Orthogonal AMP

IEEE Access

Volumn 5, Issue , 2017, Pages 2020-2033

  Ma, Junjie ^a   Ping, Li ^b  

^a Och Spine at New York Presbyterian Hospitals   (United States)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

approximate message passing (AMP); Compressed sensing; IID Gaussian; partial orthogonal matrix; replica method; state evolution; unitarily invariant

Indexed keywords

COMPRESSED SENSING; GAUSSIAN DISTRIBUTION; ITERATIVE METHODS; LINEAR SYSTEMS; MESSAGE PASSING; SIGNAL RECONSTRUCTION;

APPROXIMATE MESSAGE PASSING (AMP); GAUSSIANS; ORTHOGONAL MATRIX; REPLICA METHOD; STATE EVOLUTIONS; UNITARILY-INVARIANT;

MATRIX ALGEBRA;

EID: 85015882156     PISSN: None     EISSN: 21693536     Source Type: Journal    
DOI: 10.1109/ACCESS.2017.2653119     Document Type: Article

References (45)

1. S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Englewood Cliffs, NJ, USA: Prentice-Hall, 1993.
2. D. L. Donoho, A. Maleki, and A. Montanari, "Message-passing algorithms for compressed sensing," Proc. Nat. Acad. Sci. USA, vol. 106, no. 45, pp. 18914-18919, Nov. 2009.
3. M. Bayati and A. Montanari, "The dynamics of message passing on dense graphs, with applications to compressed sensing," IEEE Trans. Inf. Theory, vol. 57, no. 2, pp. 764-785, Feb. 2011.
4. M. Bayati, M. Lelarge, and A. Montanari, "Universality in polytope phase transitions and message passing algorithms," Ann. Appl. Probab., vol. 25, no. 2, pp. 753-822, 2015.
5. T. J. Richardson and R. L. Urbanke, "The capacity of low-density paritycheck codes under message-passing decoding," IEEE Trans. Inf. Theory, vol. 47, no. 2, pp. 599-618, Feb. 2001.
6. S. ten Brink, "Convergence behavior of iteratively decoded parallel concatenated codes," IEEE Trans. Commun., vol. 49, no. 10, pp. 1727-1737, Oct. 2001.
7. D. L. Donoho, A. Maleki, and A. Montanari, "Message passing algorithms for compressed sensing: I. Motivation and construction," in Proc. IEEE Inf. Theory Workshop (ITW Cairo), Jan. 2010, pp. 1-5.
8. D. Guo and S. Verdú, "Randomly spread CDMA: Asymptotics via statistical physics," IEEE Trans. Inf. Theory, vol. 51, no. 6, pp. 1983-2010, Jun. 2005.
9. S. Rangan, V. Goyal, and A. K. Fletcher, "Asymptotic analysis of MAP estimation via the replica method and compressed sensing," in Proc. Adv. Neural Inf. Process. Syst., 2009, pp. 1545-1553.
10. A. M. Tulino, G. Caire, S. Verdú, and S. Shamai (Shitz), "Support recovery with sparsely sampled free random matrices," IEEE Trans. Inf. Theory, vol. 59, no. 7, pp. 4243-4271, Jul. 2013.
11. C.-K. Wen and K.-K. Wong. (2014). "Analysis of compressed sensing with spatially-coupled orthogonal matrices." [Online]. Available: https://arxiv.org/abs/1402.3215
12. S.Wu, L. Kuang, Z. Ni, J. Lu, D. D. Huang, and Q. Guo, "Low-complexity iterative detection for large-scale multiuser MIMO-OFDM systems using approximate message passing," IEEE J. Sel. Topics Signal Process., vol. 8, no. 5, pp. 902-915, Oct. 2014.
13. C. Jeon, R. Ghods, A. Maleki, and C. Studer, "Optimality of large MIMO detection via approximate message passing," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2015, pp. 1227-1231.
14. C.-K. Wen, S. Jin, K.-K. Wong, C.-J. Wang, and G. Wu, "Joint channeland- data estimation for large-MIMO systems with low-precision ADCs," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2015, pp. 1237-1241.
15. C. Rush, A. Greig, and R. Venkataramanan, "Capacity-achieving sparse regression codes via approximate message passing decoding," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2015, pp. 2016-2020.
16. J. Barbier and F. Krzakala. (2015). "Approximate message-passing decoder and capacity-achieving sparse superposition codes." [Online]. Available: https://arxiv.org/abs/1503.08040
17. J. Vila, P. Schniter, S. Rangan, F. Krzakala, and L. Zdeborová, "Adaptive damping and mean removal for the generalized approximate message passing algorithm," in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), Apr. 2015, pp. 2021-2025.
18. A. Manoel, F. Krzakala, E.W. Tramel, and L. Zdeborová. (2014). "Sparse estimation with the swept approximated message-passing algorithm." [Online]. Available: https://arxiv.org/abs/1406.4311
19. S. Rangan, A. K. Fletcher, P. Schniter, and U. Kamilov. (2015). "Inference for generalized linear models via alternating directions and Bethe free energy minimization." [Online]. Available: https://arxiv. org/abs/1501.01797
20. Y. Kabashima and M. Vehkaperä, "Signal recovery using expectation consistent approximation for linear observations," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun./Jul. 2014, pp. 226-230.
21. B. Cakmak, O. Winther, and B. H. Fleury, "S-AMP: Approximate message passing for general matrix ensembles," in Proc. IEEE Inf. Theory Workshop (ITW), Nov. 2014, pp. 192-196.
22. Q. Guo and J. Xi. (2015). "Approximate message passing with unitary transformation." [Online]. Available: https://arxiv.org/abs/1504.04799
23. B. Çakmak, M. Opper, B. H. Fleury, and O. Winther. (2016). "Selfaveraging expectation propagation." [Online]. Available: https://arxiv. org/abs/1608.06602
24. M. Opper, B. Çakmak, and O.Winther, "Atheory of solving TAP equations for ising models with general invariant random matrices," J. Phys. A, Math. Theor., vol. 49, no. 11, p. 114002, 2016.
25. E. Bostan, M. Unser, and J. P. Ward, "Divergence-free wavelet frames," IEEE Signal Process. Lett., vol. 22, no. 8, pp. 1142-1146, Aug. 2015.
26. X. Yuan, J. Ma, and L. Ping, "Energy-spreading-transform based MIMO systems: Iterative equalization, evolution analysis, and precoder optimization," IEEE Trans. Wireless Commun., vol. 13, no. 9, pp. 5237-5250, Sep. 2014.
27. J. Ma, X. Yuan, and L. Ping, "Turbo compressed sensing with partial DFT sensing matrix," IEEE Signal Process. Lett., vol. 22, no. 2, pp. 158-161, Feb. 2015.
28. J. Ma and L. Ping. (2016). "Orthogonal AMP." [Online]. Available: https://arxiv.org/abs/1602.06509
29. S. Rangan, P. Schniter, and A. Fletcher. (2016). "Vector approximate message passing." [Online]. Available: https://arxiv.org/abs/1610.03082
30. J. Ma and L. Ping, "Orthogonal AMP for compressed sensing with unitarily-invariant matrices," in Proc. IEEE Inf. Theory Workshop (ITW), Sep. 2016, pp. 280-284.
31. D. L. Donoho, "De-noising by soft-thresholding," IEEE Trans. Inf. Theory, vol. 41, no. 3, pp. 613-627, May 1995.
32. A. M. Tulino and S. Verdú, Random Matrix Theory and Wireless Commu- nications, vol. 1. Norwell, MA, USA: Now Publishers Inc, 2004.
33. C. Stein, "A bound for the error in the normal approximation to the distribution of a sum of dependent random variables," in Proc. 6th Berkeley Symp. Math. Statist. Probab., 1972, pp. 583-602.
34. J. P. Vila and P. Schniter, "Expectation-maximization Gaussian-mixture approximate message passing," IEEE Trans. Signal Process., vol. 61, no. 19, pp. 4658-4672, Oct. 2013.
35. M. Vehkaperä, Y. Kabashima, and S. Chatterjee, "Analysis of regularized LS reconstruction and random matrix ensembles in compressed sensing," in Proc. IEEE Int. Symp. Inf. Theory (ISIT), Jun. 2014, pp. 3185-3189.
36. D. Guo, Y. Wu, S. Shamai (Shitz), and S. Verdú, "Estimation in Gaussian noise: Properties of the minimum mean-square error," IEEE Trans. Inf. Theory, vol. 57, no. 4, pp. 2371-2385, Apr. 2011.
37. C. Guo and M. E. Davies, "Near optimal compressed sensing without priors: Parametric SURE approximate message passing," IEEE Trans. Signal Process., vol. 63, no. 8, pp. 2130-2141, Apr. 2015.
38. Z. Xue, J. Ma, and X. Yuan. (2016). "D-OAMP: A denoising-based signal recovery algorithm for compressed sensing." [Online]. Available: https://arxiv.org/abs/1610.05991
39. J. Ma, X. Yuan, and L. Ping, "On the performance of turbo signal recovery with partial DFT sensing matrices," IEEE Trans. Signal Process., vol. 22, no. 10, pp. 1580-1584, Oct. 2015.
40. H. A. van der Vorst, Iterative Krylov Methods for Large Linear Systems, vol. 13. Cambridge, U.K.: Cambridge Univ. Press, 2003.
41. M. Lustig, D. L. Donoho, J. M. Santos, and J. M. Pauly, "Compressed sensing MRI," IEEE Signal Process. Mag., vol. 25, no. 2, pp. 72-82, Mar. 2008.
42. D. L. Donoho, I. Johnstone, and A. Montanari, "Accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising," IEEE Trans. Inf. Theory., vol. 59, no. 6, pp. 3396-3433, Jun. 2013.
43. F. Hiai and D. Petz, "Asymptotic freeness almost everywhere for random matrices," Acta Sci. Math. (Szeged), vols. 3-4, pp. 801-826, 2000.
44. S. Rangan. (2010). "Generalized approximate message passing for estimation with random linear mixing." [Online]. Available: http://arxiv.org/abs/1010.5141.
45. K. Takeuchi. (2017). "Rigorous dynamics of expectation-propagationbased signal recovery from unitarily invariant measurements." [Online]. Available: arXiv:1701.05284