## Characterization of a compressively sampled photonic link |

Applied Optics, Vol. 51, Issue 27, pp. 6448-6456 (2012)

http://dx.doi.org/10.1364/AO.51.006448

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### Abstract

The emerging field of compressive sampling has potentially powerful implications for the design of analog-to-digital sampling systems. In particular, the mathematics of compressive sampling suggests that one can recover a signal at a smaller sampling interval than is dictated by the rate at which the samples are digitized. In a recent work the authors presented an all-photonic implementation of such a system and experimentally demonstrated the basic operating principles. This paper offers a more in-depth study of the system, including a more detailed description of the hardware, issues involved in real-time implementation, and how choice of signal model and model fidelity can influence the reconstruction.

© 2012 Optical Society of America

**OCIS Codes**

(060.2330) Fiber optics and optical communications : Fiber optics communications

(070.4560) Fourier optics and signal processing : Data processing by optical means

**ToC Category:**

Fourier Optics and Signal Processing

**History**

Original Manuscript: May 4, 2012

Revised Manuscript: August 3, 2012

Manuscript Accepted: August 3, 2012

Published: September 11, 2012

**Citation**

J. M. Nichols, C. V. McLaughlin, F. Bucholtz, and J. V. Michalowicz, "Characterization of a compressively sampled photonic link," Appl. Opt. **51**, 6448-6456 (2012)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-27-6448

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### References

- 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, 520–544 (2010). [CrossRef]
- J. M. Nichols and F. Bucholtz, “Beating Nyquist with light: a compressively sampled photonic link,” Opt. Express 19, 7339–7348 (2011). [CrossRef]
- Y. Chi, L. L. Scharf, A. Pezeshki, and A. R. Calderbank, “Sensitivity to basis mismatch in compressed sensing,” IEEE Trans. Signal Process. 59, 2182–2195 (2011). [CrossRef]
- S. Pfetsch, T. Ragheb, J. Laska, H. Nejati, A. Gilbert, M. Strauss, R. Baraniuk, and Y. Massoud, “On the feasibility of hardware implementation of sub-Nyquist random-sampling based analog-to-information conversion,” in Proceedings of the IEEE International Symposium on Circuits and Systems (IEEE,2008), pp. 1480–1483.
- M. Mishali and Y. C. Eldar, “Xampling: analog data compression,” in Proceedings of the 2010 Data Compression Conference (IEEE, 2010), pp. 366–375.
- 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, 375–391 (2010). [CrossRef]
- E. J. Candes and T. Tao, “Near-optimal signal recovery from random projections: universal encoding strategies?” IEEE Trans. Inf. Theory 52, 5406–5425 (2006). [CrossRef]
- D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, 1289–1306 (2006). [CrossRef]
- R. G. Baraniuk, “Compressive sensing,” IEEE Signal Process. Mag.24(4), 118–124 (2007). [CrossRef]
- J. Romberg, “Imaging via compressive sampling,” IEEE Signal Process. Mag. 25(2), 14–20 (2008). [CrossRef]
- E. J. Candes and M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Process. Mag. 25(2), 21–30 (2008). [CrossRef]
- J. D. Blanchard, C. Cartis, and J. Tanner, “Compressed sensing: how sharp is the restricted isometry property,” SIAM Rev. 53, 105–125 (2011). [CrossRef]
- D. L. Donoho and J. Tanner, “Precise undersampling theorems,” Proc. IEEE 98, 913–924 (2010). [CrossRef]
- C. E. Shannon, “Communication in the presence of noise,” Proc. IEEE 86, 447–457 (1998), reprinted from Proc. IRE 37, 10–21 (1949). [CrossRef]
- E. J. Candes and T. Tao, “Decoding by linear programming,” IEEE Trans. Inf. Theory 51, 4203–4215 (2005). [CrossRef]
- E. J. Candes, “The restricted isometry property and its implications for compressed sensing,” C. R. Math. 346, 589–592 (2008). [CrossRef]
- D. L. Donoho and J. Tanner, “Exponential bounds implying construction of compressed sensing matrices, error-correcting codes, and neighborly polytopes by random sampling,” IEEE Trans. Inf. Theory 56, 2002–2016 (2010). [CrossRef]
- D. L. Donoho, M. Elad, and V. N. Temlyakov, “Stable recovery of sparse overcomplete representations in the presence of noise,” IEEE Trans. Inf. Theory 52, 6–18 (2006). [CrossRef]
- A. M. Bruckstein, D. L. Donoho, and M. Elad, “From sparse solutions of systems of equations to sparse modeling of signals and images,” SIAM Rev. 51, 34–81 (2009). [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, 586–597 (2007). [CrossRef]
- R. Rubinstein, M. Zibulevsky, and M. Elad, “Efficient implementation of the K-SVD algorithm using batch orthogonal matching pursuit,” CS Tech. Rep. (Technion–Israel Institute of Technology, 2008).
- A. Harms, W. U. Bajwa, and R. Calderbank, “Beating Nyquist through correlations: a constrained random demodulator for sampling of sparse bandlimited signals,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (IEEE, 2011), pp. 5968–5971.

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