Beating Nyquist with light: a compressively sampled photonic link

doi:10.1364/OE.19.007339

Beating Nyquist with light: a compressively sampled photonic link

J. M. Nichols and F. Bucholtz »View Author Affiliations

Optics Express, Vol. 19, Issue 8, pp. 7339-7348 (2011)
http://dx.doi.org/10.1364/OE.19.007339

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Abstract
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Abstract

We report the successful demonstration of a compressively sampled photonic link. The system takes advantage of recent theoretical developments in compressive sampling to enable signal recovery beyond the Nyquist limit of the digitizer. This rather remarkable result requires that (1) the signal being recovered has a sparse (low-dimensional) representation and (2) the digitized samples be incoherent with this representation. We describe an all-photonic system architecture that meets these requirements and then show that 1GHz harmonic signals can be faithfully reconstructed even when digitizing at 500MS/s, well below the Nyquist rate.

OCIS Codes
(000.3870) General : Mathematics
(060.2360) Fiber optics and optical communications : Fiber optics links and subsystems

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: January 21, 2011
Revised Manuscript: March 7, 2011
Manuscript Accepted: March 7, 2011
Published: April 1, 2011

Citation
J. M. Nichols and F. Bucholtz, "Beating Nyquist with light: a compressively sampled photonic link," Opt. Express 19, 7339-7348 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7339

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References

J. Campmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]
C. H. Lee, Microwave Photonics (CRC Press, 2007).
J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, “Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals,” IEEE Trans. Inf. Theory 56(1), 520–544 (2010). [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]
W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008). [CrossRef]
S. Gazit, A. Szameit, Y. C. Eldar, and M. Segev, “Super-resolution and reconstruction of sparse sub-wavelength images,” Opt. Express 17(26), 23920–23946 (2009). [CrossRef]
O. Katz, Y. Bromberg, and Y. Silberburg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009). [CrossRef]
D. Yang, H. Li, G. Peterson, and A. Fathy, “Compressed Sensing Based UWB Receiver: Hardware Compressing and FPGA Reconstruction,” Proceedings of the 43rd Conference on Information Sciences and Systems (CISS) (2009).
M. Mishali and Y. C. Eldar, “From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals,” IEEE J. Sel. Top. Signal Process. 4(2), 375–391 (2010). [CrossRef]
M. Mishali and Y. C. Eldar, “Xampling: Analog Data Compression,” vol. http://doi.ieeecomputersociety.org/10.1109/DCC.2010.39 of Proceedings of the 2010 Data Compression Conference, pp. 366–375 (2010).
E. J. Candes and T. Tao, “Decoding by Linear Programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005). [CrossRef]
E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006). [CrossRef]
D. L. Donoho, “Compressed Sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006). [CrossRef]
E. J. Candes and M. B. Wakin, “An Introduction to Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008). [CrossRef]
J. Romberg, “Imaging Via Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008). [CrossRef]
R. G. Baraniuk, “Compressive Sensing,” IEEE Signal Process. Mag. 24, 118–124 (2007). [CrossRef]
J. M. Nichols, M. Currie, F. Buholtz, and W. A. Link, “Bayesian Estimation of Weak Material Dispersion: Theory and Experiment,” Opt. Express 18(3), 2076–2089 (2010). [CrossRef] [PubMed]
M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007). [CrossRef]

Appl. Phys. Lett.

W. L. Chan, K. Charan, D. Takhar, K. F. Kelly, R. G. Baraniuk, and D. M. Mittleman, “A single-pixel terahertz imaging system based on compressed sensing,” Appl. Phys. Lett. 93, 121105 (2008). [CrossRef]
O. Katz, Y. Bromberg, and Y. Silberburg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009). [CrossRef]

IEEE J. Sel. Top. Signal Process.

M. Mishali and Y. C. Eldar, “From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals,” IEEE J. Sel. Top. Signal Process. 4(2), 375–391 (2010). [CrossRef]
M. A. T. Figueiredo, R. D. Nowak, and S. J. Wright, “Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems,” IEEE J. Sel. Top. Signal Process. 1(4), 586–597 (2007). [CrossRef]

IEEE Signal Process. Mag.

E. J. Candes and M. B. Wakin, “An Introduction to Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008). [CrossRef]
J. Romberg, “Imaging Via Compressive Sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008). [CrossRef]
R. G. Baraniuk, “Compressive Sensing,” IEEE Signal Process. Mag. 24, 118–124 (2007). [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]

IEEE Trans. Inf. Theory

J. A. Tropp, J. N. Laska, M. F. Duarte, J. K. Romberg, and R. G. Baraniuk, “Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals,” IEEE Trans. Inf. Theory 56(1), 520–544 (2010). [CrossRef]
E. J. Candes and T. Tao, “Decoding by Linear Programming,” IEEE Trans. Inf. Theory 51(12), 4203–4215 (2005). [CrossRef]
E. J. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52(2), 489–509 (2006). [CrossRef]
D. L. Donoho, “Compressed Sensing,” IEEE Trans. Inf. Theory 52(4), 1289–1306 (2006). [CrossRef]

Nat. Photonics

J. Campmany and D. Novak, “Microwave photonics combines two worlds,” Nat. Photonics 1(6), 319–330 (2007). [CrossRef]

Opt. Express

Other

M. Mishali and Y. C. Eldar, “Xampling: Analog Data Compression,” vol. http://doi.ieeecomputersociety.org/10.1109/DCC.2010.39 of Proceedings of the 2010 Data Compression Conference, pp. 366–375 (2010).
D. Yang, H. Li, G. Peterson, and A. Fathy, “Compressed Sensing Based UWB Receiver: Hardware Compressing and FPGA Reconstruction,” Proceedings of the 43rd Conference on Information Sciences and Systems (CISS) (2009).
C. H. Lee, Microwave Photonics (CRC Press, 2007).

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