Abstract

The compressed ultrafast photography (CUP) technique, providing the fastest receive-only camera so far, has shown to be a well-established tool to capture the ultrafast dynamical scene. This technique is based on random codes to encode and decode the ultrafast dynamical scene by a compressed sensing algorithm. The choice of random codes significantly affects the image reconstruction quality. Therefore, it is important to optimize the encoding codes. Here, we develop a new scheme to obtain the optimized codes by combining a genetic algorithm (GA) into the CUP technique. First, we measure the dynamical scene by the CUP system with random codes and obtain the dynamical scene image at each moment. Second, we use these reconstructed dynamical scene images as the optimization target and optimize the encoding codes based on the GA. Finally, we utilize the optimized codes to recapture the dynamical scene and improve the image reconstruction quality. We validate our optimization scheme by the numerical simulation of a moving double-semielliptical spot and the experimental demonstration of a time- and space-evolving pulsed laser spot.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. http://www.hamamatsu.com/us/en/5011.html .
  2. E. J. Candes, J. K. Romberg, and T. Tao, “Stable signal recovery from incomplete and inaccurate measurements,” Commun. Pure Appl. Math. 59, 1207–1223 (2006).
    [Crossref]
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  4. L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
    [Crossref]
  5. K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
    [Crossref]
  6. K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
    [Crossref]
  7. J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot realtime video recording of a photonic Mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
    [Crossref]
  8. J. Liang, L. Gao, P. Hai, C. Li, and L. V. Wang, “Encrypted threedimensional dynamic imaging using snapshot time-of-flight compressed ultrafast photography,” Sci. Rep. 5, 15504 (2015).
    [Crossref]
  9. M. Elad, “Optimal projections for compressed sensing,” IEEE Trans. Signal Process. 55, 5695–5702 (2007).
    [Crossref]
  10. J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
    [Crossref]
  11. V. Abolghasemi, S. Ferdowsi, B. Makkiabadi, and S. Sanei, “On optimization of the measurement matrix for compressive sensing,” in European Signal Processing Conference (2010), Vol. 51, p. 427.
  12. V. Abolghasemi, S. Ferdowsi, and S. Sanei, “A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing,” Signal Process. 92, 999–1009 (2012).
    [Crossref]
  13. J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).
  14. Y. Yue, J. Yu, Y. Wei, X. Liu, and T. Cui, “A improved CoSaMP algorithm based on correlation coefficient for compressed sensing image reconstruction,” J. Comput. Inf. Syst. 9, 7325 (2013).
  15. D. Kittle, K. Choi, A. Wagadarikar, and D. J. Brady, “Multiframe image estimation for coded aperture snapshot spectral imagers,” Appl. Opt. 49, 6824–6833 (2010).
    [Crossref]
  16. L. Zhu, Y. Chen, J. Liang, Q. Xu, L. Gao, C. Ma, and L. V. Wang, “Space- and intensity-constrained reconstruction for compressed ultrafast photography,” Optica 37, 694–697 (2016).
    [Crossref]

2017 (1)

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot realtime video recording of a photonic Mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

2016 (1)

L. Zhu, Y. Chen, J. Liang, Q. Xu, L. Gao, C. Ma, and L. V. Wang, “Space- and intensity-constrained reconstruction for compressed ultrafast photography,” Optica 37, 694–697 (2016).
[Crossref]

2015 (1)

J. Liang, L. Gao, P. Hai, C. Li, and L. V. Wang, “Encrypted threedimensional dynamic imaging using snapshot time-of-flight compressed ultrafast photography,” Sci. Rep. 5, 15504 (2015).
[Crossref]

2014 (2)

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

2013 (1)

Y. Yue, J. Yu, Y. Wei, X. Liu, and T. Cui, “A improved CoSaMP algorithm based on correlation coefficient for compressed sensing image reconstruction,” J. Comput. Inf. Syst. 9, 7325 (2013).

2012 (1)

V. Abolghasemi, S. Ferdowsi, and S. Sanei, “A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing,” Signal Process. 92, 999–1009 (2012).
[Crossref]

2010 (1)

2009 (2)

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[Crossref]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[Crossref]

2007 (2)

M. Elad, “Optimal projections for compressed sensing,” IEEE Trans. Signal Process. 55, 5695–5702 (2007).
[Crossref]

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).

2006 (1)

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

Abolghasemi, V.

V. Abolghasemi, S. Ferdowsi, and S. Sanei, “A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing,” Signal Process. 92, 999–1009 (2012).
[Crossref]

V. Abolghasemi, S. Ferdowsi, B. Makkiabadi, and S. Sanei, “On optimization of the measurement matrix for compressive sensing,” in European Signal Processing Conference (2010), Vol. 51, p. 427.

Bioucas-Dias, J. M.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).

Brady, D. J.

Candes, E. J.

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

Chen, Y.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot realtime video recording of a photonic Mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

L. Zhu, Y. Chen, J. Liang, Q. Xu, L. Gao, C. Ma, and L. V. Wang, “Space- and intensity-constrained reconstruction for compressed ultrafast photography,” Optica 37, 694–697 (2016).
[Crossref]

Choi, K.

Cui, T.

Y. Yue, J. Yu, Y. Wei, X. Liu, and T. Cui, “A improved CoSaMP algorithm based on correlation coefficient for compressed sensing image reconstruction,” J. Comput. Inf. Syst. 9, 7325 (2013).

Duarte-Carvajalino, J. M.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[Crossref]

Elad, M.

M. Elad, “Optimal projections for compressed sensing,” IEEE Trans. Signal Process. 55, 5695–5702 (2007).
[Crossref]

Eldar, Y. C.

Y. C. Eldar and G. Kutyniok, “Compressed sensing: theory and applications,” in Compressed Sensing: Theory and Applications (Cambridge University, 2012).

Ferdowsi, S.

V. Abolghasemi, S. Ferdowsi, and S. Sanei, “A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing,” Signal Process. 92, 999–1009 (2012).
[Crossref]

V. Abolghasemi, S. Ferdowsi, B. Makkiabadi, and S. Sanei, “On optimization of the measurement matrix for compressive sensing,” in European Signal Processing Conference (2010), Vol. 51, p. 427.

Figueiredo, M. A. T.

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).

Gao, L.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot realtime video recording of a photonic Mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

L. Zhu, Y. Chen, J. Liang, Q. Xu, L. Gao, C. Ma, and L. V. Wang, “Space- and intensity-constrained reconstruction for compressed ultrafast photography,” Optica 37, 694–697 (2016).
[Crossref]

J. Liang, L. Gao, P. Hai, C. Li, and L. V. Wang, “Encrypted threedimensional dynamic imaging using snapshot time-of-flight compressed ultrafast photography,” Sci. Rep. 5, 15504 (2015).
[Crossref]

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

Goda, K.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[Crossref]

Hai, P.

J. Liang, L. Gao, P. Hai, C. Li, and L. V. Wang, “Encrypted threedimensional dynamic imaging using snapshot time-of-flight compressed ultrafast photography,” Sci. Rep. 5, 15504 (2015).
[Crossref]

Hirosawa, K.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Horisaki, R.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Jalali, B.

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[Crossref]

Kannari, F.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Kittle, D.

Kutyniok, G.

Y. C. Eldar and G. Kutyniok, “Compressed sensing: theory and applications,” in Compressed Sensing: Theory and Applications (Cambridge University, 2012).

Li, C.

J. Liang, L. Gao, P. Hai, C. Li, and L. V. Wang, “Encrypted threedimensional dynamic imaging using snapshot time-of-flight compressed ultrafast photography,” Sci. Rep. 5, 15504 (2015).
[Crossref]

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

Liang, J.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot realtime video recording of a photonic Mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

L. Zhu, Y. Chen, J. Liang, Q. Xu, L. Gao, C. Ma, and L. V. Wang, “Space- and intensity-constrained reconstruction for compressed ultrafast photography,” Optica 37, 694–697 (2016).
[Crossref]

J. Liang, L. Gao, P. Hai, C. Li, and L. V. Wang, “Encrypted threedimensional dynamic imaging using snapshot time-of-flight compressed ultrafast photography,” Sci. Rep. 5, 15504 (2015).
[Crossref]

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

Liao, H.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Liu, X.

Y. Yue, J. Yu, Y. Wei, X. Liu, and T. Cui, “A improved CoSaMP algorithm based on correlation coefficient for compressed sensing image reconstruction,” J. Comput. Inf. Syst. 9, 7325 (2013).

Lwasaki, A.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Ma, C.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot realtime video recording of a photonic Mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

L. Zhu, Y. Chen, J. Liang, Q. Xu, L. Gao, C. Ma, and L. V. Wang, “Space- and intensity-constrained reconstruction for compressed ultrafast photography,” Optica 37, 694–697 (2016).
[Crossref]

Makkiabadi, B.

V. Abolghasemi, S. Ferdowsi, B. Makkiabadi, and S. Sanei, “On optimization of the measurement matrix for compressive sensing,” in European Signal Processing Conference (2010), Vol. 51, p. 427.

Nakagawa, K.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Nakamura, A.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Oishi, Y.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Romberg, J. K.

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

Sakuma, I.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Sanei, S.

V. Abolghasemi, S. Ferdowsi, and S. Sanei, “A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing,” Signal Process. 92, 999–1009 (2012).
[Crossref]

V. Abolghasemi, S. Ferdowsi, B. Makkiabadi, and S. Sanei, “On optimization of the measurement matrix for compressive sensing,” in European Signal Processing Conference (2010), Vol. 51, p. 427.

Sapiro, G.

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[Crossref]

Tao, T.

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

Tsia, K. K.

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[Crossref]

Tsukamoto, A.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Ushida, T.

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Wagadarikar, A.

Wang, L. V.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot realtime video recording of a photonic Mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

L. Zhu, Y. Chen, J. Liang, Q. Xu, L. Gao, C. Ma, and L. V. Wang, “Space- and intensity-constrained reconstruction for compressed ultrafast photography,” Optica 37, 694–697 (2016).
[Crossref]

J. Liang, L. Gao, P. Hai, C. Li, and L. V. Wang, “Encrypted threedimensional dynamic imaging using snapshot time-of-flight compressed ultrafast photography,” Sci. Rep. 5, 15504 (2015).
[Crossref]

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

Wei, Y.

Y. Yue, J. Yu, Y. Wei, X. Liu, and T. Cui, “A improved CoSaMP algorithm based on correlation coefficient for compressed sensing image reconstruction,” J. Comput. Inf. Syst. 9, 7325 (2013).

Xu, Q.

L. Zhu, Y. Chen, J. Liang, Q. Xu, L. Gao, C. Ma, and L. V. Wang, “Space- and intensity-constrained reconstruction for compressed ultrafast photography,” Optica 37, 694–697 (2016).
[Crossref]

Yu, J.

Y. Yue, J. Yu, Y. Wei, X. Liu, and T. Cui, “A improved CoSaMP algorithm based on correlation coefficient for compressed sensing image reconstruction,” J. Comput. Inf. Syst. 9, 7325 (2013).

Yue, Y.

Y. Yue, J. Yu, Y. Wei, X. Liu, and T. Cui, “A improved CoSaMP algorithm based on correlation coefficient for compressed sensing image reconstruction,” J. Comput. Inf. Syst. 9, 7325 (2013).

Zhu, L.

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot realtime video recording of a photonic Mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

L. Zhu, Y. Chen, J. Liang, Q. Xu, L. Gao, C. Ma, and L. V. Wang, “Space- and intensity-constrained reconstruction for compressed ultrafast photography,” Optica 37, 694–697 (2016).
[Crossref]

Appl. Opt. (1)

Commun. Pure Appl. Math. (1)

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

IEEE Trans. Image Process. (2)

J. M. Bioucas-Dias and M. A. T. Figueiredo, “A new TwIST: two-step iterative shrinkage/thresholding algorithms for image restoration,” IEEE Trans. Image Process. 16, 2992–3004 (2007).

J. M. Duarte-Carvajalino and G. Sapiro, “Learning to sense sparse signals: simultaneous sensing matrix and sparsifying dictionary optimization,” IEEE Trans. Image Process. 18, 1395–1408 (2009).
[Crossref]

IEEE Trans. Signal Process. (1)

M. Elad, “Optimal projections for compressed sensing,” IEEE Trans. Signal Process. 55, 5695–5702 (2007).
[Crossref]

J. Comput. Inf. Syst. (1)

Y. Yue, J. Yu, Y. Wei, X. Liu, and T. Cui, “A improved CoSaMP algorithm based on correlation coefficient for compressed sensing image reconstruction,” J. Comput. Inf. Syst. 9, 7325 (2013).

Nat. Photonics (1)

K. Nakagawa, A. Lwasaki, Y. Oishi, R. Horisaki, A. Tsukamoto, A. Nakamura, K. Hirosawa, H. Liao, T. Ushida, K. Goda, F. Kannari, and I. Sakuma, “Sequentially timed all-optical mapping photography (STAMP),” Nat. Photonics 8, 695–700 (2014).
[Crossref]

Nature (2)

K. Goda, K. K. Tsia, and B. Jalali, “Serial time-encoded amplified imaging for real-time observation of fast dynamic phenomena,” Nature 458, 1145–1149 (2009).
[Crossref]

L. Gao, J. Liang, C. Li, and L. V. Wang, “Single-shot compressed ultrafast photography at one hundred billion frames per second,” Nature 516, 74–77 (2014).
[Crossref]

Optica (1)

L. Zhu, Y. Chen, J. Liang, Q. Xu, L. Gao, C. Ma, and L. V. Wang, “Space- and intensity-constrained reconstruction for compressed ultrafast photography,” Optica 37, 694–697 (2016).
[Crossref]

Sci. Adv. (1)

J. Liang, C. Ma, L. Zhu, Y. Chen, L. Gao, and L. V. Wang, “Single-shot realtime video recording of a photonic Mach cone induced by a scattered light pulse,” Sci. Adv. 3, e1601814 (2017).
[Crossref]

Sci. Rep. (1)

J. Liang, L. Gao, P. Hai, C. Li, and L. V. Wang, “Encrypted threedimensional dynamic imaging using snapshot time-of-flight compressed ultrafast photography,” Sci. Rep. 5, 15504 (2015).
[Crossref]

Signal Process. (1)

V. Abolghasemi, S. Ferdowsi, and S. Sanei, “A gradient-based alternating minimization approach for optimization of the measurement matrix in compressive sensing,” Signal Process. 92, 999–1009 (2012).
[Crossref]

Other (3)

V. Abolghasemi, S. Ferdowsi, B. Makkiabadi, and S. Sanei, “On optimization of the measurement matrix for compressive sensing,” in European Signal Processing Conference (2010), Vol. 51, p. 427.

http://www.hamamatsu.com/us/en/5011.html .

Y. C. Eldar and G. Kutyniok, “Compressed sensing: theory and applications,” in Compressed Sensing: Theory and Applications (Cambridge University, 2012).

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Figures (5)

Fig. 1.
Fig. 1. Flow chart for optimizing the encoding codes in the CUP system based on a GA.
Fig. 2.
Fig. 2. (a) Flow chart for the GA that is used to optimize the encoding codes. (b) The image stitching method based on the reconstructed images with the random (left image) and optimizing codes (right image). Here, the two stitching images are compared to calculate the CC value. (c) The configured parameters in the GA.
Fig. 3.
Fig. 3. Numerical simulation results: (a) the original nine images for the moving double-semielliptical spot; the reconstructed nine images by the (b) random and (c) optimized codes; (d) the CC value evolution in the optimization process; and (e) the CC values with the random (red circles) and optimized codes (black line).
Fig. 4.
Fig. 4. Experimental arrangement for the temporal and spatial measurement of the 3 ns pulsed laser spot by using the CUP system.
Fig. 5.
Fig. 5. Experimental measurement results: (a) the measured laser spot image by an external CCD; (b) the CC value evolution in the optimization process; the reconstructed images with the (c) optimized and (d) random codes; and (e) the CC values with the random codes (red circles) and optimized codes (black line).

Equations (1)

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CC=n=1N(ana¯n)(ene¯n)n=1N(ana¯n)2n=1N(ene¯n)2×100%,

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