(fx,fy)=ΩR(x,y)Pφ(x,y;fx,fy)dxdy,
C(fx,fy)=[I0(fx,fy)Iπ(fx,fy)]+j[Iπ/2(fx,fy)I3π/2(fx,fy)],
R^=IFFT(C),
Wφ(fx,fy)=ΩRW(x,y)Pφ(x,y;fx,fy)dxdy,
CW(fx,fy)=[W0(fx,fy)Wπ(fx,fy)]+j[Wπ/2(fx,fy)W3π/2(fx,fy)],
R^W=IFFT(CW).
Iφ(fx,fy)=ΩR(x,y)[Wφ(fx,fy)Pφ(x,y;fx,fy)]dxdy,
C(fx,fy)=[I0(fx,fy)W0(fx,fy)Iπ(fx,fy)Wπ(fx,fy)]+j[Iπ/2(fx,fy)Wπ/2(fx,fy)I3π/2(fx,fy)W3π/2(fx,fy)]=12[(W0+Wπ+Wπ/2+W3π/2)C(fx,fy)+(I0+Iπ+Iπ/2+I3π/2)CW(fx,fy)]12[(W0Wπ)(Iπ/2+I3π/2)+(I0Iπ)(Wπ/2+W3π/2)]j12[(Wπ/2W3π/2)(I0+Iπ)+(W0+Wπ)(Iπ/2I3π/2)].
P0(x,y;fx,fy)+Pπ(x,y;fx,fy)=Pπ/2(x,y;fx,fy)+P3π/2(x,y;fx,fy)=2a.
K1=I0+Iπ=Iπ/2+I3π/2=2aΩR(x,y)dxdy,
K2=W0+Wπ=Wπ/2+W3π/2=2aΩRW(x,y)dxdy,
C(fx,fy)=12[K2C(fx,fy)+K1CW(fx,fy)].
R^=IFFT(C)=K22R^+K12RW.
Q=K1K2.
PSNR=10log10[(2n1)2MSE],
MSE=1lwi=1lj=1w[x(i,j)y(i,j)]2,
SSIM=(2uxuy+c1)(2σxy+c2)(ux2+uy2+c1)(σx2+σy2+c2),
Wφ(fx1,fy1)=I0(fx,fy)+Iπ/2(fx,fy)+Iπ(fx,fy)+I3π/2(fx,fy).

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