A typical reconstruction limit for compressed sensing based on L p-norm minimization

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2009, Issue 9, 2009, Pages

  Kabashima, Y ^a   Wadayama, T ^b   Tanaka, T ^c  

^a TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

^b NAGOYA INSTITUTE OF TECHNOLOGY   (Japan)

^c KYOTO UNIVERSITY   (Japan)

Author keywords

Analysis of algorithms; Communication; Robust and stochastic optimization; Source and channel coding; Supply and information networks

Indexed keywords

EID: 72449137292     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2009/09/L09003     Document Type: Article

References (28)

1. Claerbout J F and Muir F 1973 Geophys. Mag. 38 826
2. Santosa F and Symes W W 1986 SIAM J. Sci. Stat. Comput. 7 1307
3. Donoho D L and Stark P B 1989 SIAM J. Appl. Math. 49 906
4. Donoho D 2006 IEEE Trans. Inform. Theory 52 1289
5. Candès E J and Tao T 2005 IEEE Trans. Inform. Theory 51 4203
6. Candès E J, Romberg J and Tao T 2006 IEEE Trans. Inform. Theory 52 489
7. Candès E J and Tao T 2006 IEEE Trans. Inform. Theory 52 5406
8. Candès E J and Tao T 2007 Ann. Stat. 35 2313
9. Haupt J and Nowak R 2006 IEEE Trans. Inform. Theory 52 4036
10. Tibshirani R 1996 J. R. Stat. Soc. B 58 267
11. Chen S S, Donoho D L and Saunders M A 1998 SIAM J. Sci. Comput. 20 33
12. Candès E J 2008 C. R. Acad. Sci. Paris I 346 589
13. Gilbert E N 1952 Bell Syst. Tech. J. 31 504
14. Vapnik V N and Chervonenkis A Y 1971 Theor. Probl. Appl. 16 264
15. Shannon C E 1948 Bell Syst. Tech. J. 27 379
16. Shannon C E 1948 Bell Syst. Tech. J. 27 623
17. Cover T M 1965 IEEE Trans. Electron. Comput. 14 326
18. Rangan S, Fletcher A K and Goyal V K 2009 Asymptotic analysis of MAP estimation via the replica method and applications to compressed sensing arXiv:0906.3234v2
19. Dotsenko V S 2001 Introduction to the Replica Theory of Disordered Statistical Systems (Cambridge: Cambridge University Press)
20. Mézard M, Parisi G and Virasoro M A 1987 Spin Glass Theory and Beyond (Singapore: World Scientific)
21. de Almeida J R L and Thouless D J 1978 J. Phys. A: Math. Gen. 11 983
22. Boyd S and Vandenberghe L 2004 Convex Optimization (Cambridge: Cambridge University Press)
23. Grant M and Boyd S 2009 CVX. Matlab software for disciplined convex programming (web page and software) http://stanford.edu/∼boyd/cvx
24. Grant M and Boyd S 2008 Graph implementations for nonsmooth convex programs Recent Advances in Learning and Control (Springer Lecture Notes in Control and Information Sciences) ed V Blondel, S Boyd and H Kimura (Berlin: Springer) p95 http:// stanford.edu/∼boyd/graph-dcp.html (a tribute to MVidyasagar)
25. Talagrand M 2003 Spin Glasses: A Challenge for Mathematicians: Cavity and Mean field Models (Berlin: Springer)
26. Takeda K, Uda S and Kabashima Y 2006 Europhys. Lett. 76 1193
27. Donoho D L 2006 Discrete Comput. Geom. 35 617
28. Donoho D L and Tanner J 2009 J. Am. Math. Soc. 22 1