Typical l1-recovery limit of sparse vectors represented by concatenations of random orthogonal matrices

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2012, Issue 12, 2012, Pages

  Kabashima, Yoshiyuki ^a   Vehkaperä, Mikko ^b,c   Chatterjee, Saikat ^b  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^c AALTO UNIVERSITY   (Finland)

Author keywords

error correcting codes; source and channel coding; statistical inference

Indexed keywords

EID: 84871207413     PISSN: None     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2012/12/P12003     Document Type: Article

References (31)

1. Miller A 2002 Subset Selection in Regression 2nd edn (Boca Raton, FL: Chapman and Hall/CRC)
2. Fletcher A, Goyal V and Rangan S 2009 Proc. IEEE Int. Symp. Inform. Theory 2009 pp 169-73
3. Bajwa W, Haupt J, Sayeed A and Nowak R 2010 Proc. IEEE 98 1058
4. Yang A, Gastpar M, Bajcsy R and Sastry S 2010 Proc. IEEE 98 1077
5. Plumbley M, Blumensath T, Daudet L, Gribonval R and Davies M 2010 Proc. IEEE 98 995
6. Wright J, Yang A, Ganesh A, Sastry S and Yi M 2009 IEEE Trans. Pattern Anal. Mach. Intell. 31 210
7. Elad M 2010 Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing (Berlin: Springer)
8. Donoho D 2006 IEEE Trans. Inform. Theory 52 1289
9. Candes E and Wakin M 2008 IEEE Signal Proc. Mag. 25 21
10. Krzakala F, Mézard M, Sausset F, Sun Y F and Zdeborová L 2012 Phys. Rev. X 2 021005
11. Krzakala F, Mézard M, Sausset F, Sun Y F and Zdeborová L 2012 J. Stat. Mech. P08009
12. Kabashima Y, Wadayama T and Tanaka T 2009 J. Stat. Mech. L09003
13. Kabashima Y, Wadayama T and Tanaka T 2012 J. Stat. Mech. E07001
14. Takeda K and Kabashima Y 2010 Proc. IEEE Int. Symp. Inform. Theory pp 1538-42
15. Donoho D and Huo X 2001 IEEE Trans. Inform. Theory 47 2845
16. Elad M and Bruckstein A 2002 IEEE Trans. Inform. Theory 48 2558
17. Donoho D and Elad M 2003 Proc. Natl Acad. Sci. 100 2197
18. Rubinstein R, Bruckstein A and Elad M 2010 Proc. IEEE 98 1045
19. Ravelli E, Richard G and Daudet L 2008 IEEE Trans. Audio, Speech, Language Processing 16 1361
20. Dotsenko V 2001 Introduction to the Replica Theory of Disordered Statistical Systems (Cambridge: Cambridge University Press)
21. Itzykson C and Zuber J B 1980 J. Math. Phys. 21 411
22. Marinari E, Parisi G and Ritort F 1994 J. Phys. A: Math. Gen. 27 7647
23. Cherrier R, Dean D S and Lefévre A 2003 Phys. Rev. E 67 046112
24. Takeda K, Uda S and Kabashima Y 2006 Europhys. Lett. 76 1193
25. Kabashima Y 2008 J. Phys.: Conf. Ser. 95 012001
26. Shinzato T and Kabashima Y 2008 J. Phys. A: Math. Theor. 41 324013
27. Vehkaperä M, Kabashima Y, Chatterjee S, Aurell E, Skoglund M and Rasmussen L 2012 Proc. IEEE Inform. Theory Workshop 2012 pp 652-6
28. de Almeida J R L and Thouless D J 1978 J. Phys. A: Math. Gen. 11 983
29. Donoho D L 2006 Discrete Comput. Geom. 35 617
30. Donoho D L and Tanner J 2009 J. Am. Math. Soc. 22 1
31. Vila J and Schniter P 2011 Proc. Asilomar Conf. on Signals, Systems, and Computers (Pacific Grove, CA) pp 799-803