Abstract

In this Letter, we present a novel structure to realize photonics-assisted compressive sensing (CS) with optical integration. In the system, a spectrally sparse signal modulates a multiwavelength continuous-wave light and then is mixed with a random sequence in optical domain. The optical signal passes through a length of dispersive fiber, the dispersion amount of which is set to ensure that the group delay between the adjacent wavelength channels is equal to the bit duration of the applied random sequence. As a result, the detected signal is a delay-and-sum version of the randomly mixed signal, which is equivalent to the function of integration required in CS. A proof-of-concept experiment with four wavelengths, corresponding to a compression factor of 4, is demonstrated. More simulation results are also given to show the potential of the technique.

© 2014 Optical Society of America

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References

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2013 (4)

2012 (4)

2011 (2)

H. Nan, Y. T. Gu, and H. M. Zhang, IEEE Photon. Technol. Lett. 23, 67 (2011).
[CrossRef]

J. M. Nichols and F. Bucholtz, Opt. Express 19, 7339 (2011).
[CrossRef]

2010 (1)

G. C. Valley and G. A. Sefler, Proc. SPIE 7797, 77970F (2010).
[CrossRef]

2008 (1)

E. J. Candes and M. B. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

2007 (1)

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
[CrossRef]

Bosworth, B. T.

Bucholtz, F.

Candes, E. J.

E. J. Candes and M. B. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

Chen, H.

Chen, M.

Chen, Y.

Chi, H.

Dai, Y.

F. Yin, Y. Gao, Y. Dai, J. Zhang, K. Xu, Z. Zhang, J. Li, and J. Lin, Opt. Lett. 38, 4386 (2013).
[CrossRef]

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Figueiredo, M. A. T.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
[CrossRef]

Foster, M. A.

Gao, Y.

Gu, Y. T.

H. Nan, Y. T. Gu, and H. M. Zhang, IEEE Photon. Technol. Lett. 23, 67 (2011).
[CrossRef]

Ji, Y.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Jin, T.

Jin, X. F.

Lei, C.

Li, J.

Li, P.

Li, Y.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Liang, Y.

Lin, J.

F. Yin, Y. Gao, Y. Dai, J. Zhang, K. Xu, Z. Zhang, J. Li, and J. Lin, Opt. Lett. 38, 4386 (2013).
[CrossRef]

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

McLaughlin, C. V.

Mei, Y.

Michalowicz, J. V.

Nan, H.

H. Nan, Y. T. Gu, and H. M. Zhang, IEEE Photon. Technol. Lett. 23, 67 (2011).
[CrossRef]

Nichols, J. M.

Nowak, R. D.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
[CrossRef]

Sefler, G. A.

G. C. Valley, G. A. Sefler, and T. J. Shaw, Opt. Lett. 37, 4675 (2012).
[CrossRef]

G. C. Valley and G. A. Sefler, Proc. SPIE 7797, 77970F (2010).
[CrossRef]

Shaw, T. J.

Valley, G. C.

G. C. Valley, G. A. Sefler, and T. J. Shaw, Opt. Lett. 37, 4675 (2012).
[CrossRef]

G. C. Valley and G. A. Sefler, Proc. SPIE 7797, 77970F (2010).
[CrossRef]

Wakin, M. B.

E. J. Candes and M. B. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

Wright, S. J.

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
[CrossRef]

Wu, J.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Xie, S.

Xu, K.

F. Yin, Y. Gao, Y. Dai, J. Zhang, K. Xu, Z. Zhang, J. Li, and J. Lin, Opt. Lett. 38, 4386 (2013).
[CrossRef]

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Yan, L.

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

Yin, F.

Zhang, H. M.

H. Nan, Y. T. Gu, and H. M. Zhang, IEEE Photon. Technol. Lett. 23, 67 (2011).
[CrossRef]

Zhang, J.

Zhang, X. M.

Zhang, Z.

Zheng, S. L.

Appl. Opt. (1)

IEEE J. Sel. Top. Signal Process. (1)

M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, IEEE J. Sel. Top. Signal Process. 1, 586 (2007).
[CrossRef]

IEEE Photon. J. (1)

L. Yan, Y. Dai, K. Xu, J. Wu, Y. Li, Y. Ji, and J. Lin, IEEE Photon. J. 4, 664 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

H. Nan, Y. T. Gu, and H. M. Zhang, IEEE Photon. Technol. Lett. 23, 67 (2011).
[CrossRef]

IEEE Signal Process. Mag. (1)

E. J. Candes and M. B. Wakin, IEEE Signal Process. Mag. 25(2), 21 (2008).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (2)

Opt. Lett. (4)

Proc. SPIE (1)

G. C. Valley and G. A. Sefler, Proc. SPIE 7797, 77970F (2010).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(a) Schematic illustration of the proposed photonic CS structure and (b) the principle of optical integration (MZM, Mach–Zehnder modulator; PRBS, pseudo-random bit sequence; DCF, dispersion-compensation fiber; PD, photodetector; DSP, digital signal processing).

Fig. 2.
Fig. 2.

Experimental results for single-tone signal recovery with compression factor of 4 (N=8192). (a) Incoming time domain signal, (b) downsampled signal after the process of optical integration, (c) recovered spectrum, and (d) time domain comparison between the original signal (solid) and the reconstructed signal (dashed).

Fig. 3.
Fig. 3.

Signal reconstruction with different compression factors (N=8192, SNR=25dB). (a) and (c) recovered spectra with compression factors of 8 and 16, respectively. (b) and (d) Time domain comparison between the original signal (solid) and the reconstructed signal (dotted) with compression factors of 8 and 16, respectively.

Fig. 4.
Fig. 4.

Averaged recovery error as a function of (a) SNR (compression factor=4) and (b) compression factor (SNR=25dB).

Equations (2)

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k=0S1[1+αx(tkT)]r(tkT),
m=0Mk=0S1[1+αx(mSTkT)]r(mSTkT).

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