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Volumn 21, Issue 2, 2011, Pages 572-596

Rank-sparsity incoherence for matrix decomposition

Author keywords

Convex relaxation; L1 norm minimization; Matrix decomposition; Nuclear norm minimization; Rank; Semidefinite programming; Sparsity; Uncertainty principle

Indexed keywords

CONVEX RELAXATION; L1 NORM MINIMIZATION; MATRIX DECOMPOSITION; NUCLEAR NORM MINIMIZATION; RANK; SEMI-DEFINITE PROGRAMMING; SPARSITY; UNCERTAINTY PRINCIPLES;

EID: 79960591511     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/090761793     Document Type: Article
Times cited : (915)

References (33)
  • 2
    • 11944253901 scopus 로고    scopus 로고
    • Cambridge University Press, London
    • B. BOLLOBÁS, Random Graphs, Cambridge University Press, London, 2001.
    • (2001) Random Graphs
    • BollobáS, B.1
  • 3
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • DOI 10.1109/TIT.2005.862083
    • E. J. CANDEÀS, J. ROMBERG, AND T. TAO, Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information, IEEE Trans. Inform. Theory, 52 (2006), pp. 489-509. (Pubitemid 43174093)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.2 , pp. 489-509
    • Candes, E.J.1    Romberg, J.2    Tao, T.3
  • 8
  • 9
    • 0035504028 scopus 로고    scopus 로고
    • Uncertainty principles and ideal atomic decomposition
    • DOI 10.1109/18.959265, PII S0018944801089465
    • D. L. DONOHO AND X. HUO, Uncertainty principles and ideal atomic decomposition, IEEE Trans. Inform. Theory, 47 (2001), pp. 2845-2862. (Pubitemid 33053488)
    • (2001) IEEE Transactions on Information Theory , vol.47 , Issue.7 , pp. 2845-2862
    • Donoho, D.L.1    Huo, X.2
  • 11
  • 14
    • 0142257025 scopus 로고    scopus 로고
    • Ph.D. thesis, Department of Electrical Engineering, Stanford University, Palo Alto, CA
    • M. FAZEL, Matrix Rank Minimization with Applications, Ph.D. thesis, Department of Electrical Engineering, Stanford University, Palo Alto, CA, 2002.
    • (2002) Matrix Rank Minimization with Applications
    • Fazel, M.1
  • 15
    • 0142215333 scopus 로고    scopus 로고
    • Log-det heuristic for matrix rank minimization with applications to hankel and euclidean distance matrices
    • M. FAZEL, H. HINDI, AND S. BOYD, Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices, in Proceedings of the American Control Conference, 2003.
    • (2003) Proceedings of the American Control Conference
    • Fazel, M.1    Hindi, H.2    Boyd, S.3
  • 20
    • 20344396845 scopus 로고    scopus 로고
    • YALMIP: A toolbox for modeling and optimization in MATLAB
    • 2004 IEEE International Symposium on Computer Aided Control Systems Design - 2004 CACSD
    • J. LOFBERG, YALMIP: A toolbox for modeling and optimization in MATLAB, in Proceedings of the 2004 IEEE International Symposium on Computer Aided Control Systems Design, Taiwan, 2004, pp. 284-289; also available online from http://control.ee.ethz.ch/~joloef/yalmip.php. (Pubitemid 40788529)
    • (2004) Proceedings of the IEEE International Symposium on Computer-Aided Control System Design , pp. 284-289
    • Lofberg, J.1
  • 21
    • 0029488086 scopus 로고
    • Spectral methods for matrix rigidity with applications to size-depth tradeoffs and communication complexity
    • S. LOKAM, Spectral methods for matrix rigidity with applications to size-depth tradeoffs and communication complexity, in Proceedings of the 36th IEEE Symposium on Foundations of Computer Science, 1995, pp. 6-15.
    • (1995) Proceedings of the 36th IEEE Symposium on Foundations of Computer Science , pp. 6-15
    • Lokam, S.1
  • 22
    • 72249083804 scopus 로고    scopus 로고
    • On the compelxity of matrix rank and rigidity
    • M. MAHAJAN AND J. SARMA, On the compelxity of matrix rank and rigidity, Theory Comput. Syst., 46 (2010), pp. 9-26.
    • (2010) Theory Comput. Syst. , vol.46 , pp. 9-26
    • Mahajan, M.1    Sarma, J.2
  • 23
    • 0031079528 scopus 로고    scopus 로고
    • On the rank minimization problem over a positive semidefinite linear matrix inequality
    • PII S0018928697005011
    • M. MESBAHI AND G. P. PAPAVASSILOPOULOS, On the rank minimization problem over a positive semidefinite linear matrix inequality, IEEE Trans. Automat. Control, 42 (1997), pp. 239-243. (Pubitemid 127760583)
    • (1997) IEEE Transactions on Automatic Control , vol.42 , Issue.2 , pp. 239-243
    • Mesbahi, M.1    Papavassilopoulos, G.P.2
  • 24
    • 0028515483 scopus 로고
    • Phase-shifting masks for microlithography: Automated design and mask requirements
    • Y. C. PATI AND T. KAILATH, Phase-shifting masks for microlithography: Automated design and mask requirements, J. Opti. Soc. Amer. A, 11 (1994), pp. 2438-2452.
    • (1994) J. Opti. Soc. Amer. A , vol.11 , pp. 2438-2452
    • Pati, Y.C.1    Kailath, T.2
  • 25
    • 78549288866 scopus 로고    scopus 로고
    • Guaranteed minimum rank solutions to linear matrix equations via nuclear norm minimization
    • B. RECHT, M. FAZEL, AND P. A. PARRILO, Guaranteed minimum rank solutions to linear matrix equations via nuclear norm minimization, SIAM Rev., 52 (2007), pp. 471-501.
    • (2007) SIAM Rev. , vol.52 , pp. 471-501
    • Recht, B.1    Fazel, M.2    Parrilo, P.A.3
  • 26
    • 79960575253 scopus 로고    scopus 로고
    • personal communication
    • B. RECHT, personal communication, 2009.
    • (2009)
    • Recht, B.1
  • 27
    • 0004267646 scopus 로고    scopus 로고
    • Princeton University Press, Princeton, NJ
    • R. T. ROCKAFELLAR, Convex Analysis, Princeton University Press, Princeton, NJ, 1996.
    • (1996) Convex Analysis
    • Rockafellar, R.T.1
  • 28
    • 84943488562 scopus 로고
    • Bemerkungen zur theorie der beschrankten bilinearformen mit unendlich vielen verander-lischen
    • I. SCHUR, Bemerkungen zur Theorie der beschrankten Bilinearformen mit unendlich vielen Verander-lischen, J. Reine. Angew. Math., 140 (1911), pp. 1-28.
    • (1911) J. Reine. Angew. Math. , vol.140 , pp. 1-28
    • Schur, I.1
  • 32
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • L. VANDENBERGHE AND S. BOYD, Semidefinite programming, SIAM Rev., 38 (1996), pp. 49-95. (Pubitemid 126610912)
    • (1996) SIAM Review , vol.38 , Issue.1 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2
  • 33
    • 0011336092 scopus 로고
    • Characterization of the subdifferential of some matrix norms
    • G. A. WATSON, Characterization of the subdifferential of some matrix norms, Linear Algebra Appl., 170 (1992), pp. 1039-1053.
    • (1992) Linear Algebra Appl. , vol.170 , pp. 1039-1053
    • Watson, G.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.