Bayesian signal reconstruction for 1-bit compressed sensing

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2014, Issue 11, 2014, Pages

  Xu, Yingying ^a   Kabashima, Yoshiyuki ^a   Zdeborová, Lenka ^b  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b CNRS   (France)

Author keywords

Analysis of algorithms; Cavity and replica method; Message passing algorithms; Statistical inference

Indexed keywords

EID: 84914141245     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2014/11/P11015     Document Type: Article

References (39)

1. https://sites.google.com/site/igorcarron2/compressedsensinghardware
2. Elad M 2010 Sparse and Redundant Representations: from Theory to Applications in Signal and Image Processing (New York: Springer)
3. Starck J-L, Murtagh F and Fadili J M 2010 Sparse Image and Signal Processing: Wavelets, Curvelets, Morphological Diversity (New York: Cambridge University Press)
4. Candès E J and Wakin M B 2008 IEEE Signal Proc. Mag. 25 21
5. Donoho D L 2006 IEEE Trans. Inform. Theory 52 1289
6. Candés E J, Romberg J and Tao T 2006 IEEE Trans. Inform. Theory 52 489
7. Kabashima Y, Wadayama T and Tanaka T 2009 J. Stat. Mech. L09003
8. Kabashima Y, Wadayama T and Tanaka T 2012 J. Stat. Mech. E07001
9. Ganguli S and Sompolinsky H 2010 Phys. Rev. Lett. 104 188701
10. Krzakala F, Mézard M, Sausset F, Sun Y F and Zdeborová L 2012 Phys. Rev. X 2 021005
11. Boufounos P T and Baraniuk R G 2008 Proc. Conf. on Information Sciences and Systems (Princeton, NJ, 19-21 March 2008) (New York: IEEE) p 16
12. Lee D, Sasaki T, Yamada T, Akabane K, Yamaguchi Y and Uehara K 2012 Proc. IEEE 75th Vehicular Technology Conf. (VTC Spring) (Yokohama, 6-9 May 2012) (New York: IEEE) no 8A-4, pp 1-5
13. Xu Y and Kabashima Y 2013 J. Stat. Mech. P02041
14. Rangan S 2010 Generalized approximate message passing for estimation with random linear mixing Proc. IEEE Int. Symp. on Information Theory (St. Petersburg, Russia, 31 July-5 August 2011) pp 2168-72
15. Kabashima Y and Uda S 2004 A BP-based algorithm for performing Bayesian inference in large perceptron-type networks Algorithmic Learning Theory ed S Ben-David et al (Lecture Notes in AI vol 3244) (Berlin: Springer) pp 479-93
16. Dotsenko V S 2001 Introduction to the Replica Theory of Disordered Statistical Systems (Cambridge: Cambridge University Press)
17. Nishimori H 2001 Statistical Physics of Spin Glasses and Information Processing (Oxford: Oxford University Press)
18. Nishimori H and Sherrington D 2001 Absence of replica symmetry breaking in a region of the phase diagram of the Ising spin glass Disordered, Complex Systems (AIP Conf. Proc. vol 553) ed P Sollich et al (Melville, NY: American Institute of Physics) p 67
19. Montanari A 2008 Estimating random variables from random sparse observations Eur. Trans. Telecommun. 19 385-403
20. Donoho D L, Maleki A and Montanari A 2009 Message-passing algorithms for compressed sensing Proc. Natl Acad. Sci. 106 18914
21. Thouless D J, Anderson P W and Palmer R G 1977 Phil. Mag. 35 593
22. Shiino M and Fukai T 1992 J. Phys. A: Math. Gen. 25 L375
23. Seung H S, Sompolinsky H and Tishby N 1992 Phys. Rev. A 45 6056
24. Watkin T L H, Rau A and Biehl M 1993 Rev. Mod. Phys. 65 499
25. Akaike H 1974 IEEE Trans. Automat. Control 19 716
26. Rissanen J 1978 Automatica 14 465
27. Watanabe S 2009 Algebraic Geometry and Statistical Learning Theory (Cambridge: Cambridge University Press)
28. Mézard M, Parisi G and Virasoro M A 1987 Spin Glass Theory and Beyond (Singapore: World Scientific)
29. Mézard M and Montanari M 2009 Information, Physics and Computation (New York: Oxford University Press)
30. MacKay D J C 1999 IEEE Trans. Inform. Theory 45 399
31. MacKay D J C and Neal R M 1997 Electron. Lett. 33 457
32. Kabashima Y and Saad D 1998 Europhys. Lett. 44 668
33. de Almeida J R L and Thouless D J 1978 J. Phys. A: Math. Gen. 11 983
34. Shizato T and Kabashima Y 2009 J. Phys. A 42 015005
35. Kabashima Y, Vehkaperä M and Chatterjee S 2012 J. Stat. Mech. P12003
36. Vehkaperä M, Kabashima Y and Chatterjee S 2014 Analysis of regularized LS reconstruction and random matrix ensembles in compressed sensing Proc. IEEE Int. Symp. on Information Theory (Honolulu, HI, 29 June-4 July 2014) pp 3185-9
37. Kabashima Y and Vehkaperä M 2014 Signal recovery using expectation consistent approximation for linear observations Proc. IEEE Int. Symp. on Information Theory (Honolulu, HI, 29 June-4 July 2014) pp 226-30
38. Oymak S and Hassibi B 2014 A case for orthogonal measurements in linear inverse problems Proc. IEEE Int. Symp. on Information Theory (Honolulu, HI, 29 June-4 July 2014) pp 3175-9
39. Wen C-K and Wong K-K 2014 Analysis of compressed sensing with spatially-coupled orthogonal matrices arXiv:1402.3215