Compressive Multiplexing of Correlated Signals

IEEE Transactions on Information Theory

Volumn 61, Issue 1, 2015, Pages 479-498

  Ahmed, Ali ^a,b   Romberg, Justin ^b  

^a UNIVERSITY OF ENGINEERING AND TECHNOLOGY   (Pakistan)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

channel estimation; compressed sensing; compressive multiplexers; Compressive sampling; correlated signals; low rank matrix; matrix factorizations; modulated multiplexing and nuclear norm minimization

Indexed keywords

CHANNEL ESTIMATION; COMPRESSED SENSING; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; MIXING; MULTIPLEXING; RECOVERY;

COMPRESSIVE MULTIPLEXERS; COMPRESSIVE SAMPLING; CORRELATED SIGNALS; LOW-RANK MATRICES; MATRIX FACTORIZATIONS; NUCLEAR NORM MINIMIZATIONS;

SIGNAL SAMPLING;

EID: 84937551013     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2014.2366459     Document Type: Article

References (46)

1. M. Fazel, "Matrix rank minimization with applications," Ph.D. dissertation, Dept. Elect. Eng., Stanford Univ., Stanford, CA, USA, Mar. 2002.
2. B. Recht, M. Fazel, and P. Parrilo, "Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization," SIAM Rev., vol. 52, no. 3, pp. 471-501, 2010.
3. E. J. Candès and B. Recht, "Exact matrix completion via convex optimization," Found. Comput. Math., vol. 9, no. 6, pp. 717-772, 2009.
4. R. H. Keshavan, A. Montanari, and S. Oh, "Matrix completion from a few entries," IEEE Trans. Inf. Theory, vol. 56, no. 6, pp. 2980-2998, Jun. 2010.
5. M. Fazel, E. Candès, B. Recht, and P. Parrilo, "Compressed sensing and robust recovery of low rank matrices," in Proc. IEEE Asilomar Conf. Sig. Syst. Comp., Pacific Grove, CA, USA, Oct. 2008, pp. 1043-1047.
6. D. Gross, "Recovering low-rank matrices from few coefficients in any basis," IEEE Trans. Inf. Theory, vol. 57, no. 3, pp. 1548-1566, Mar. 2011.
7. E. J. Candès and Y. Plan, "Matrix completion with noise," Proc. IEEE, vol. 98, no. 6, pp. 925-936, Jun. 2010.
8. J. N. Laska, S. Kirilos, M. F. Duarte, T. S. Raghed, R. G. Baraniuk, and Y. Massoud, "Theory and implementation of an analog-to-information converter using random demodulation," in Proc. IEEE Int. Symp. Circuits Syst., May 2007, pp. 1959-1962.
9. J. Yoo, S. Becker, M. Loh, M. Monge, and E. Candès, "A 100MHz-2GHz 12.5x sub-Nyquist rate receiver in 90 nm CMOS," in Proc. IEEE Radio Freq. Integr. Circuits Symp. (RFIC), Jun. 2012, pp. 31-34.
10. J. Yoo et al., "A compressed sensing parameter extraction platform for radar pulse signal acquisition," IEEE J. Emerg. Sel. Topics Circuits Syst., vol. 2, no. 3, pp. 626-638, Sep. 2012.
11. M. Mishali, Y. Eldar, O. Dounaevsky, and E. Shoshan, "Xampling: Analog to digital at sub-Nyquist rates," IET Circuits Devices Syst., vol. 5, no. 1, pp. 8-20, Jan. 2011.
12. T. Murray, P. Pouliquen, A. Andreou, and K. Lauritzen, "Design of a CMOS A2I data converter: Theory, architecture and implementation," in Proc. 45th IEEE Annu. Conf. Inf. Sci. Syst. (CISS), Baltimore, MD, USA, Mar. 2011, pp. 1-6.
13. R. O. Schmidt, "Multiple emitter location and signal parameter estimation," IEEE Trans. Antennas Propag., vol. 34, no. 3, pp. 276-280, Mar. 1986.
14. T. Blanche. CRCNS.org. (2009). Multi-Neuron Recordings in Primary Visual Cortex. [Online]. Available: http://dx.doi.org/10.6080/ K0MW2F2J
15. T. Blanche, M. Spacek, J. Hetke, and N. Swindale, "Polytrodes: Highdensity silicon electrode arrays for large-scale multiunit recording," J. Neurophysiol., vol. 93, no. 5, pp. 2987-3000, 2005.
16. U. Frey et al., "Cell recordings with a CMOS high-density microelectrode array," in Proc. Conf. IEEE Eng. Med. Biol. Soc. (EMBS), Aug. 2007, pp. 167-170.
17. K. Imfeld et al., "Large-scale, high-resolution data acquisition system for extracellular recording of electrophysiological activity," IEEE Trans. Biomed. Eng., vol. 55, no. 8, pp. 2064-2073, Aug. 2008.
18. A. M. Haas, "Programmable high density CMOS microelectrode array," in Proc. IEEE Sensors, Lecce, Italy, Oct. 2008, pp. 890-893.
19. D. S. Gray, J. L. Tan, J. Voldman, and C. S. Chen, "Dielectrophoretic registration of living cells to a microelectrode array," J. Biosens. Bioelectron., vol. 19, no. 7, pp. 771-780, 2004.
20. J. P. Slavinsky, J. N. Laska, M. A. Davenport, and R. G. Baraniuk, "The compressive multiplexer for multi-channel compressive sensing," in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Prague, Czech Republic, May 2011, pp. 3980-3983.
21. J. Romberg and R. Neelamani, "Sparse channel separation using random probes," Inverse Problems, vol. 26, no. 11, p. 115015, 2010.
22. 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, vol. 56, no. 1, pp. 520-544, Jan. 2010.
23. M. Mishali and Y. C. Eldar, "Blind multiband signal reconstruction: Compressed sensing for analog signals," IEEE Trans. Signal Process., vol. 57, no. 3, pp. 993-1009, Mar. 2009.
24. E. Candès, T. Strohmer, and V. Voroninski, "Phaselift: Exact and stable signal recovery from magnitude measurements via convex programming," Commun. Pure Appl. Math., vol. 66, no. 8, pp. 1241-1274, 2013.
25. E. J. Candès and X. Li, "Solving quadratic equations via phaselift when there are about as many equations as unknowns," Found. Comput. Math., vol. 14, no. 5, pp. 1017-1026, Oct. 2014.
26. L. Demanet and P. Hand, "Stable optimizationless recovery from phaseless linear measurements," J. Fourier Anal. Appl., vol. 20, no. 1, pp. 199-221, 2014.
27. A. Ahmed, B. Recht, and J. Romberg, "Blind deconvolution using convex programming," IEEE Trans. Inf. Theory, vol. 60, no. 3, pp. 1711-1732, Mar. 2014.
28. J. Tropp, M. Wakin, M. Duarte, D. Baron, and R. Baraniuk, "Random filters for compressive sampling and reconstruction," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), Toulouse, France, May 2006, pp. 872-875.
29. J. Romberg, "Compressive sensing by random convolution," SIAM J. Imag. Sci., vol. 2, no. 4, pp. 1098-1128, 2009.
30. J. Haupt, W. U. Bajwa, G. Raz, and R. Nowak, "Toeplitz compressed sensing matrices with applications to sparse channel estimation," IEEE Trans. Inf. Theory, vol. 56, no. 11, pp. 5862-5875, Nov. 2010.
31. H. Rauhut, J. Romberg, and J. Tropp, "Restricted isometries for partial random circulant matrices," Appl. Comput. Harmonic Anal., vol. 32, no. 2, pp. 242-254, 2012.
32. S. Becker, E. J. Candès, and M. Grant, "Templates for convex cone problems with applications to sparse signal recovery," Math. Program. Comput., vol. 3, no. 3, pp. 165-218, 2010.
33. M. Schmidt. (2012). minFunc: Unconstrained Differentiable Multivariate Optimization in Matlab. [Online]. Available: http://www.di.ens.fr/~mschmidt/Software/minFunc.html
34. B. Recht and C. Ré, "Parallel stochastic gradient algorithms for largescale matrix completion," Math. Program. Comput., vol. 5, no. 2, pp. 201-226, 2013.
35. J. Lee, B. Recht, N. Srebro, R. Salakhutdinov, and J. Tropp, "Practical large-scale optimization for max-norm regularization," in Proc. Adv. Neural Inf. Process. Syst. (NIPS), 2010, pp. 1297-1305.
36. E. J. Candès and Y. Plan, "Tight oracle inequalities for low-rank matrix recovery from a minimal number of noisy random measurements," IEEE Trans. Inf. Theory, vol. 57, no. 4, pp. 2342-2359, Apr. 2011.
37. B. Recht, "A simpler approach to matrix completion," J. Mach. Learn. Res., vol. 12, no. 12, pp. 3413-3430, Dec. 2011.
38. V. Koltchinskii, K. Lounici, and A. Tsybakov, "Nuclear-norm penalization and optimal rates for noisy low-rank matrix completion," Ann. Statist., vol. 39, no. 5, pp. 2302-2329, 2011.
39. K. Mohan and M. Fazel, "New restricted isometry results for noisy lowrank recovery," in Proc. IEEE Int. Symp. Inform. Theory (ISIT), Austin, TX, USA, Jun. 2010, pp. 1573-1577.
40. H. S. Malvar and D. H. Staelin, "The LOT: Transform coding without blocking effects," IEEE Trans. Acoust., Speech, Signal Process., vol. 37, no. 4, pp. 553-559, Apr. 1989.
41. M. S. Asif and J. Romberg, "Sparse recovery of streaming signals using l1-homotopy," IEEE Trans. Signal Process., vol. 62, no. 16, pp. 4209-4223, Aug. 2014.
42. J. Tropp, "User-friendly tail bounds for sums of random matrices," Found. Comput. Math., vol. 12, no. 4, pp. 389-434, 2012.
43. R. Vershynin, Compressed Sensing: Theory and Applications, Y. C. Eldar and G. Kutyniok, Eds. Cambridge, U.K.: Cambridge Univ. Press, Nov. 2012, pp. 210-268.
44. A. V. der Vaart and J. Wellner, Weak Convergence and Empirical Processes. New York, NY, USA: Springer-Verlag, 1996.
45. F. Krahmer and R. Ward, "New and improved Johnson-Lindenstrauss embeddings via the restricted isometry property," SIAM J. Math. Anal., vol. 43, no. 3, pp. 1269-1281, 2011.
46. J. Romberg, "Multiple channel estimation using spectrally random probes," Proc. SPIE, vol. 7446, pp. 744606-1-744606-6, Aug. 2009.