Abstract

We present a prototype of gated viewing laser imaging with compressive sensing (GVLICS). By a new framework named compressive sensing, it is possible for us to perform laser imaging using a single-pixel detector where the transverse spatial resolution is obtained. Moreover, combining compressive sensing with gated viewing, the three-dimensional (3D) scene can be reconstructed by the time-slicing technique. The simulations are accomplished to evaluate the characteristics of the proposed GVLICS prototype. Qualitative analysis of Lissajous-type eye-pattern figures indicates that the range accuracy of the reconstructed 3D images is affected by the sampling rate, the image’s noise, and the complexity of the scenes.

© 2012 Optical Society of America

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References

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  1. X. Zhang, Y. Li, J. Wang, and Y. Chen, “Design of high-speed image processing system based on FPGA,” Electron. Meas. Instrum. 4, 65–69 (2009).
    [CrossRef]
  2. M. Laurenzis, F. Christnacher, and D. Monnin, “Long-range three-dimensional active imaging with superresolution depth mapping,” Opt. Lett. 32, 3146–3148 (2007).
    [CrossRef]
  3. Z.-H. Sun, J.-H. Deng, and X.-W. Yan, “Progress and current state of the development of laser imaging detection system and its key techniques,” Sci. Technol. Rev. 26(3), 74–79 (2008).
  4. O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE 3707, 432–448 (1999).
    [CrossRef]
  5. R. Marino, T. Stephens, and R. Hatch, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: System and measurements,” Proc. SPIE 5086, 1–15 (2003).
    [CrossRef]
  6. B. F. Aull, A. H. Loomis, and D. J. Young, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).
  7. R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
    [CrossRef]
  8. J. Busck and H. Heiselberg, “Gated viewing and high-accuracy three-dimensional laser radar,” Appl. Opt. 43, 4705–4710 (2004).
    [CrossRef]
  9. J. Busck, “Underwater 3-D optical imaging with a gated viewing laser radar,” Opt. Eng. 44, 116001 (2005).
    [CrossRef]
  10. P. Andersson, “Long-range three-dimensional imaging using range-gated laser radar images,” Opt. Eng. 45, 034301 (2006).
    [CrossRef]
  11. P. X. Zhang, H. Yan, and Y. Jiang, “Pulse-shape-free method for long-range three dimensional active imaging with high linear accuracy,” Opt. Lett. 33, 1219–1221 (2008).
    [CrossRef]
  12. D. Keim and P. T. C. So, “Three-dimensional (3D) high-speed imaging and fabrication system based on ultrafast optical pulse manipulation,” Proc. SPIE 7183, 71831B (2009).
  13. J. Sun, J. Gao, and J. Wei, “Experiments research on ocean surface wave detecting using streak tube imaging lidar,” Laser Physics and Laser Technologies (2010), pp. 228–231.
    [CrossRef]
  14. J. W. Ma, “A Single-Pixel imaging system for remote sensing by two-step iterative curvelet thresholding,” IEEE Geosci. Remote Sens. Lett. 6, 676–680 (2009).
    [CrossRef]
  15. D. Takhar, J. N. Laska, and M. B. Wakin, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 1–10 (2006).
    [CrossRef]
  16. M. F. Duarte, M. A. Davenport, D. Takhar, J. N. Laska, T. Sun, K. F. Kelly, and R. G. Baraniuk, “Single-pixel imaging via compressive sampling,” IEEE Signal Process. Mag. 25, 83–91 (2008).
    [CrossRef]
  17. E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
    [CrossRef]
  18. E. Candès and T. Tao, “Near optimal signal recovery from random projections: Universal encoding strategies,” IEEE Trans. Inf. Theory 52, 5406–5425 (2006).
    [CrossRef]
  19. D. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006).
    [CrossRef]
  20. C. Li, “An efficient algorithm for total variation regularization with applications to the single pixel,” Camera and Compressive Sensing, Master’s thesis, Rice University (2009).
  21. M. Laurenzis, “Evaluation metrics for range-gated active imaging systems using a Lissajous-type eye pattern,” Appl. Opt. 49, 2271–2276 (2010).
    [CrossRef]
  22. J. F. Andersen, J. Busck, and H. Heiselberg, “Pulsed Raman fiber laser and multispectral imaging in three dimensions,” Appl. Opt. 45, 6198–6204 (2006).

2010 (1)

2009 (3)

X. Zhang, Y. Li, J. Wang, and Y. Chen, “Design of high-speed image processing system based on FPGA,” Electron. Meas. Instrum. 4, 65–69 (2009).
[CrossRef]

D. Keim and P. T. C. So, “Three-dimensional (3D) high-speed imaging and fabrication system based on ultrafast optical pulse manipulation,” Proc. SPIE 7183, 71831B (2009).

J. W. Ma, “A Single-Pixel imaging system for remote sensing by two-step iterative curvelet thresholding,” IEEE Geosci. Remote Sens. Lett. 6, 676–680 (2009).
[CrossRef]

2008 (3)

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

Z.-H. Sun, J.-H. Deng, and X.-W. Yan, “Progress and current state of the development of laser imaging detection system and its key techniques,” Sci. Technol. Rev. 26(3), 74–79 (2008).

P. X. Zhang, H. Yan, and Y. Jiang, “Pulse-shape-free method for long-range three dimensional active imaging with high linear accuracy,” Opt. Lett. 33, 1219–1221 (2008).
[CrossRef]

2007 (1)

2006 (6)

J. F. Andersen, J. Busck, and H. Heiselberg, “Pulsed Raman fiber laser and multispectral imaging in three dimensions,” Appl. Opt. 45, 6198–6204 (2006).

D. Takhar, J. N. Laska, and M. B. Wakin, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 1–10 (2006).
[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

E. Candès and T. Tao, “Near optimal signal recovery from random projections: Universal encoding strategies,” IEEE Trans. Inf. Theory 52, 5406–5425 (2006).
[CrossRef]

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

P. Andersson, “Long-range three-dimensional imaging using range-gated laser radar images,” Opt. Eng. 45, 034301 (2006).
[CrossRef]

2005 (1)

J. Busck, “Underwater 3-D optical imaging with a gated viewing laser radar,” Opt. Eng. 44, 116001 (2005).
[CrossRef]

2004 (1)

2003 (2)

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[CrossRef]

R. Marino, T. Stephens, and R. Hatch, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: System and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

2002 (1)

B. F. Aull, A. H. Loomis, and D. J. Young, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

1999 (1)

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE 3707, 432–448 (1999).
[CrossRef]

Andersen, J. F.

Andersson, P.

P. Andersson, “Long-range three-dimensional imaging using range-gated laser radar images,” Opt. Eng. 45, 034301 (2006).
[CrossRef]

Aull, B. F.

B. F. Aull, A. H. Loomis, and D. J. Young, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

Baraniuk, R. G.

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

Barnard, K. J.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[CrossRef]

Bolander, G.

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE 3707, 432–448 (1999).
[CrossRef]

Busck, J.

Candès, E.

E. Candès and T. Tao, “Near optimal signal recovery from random projections: Universal encoding strategies,” IEEE Trans. Inf. Theory 52, 5406–5425 (2006).
[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Carlsson, C.

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE 3707, 432–448 (1999).
[CrossRef]

Chen, Y.

X. Zhang, Y. Li, J. Wang, and Y. Chen, “Design of high-speed image processing system based on FPGA,” Electron. Meas. Instrum. 4, 65–69 (2009).
[CrossRef]

Christnacher, F.

Davenport, M. A.

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

Deng, J.-H.

Z.-H. Sun, J.-H. Deng, and X.-W. Yan, “Progress and current state of the development of laser imaging detection system and its key techniques,” Sci. Technol. Rev. 26(3), 74–79 (2008).

Devitt, N.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[CrossRef]

Donoho, D.

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

Driggers, R. G.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[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, 83–91 (2008).
[CrossRef]

Gao, J.

J. Sun, J. Gao, and J. Wei, “Experiments research on ocean surface wave detecting using streak tube imaging lidar,” Laser Physics and Laser Technologies (2010), pp. 228–231.
[CrossRef]

Halford, C.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[CrossRef]

Hatch, R.

R. Marino, T. Stephens, and R. Hatch, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: System and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Heiselberg, H.

Jiang, Y.

Keim, D.

D. Keim and P. T. C. So, “Three-dimensional (3D) high-speed imaging and fabrication system based on ultrafast optical pulse manipulation,” Proc. SPIE 7183, 71831B (2009).

Kelly, K. F.

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

Laska, J. N.

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

D. Takhar, J. N. Laska, and M. B. Wakin, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 1–10 (2006).
[CrossRef]

Laurenzis, M.

Letalick, D.

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE 3707, 432–448 (1999).
[CrossRef]

Li, C.

C. Li, “An efficient algorithm for total variation regularization with applications to the single pixel,” Camera and Compressive Sensing, Master’s thesis, Rice University (2009).

Li, Y.

X. Zhang, Y. Li, J. Wang, and Y. Chen, “Design of high-speed image processing system based on FPGA,” Electron. Meas. Instrum. 4, 65–69 (2009).
[CrossRef]

Loomis, A. H.

B. F. Aull, A. H. Loomis, and D. J. Young, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

Ma, J. W.

J. W. Ma, “A Single-Pixel imaging system for remote sensing by two-step iterative curvelet thresholding,” IEEE Geosci. Remote Sens. Lett. 6, 676–680 (2009).
[CrossRef]

Marino, R.

R. Marino, T. Stephens, and R. Hatch, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: System and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Monnin, D.

Olsson, H.

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE 3707, 432–448 (1999).
[CrossRef]

Romberg, J.

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

So, P. T. C.

D. Keim and P. T. C. So, “Three-dimensional (3D) high-speed imaging and fabrication system based on ultrafast optical pulse manipulation,” Proc. SPIE 7183, 71831B (2009).

Steinvall, O.

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE 3707, 432–448 (1999).
[CrossRef]

Stephens, T.

R. Marino, T. Stephens, and R. Hatch, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: System and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

Sun, J.

J. Sun, J. Gao, and J. Wei, “Experiments research on ocean surface wave detecting using streak tube imaging lidar,” Laser Physics and Laser Technologies (2010), pp. 228–231.
[CrossRef]

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 Signal Process. Mag. 25, 83–91 (2008).
[CrossRef]

Sun, Z.-H.

Z.-H. Sun, J.-H. Deng, and X.-W. Yan, “Progress and current state of the development of laser imaging detection system and its key techniques,” Sci. Technol. Rev. 26(3), 74–79 (2008).

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, 83–91 (2008).
[CrossRef]

D. Takhar, J. N. Laska, and M. B. Wakin, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 1–10 (2006).
[CrossRef]

Tao, T.

E. Candès and T. Tao, “Near optimal signal recovery from random projections: Universal encoding strategies,” IEEE Trans. Inf. Theory 52, 5406–5425 (2006).
[CrossRef]

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

Vollmerhausen, R. H.

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[CrossRef]

Wakin, M. B.

D. Takhar, J. N. Laska, and M. B. Wakin, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 1–10 (2006).
[CrossRef]

Wang, J.

X. Zhang, Y. Li, J. Wang, and Y. Chen, “Design of high-speed image processing system based on FPGA,” Electron. Meas. Instrum. 4, 65–69 (2009).
[CrossRef]

Wei, J.

J. Sun, J. Gao, and J. Wei, “Experiments research on ocean surface wave detecting using streak tube imaging lidar,” Laser Physics and Laser Technologies (2010), pp. 228–231.
[CrossRef]

Yan, H.

Yan, X.-W.

Z.-H. Sun, J.-H. Deng, and X.-W. Yan, “Progress and current state of the development of laser imaging detection system and its key techniques,” Sci. Technol. Rev. 26(3), 74–79 (2008).

Young, D. J.

B. F. Aull, A. H. Loomis, and D. J. Young, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

Zhang, P. X.

Zhang, X.

X. Zhang, Y. Li, J. Wang, and Y. Chen, “Design of high-speed image processing system based on FPGA,” Electron. Meas. Instrum. 4, 65–69 (2009).
[CrossRef]

Appl. Opt. (3)

Electron. Meas. Instrum. (1)

X. Zhang, Y. Li, J. Wang, and Y. Chen, “Design of high-speed image processing system based on FPGA,” Electron. Meas. Instrum. 4, 65–69 (2009).
[CrossRef]

IEEE Geosci. Remote Sens. Lett. (1)

J. W. Ma, “A Single-Pixel imaging system for remote sensing by two-step iterative curvelet thresholding,” IEEE Geosci. Remote Sens. Lett. 6, 676–680 (2009).
[CrossRef]

IEEE Signal Process. Mag. (1)

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

IEEE Trans. Inf. Theory (3)

E. Candès, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489–509 (2006).
[CrossRef]

E. Candès and T. Tao, “Near optimal signal recovery from random projections: Universal encoding strategies,” IEEE Trans. Inf. Theory 52, 5406–5425 (2006).
[CrossRef]

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

Lincoln Lab. J. (1)

B. F. Aull, A. H. Loomis, and D. J. Young, “Geiger-mode avalanche photodiodes for three-dimensional imaging,” Lincoln Lab. J. 13, 335–350 (2002).

Opt. Eng. (3)

R. G. Driggers, R. H. Vollmerhausen, N. Devitt, C. Halford, and K. J. Barnard, “Impact of speckle on laser range-gated shortwave infrared imaging system target identification performance,” Opt. Eng. 42, 738–746 (2003).
[CrossRef]

J. Busck, “Underwater 3-D optical imaging with a gated viewing laser radar,” Opt. Eng. 44, 116001 (2005).
[CrossRef]

P. Andersson, “Long-range three-dimensional imaging using range-gated laser radar images,” Opt. Eng. 45, 034301 (2006).
[CrossRef]

Opt. Lett. (2)

Proc. SPIE (4)

O. Steinvall, H. Olsson, G. Bolander, C. Carlsson, and D. Letalick, “Gated viewing for target detection and target recognition,” Proc. SPIE 3707, 432–448 (1999).
[CrossRef]

R. Marino, T. Stephens, and R. Hatch, “A compact 3D imaging laser radar system using Geiger-mode APD arrays: System and measurements,” Proc. SPIE 5086, 1–15 (2003).
[CrossRef]

D. Keim and P. T. C. So, “Three-dimensional (3D) high-speed imaging and fabrication system based on ultrafast optical pulse manipulation,” Proc. SPIE 7183, 71831B (2009).

D. Takhar, J. N. Laska, and M. B. Wakin, “A new compressive imaging camera architecture using optical-domain compression,” Proc. SPIE 6065, 1–10 (2006).
[CrossRef]

Sci. Technol. Rev. (1)

Z.-H. Sun, J.-H. Deng, and X.-W. Yan, “Progress and current state of the development of laser imaging detection system and its key techniques,” Sci. Technol. Rev. 26(3), 74–79 (2008).

Other (2)

J. Sun, J. Gao, and J. Wei, “Experiments research on ocean surface wave detecting using streak tube imaging lidar,” Laser Physics and Laser Technologies (2010), pp. 228–231.
[CrossRef]

C. Li, “An efficient algorithm for total variation regularization with applications to the single pixel,” Camera and Compressive Sensing, Master’s thesis, Rice University (2009).

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Figures (12)

Fig. 1.
Fig. 1.

Schematic of gated viewing laser imaging with compressive sensing.

Fig. 2.
Fig. 2.

Time sequence of emitted light pulse, sensor gate, and received light pulse.

Fig. 3.
Fig. 3.

Images of a scene captured at six different settings of the gate delay time, resulting in a set of slicing images of the observed scene being imaged. The target distance is 30 m and the gate width is 100 ns.

Fig. 7.
Fig. 7.

Images of a scene captured at six different settings of the gate delay time, resulting in a set of slicing images of the observed scene being imaged. The target distance is 90 m and the delay step is 20 ns.

Fig. 5.
Fig. 5.

(i) Wherein (a)–(f) represent the CS reconstructed gated image (PSNR=22.15dB, 22.15 dB, 24.59 dB, 25.63 dB, 25.41 dB, and 20.81 dB). (ii) 3D images reconstructed by the recovered gated image sequence using TVAL3 based on a 25% sampling rate.

Fig. 6.
Fig. 6.

(i) Wherein (a)–(f) represent recovered gated images (PSNR=25.78dB, 25.78 dB, 27.17 dB, 23.61 dB, 25.42 dB, and 24.82 dB) by TVAL3. (ii) 3D images reconstructed by the recovered gated image sequence based on a 50% sampling rate.

Fig. 4.
Fig. 4.

(i) Image size of (a)–(f) is 240×240; (ii) 3D images reconstructed by the slices from the original gated image sequence simulated using the time-slicing technique by Matlab.

Fig. 9.
Fig. 9.

(i) Wherein (a)–(f) represent the CS reconstructed gated images (PSNR=14.16dB, 14.16 dB, 13.46 dB, 13.88 dB, 13.68 dB, and 14.86 dB). (ii) Reconstructed 3D images of observed scene reconstructed by the recovered gated image sequence using TVAL3 based on a 25% sampling rate.

Fig. 10.
Fig. 10.

(i) Wherein (a)–(f) represent recovered gated images (PSNR=15.77dB, 15.77 dB, 14.76 dB, 15.50 dB, 14.28 dB, and 16.88 dB) by TVAL3. (ii) 3D images of observed scene reconstructed from the recovered gated image sequence based on a 50% sampling rate.

Fig. 8.
Fig. 8.

(i) Image size of (a)–(f) is 640×480. (ii) 3D images reconstructed by the slices from the original gated image sequence simulated using the time-slicing technique by Matlab.

Fig. 11.
Fig. 11.

(a) Lissajous-type eye-pattern figures for Fig. 5(ii) and Fig. 4(ii). (b) Lissajous-type eye-pattern figures for Fig. 6(ii) and Fig. 4(ii). (c) Lissajous-type eye-pattern figures for 3D images reconstructed from the recovered gated image sequence of Fig. 3 at 80% sampling rates and Fig. 4(ii).

Fig. 12.
Fig. 12.

(a) Lissajous-type eye-pattern figures for Fig. 9(ii) and Fig. 8(ii). (b) Lissajous-type eye-pattern figures for Fig. 10(ii) and Fig. 8(ii). (c) Lissajous-type eye-pattern figures for 3D images reconstructed from the recovered gated image sequence of Fig. 7 at 80% sampling rates and Fig. 8(ii).

Equations (10)

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

minXiDiXPs.t.ΦX=Y,
Ii=P(t2r/c)G(tti)dt
Ii={pi1,pi2,pi3,pin},n{1,2,3N},i{1,2,3}.
Y=AI+ε,
Yi={yi1,yi2,yi3,yim},m{1,2,3M},i{1,2,3}.
Ii={pi1,pi2,pi3pin},n{1,2,3N},i{1,2,3G},
I={I1,I2,I3,In}.
Ir=i=1GIi(x,y).
t=2rc=Ir1iIiti=Ir1iIi(t0+iΔt)=t0+Δt*Ir1ii*Ii.
z(x,y)=c2t=c2(t0+Δt*Ir1ii*Ii).

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