메뉴 건너뛰기




Volumn 110, Issue 4, 2013, Pages 1181-1186

Deterministic matrices matching the compressed sensing phase transitions of Gaussian random matrices

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; KERNEL METHOD; MONTE CARLO METHOD; PHASE TRANSITION; PRIORITY JOURNAL; PROBABILITY; PROCESS OPTIMIZATION; RANDOMIZATION;

EID: 84872876101     PISSN: 00278424     EISSN: 10916490     Source Type: Journal    
DOI: 10.1073/pnas.1219540110     Document Type: Article
Times cited : (88)

References (45)
  • 1
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Donoho DL (2006) Compressed sensing. IEEE Trans Inf Theory 52(4):1289-1306.
    • (2006) IEEE Trans Inf Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.L.1
  • 2
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • Candès EJ, Tao T (2005) Decoding by linear programming. IEEE Trans Inf Theory 51(1): 4203-4215.
    • (2005) IEEE Trans Inf Theory , vol.51 , Issue.1 , pp. 4203-4215
    • Candès, E.J.1    Tao, T.2
  • 3
    • 73149095252 scopus 로고    scopus 로고
    • Observed universality of phase transitions in highdimensional geometry, with implications for modern data analysis and signal processing
    • Donoho D, Tanner J (2009) Observed universality of phase transitions in highdimensional geometry, with implications for modern data analysis and signal processing. Philos Transact A Math Phys Eng Sci 367(1906):4273-4293.
    • (2009) Philos Transact A Math Phys Eng Sci , vol.367 , Issue.1906 , pp. 4273-4293
    • Donoho, D.1    Tanner, J.2
  • 5
    • 85014561619 scopus 로고    scopus 로고
    • Fast iterative shrinkage-thresholding algorithm for linear inverse problems
    • Beck A, Teboulle M (2009) Fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci 2(1):183-202.
    • (2009) SIAM J Imaging Sci , vol.2 , Issue.1 , pp. 183-202
    • Beck, A.1    Teboulle, M.2
  • 6
    • 73149095169 scopus 로고    scopus 로고
    • Message-passing algorithms for compressed sensing
    • Donoho DL, Maleki A, Montanari A (2009) Message-passing algorithms for compressed sensing. Proc Natl Acad Sci USA 106(45):18914-18919.
    • (2009) Proc Natl Acad Sci USA , vol.106 , Issue.45 , pp. 18914-18919
    • Donoho, D.L.1    Maleki, A.2    Montanari, A.3
  • 7
    • 51849129654 scopus 로고    scopus 로고
    • Fast reconstruction algorithm for deterministic compressive sensing using second order reed-muller codes
    • IEEE, Piscataway, NJ
    • Howard S, Calderbank R, Searle S (2008) Fast reconstruction algorithm for deterministic compressive sensing using second order reed-muller codes. Conference on Information Sciences and Systems (CISS) (IEEE, Piscataway, NJ), pp 11-15.
    • (2008) Conference on Information Sciences and Systems (CISS) , pp. 11-15
    • Howard, S.1    Calderbank, R.2    Searle, S.3
  • 8
    • 44249104733 scopus 로고    scopus 로고
    • On the conditioning of random subdictionaries
    • Tropp J (2008) On the conditioning of random subdictionaries. Appl Comput Harmon Anal 25(1):1-24.
    • (2008) Appl Comput Harmon Anal , vol.25 , Issue.1 , pp. 1-24
    • Tropp, J.1
  • 9
    • 69049120308 scopus 로고    scopus 로고
    • Near-ideal model selection by l1 minimization
    • Candès EJ, Plan Y (2009) Near-ideal model selection by l1 minimization. Ann Stat 37(5A):2145-2177.
    • (2009) Ann Stat , vol.37 , Issue.5 A , pp. 2145-2177
    • Candès, E.J.1    Plan, Y.2
  • 10
    • 77950517814 scopus 로고    scopus 로고
    • Counting the faces of randomly-projected hypercubes and orthants, with applications
    • Donoho D, Tanner J (2010) Counting the faces of randomly-projected hypercubes and orthants, with applications. Discrete Comput Geom 43(3):522-541.
    • (2010) Discrete Comput Geom , vol.43 , Issue.3 , pp. 522-541
    • Donoho, D.1    Tanner, J.2
  • 11
    • 0001616908 scopus 로고
    • Uncertainty principles and signal recovery
    • Donoho DL, Stark PB (1989) Uncertainty principles and signal recovery. SIAM J Appl Math 49(3):906-931.
    • (1989) SIAM J Appl Math , vol.49 , Issue.3 , pp. 906-931
    • Donoho, D.L.1    Stark, P.B.2
  • 12
    • 0035504028 scopus 로고    scopus 로고
    • Uncertainty principles and ideal atomic decomposition
    • Donoho DL, Huo X (2001) Uncertainty principles and ideal atomic decomposition. IEEE Trans Inf Theory 47(7):2845-2862.
    • (2001) IEEE Trans Inf Theory , vol.47 , Issue.7 , pp. 2845-2862
    • Donoho, D.L.1    Huo, X.2
  • 13
    • 57349172766 scopus 로고    scopus 로고
    • On the linear independence of spikes and sines
    • Tropp J (2008) On the linear independence of spikes and sines. J Fourier Anal Appl 14(5-6):838-858.
    • (2008) J Fourier Anal Appl , vol.14 , Issue.5-6 , pp. 838-858
    • Tropp, J.1
  • 14
    • 0242323185 scopus 로고    scopus 로고
    • Grassmannian frames with applications to coding and communication
    • Strohmer T, Heath R (2003) Grassmannian frames with applications to coding and communication. Appl Comput Harmon Anal 14(3):257-275.
    • (2003) Appl Comput Harmon Anal , vol.14 , Issue.3 , pp. 257-275
    • Strohmer, T.1    Heath, R.2
  • 17
    • 0032131292 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • Chen S, Donoho D, Saunders M (1999) Atomic decomposition by Basis Pursuit. SIAM J Sci Comput 20(1):33-61.
    • (1999) SIAM J Sci Comput , vol.20 , Issue.1 , pp. 33-61
    • Chen, S.1    Donoho, D.2    Saunders, M.3
  • 19
    • 33646479497 scopus 로고    scopus 로고
    • High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension
    • Donoho D (2006) High-dimensional centrally symmetric polytopes with neighborliness proportional to dimension. Discrete Comput Geom 35(4):617-652.
    • (2006) Discrete Comput Geom , vol.35 , Issue.4 , pp. 617-652
    • Donoho, D.1
  • 20
    • 22144471532 scopus 로고    scopus 로고
    • Neighborliness of randomly projected simplices in high dimensions
    • Donoho DL, Tanner J (2005) Neighborliness of randomly projected simplices in high dimensions. Proc Natl Acad Sci USA 102(27):9452-9457.
    • (2005) Proc Natl Acad Sci USA , vol.102 , Issue.27 , pp. 9452-9457
    • Donoho, D.L.1    Tanner, J.2
  • 21
    • 57349138185 scopus 로고    scopus 로고
    • Counting faces of randomly-projected polytopes when the projection radically lowers dimension
    • Donoho D, Tanner J (2009) Counting faces of randomly-projected polytopes when the projection radically lowers dimension. J Amer Math Soc 22(1):1-53.
    • (2009) J Amer Math Soc , vol.22 , Issue.1 , pp. 1-53
    • Donoho, D.1    Tanner, J.2
  • 28
    • 65649137930 scopus 로고    scopus 로고
    • Probing the pareto frontier for basis pursuit solutions
    • van den Berg E, Friedlander MP (2008) Probing the pareto frontier for basis pursuit solutions. SIAM J Sci Comput 31(4):890-912.
    • (2008) SIAM J Sci Comput , vol.31 , Issue.4 , pp. 890-912
    • Van Den Berg, E.1    Friedlander, M.P.2
  • 30
    • 38649130725 scopus 로고    scopus 로고
    • Mosek APS Available at Accessed December 12 2012
    • Mosek APS (2012) Mosek Optimization Software. Available at http://www.mosek. com. Accessed December 12, 2012.
    • (2012) Mosek Optimization Software.
  • 31
    • 84872831331 scopus 로고    scopus 로고
    • Available at Accessed December 27 2012
    • Andersen M, Vandeberghe L (2012) CVXOPT. Available at http://abel.ee.ucla.edu/cvxopt/index.html. Accessed December 27, 2012.
    • (2012) CVXOPT
    • Andersen, M.1    Vandeberghe, L.2
  • 34
    • 77953126052 scopus 로고    scopus 로고
    • Precise undersampling theorems
    • Donoho D, Tanner J (2010) Precise undersampling theorems. Proc IEEE 98(6):913-924.
    • (2010) Proc IEEE , vol.98 , Issue.6 , pp. 913-924
    • Donoho, D.1    Tanner, J.2
  • 35
    • 51849129654 scopus 로고    scopus 로고
    • A fast reconstruction algorithm for deterministic compressive sensing using second order reed-muller codes. Proceedings of 42nd annual
    • (IEEE, Piscataway NJ
    • Howard S, Calderbank A, Searle S (2008) A fast reconstruction algorithm for deterministic compressive sensing using second order reed-muller codes. Proceedings of 42nd Annual IEEE Conference on Information Sciences and Systems (IEEE, Piscataway NJ), pp 11-15.
    • (2008) IEEE Conference on Information Sciences and Systems , pp. 11-15
    • Howard, S.1    Calderbank, A.2    Searle, S.3
  • 36
    • 77949687001 scopus 로고    scopus 로고
    • Construction of a large class of deterministic matrices that satisfy a statistical restricted isometry property
    • Calderbank AR, Howard S, Jafarpour S (2010) Construction of a large class of deterministic matrices that satisfy a statistical restricted isometry property. IEEE J Sel Top Signal Process 4(2):358-374.
    • (2010) IEEE J Sel Top Signal Process , vol.4 , Issue.2 , pp. 358-374
    • Calderbank, A.R.1    Howard, S.2    Jafarpour, S.3
  • 41
    • 14544270853 scopus 로고    scopus 로고
    • Convex polytopes
    • Springer, New York), 2nd Ed
    • Grünbaum B (2003) Convex Polytopes, Graduate Texts in Mathematics, Vol 221 (Springer, New York), 2nd Ed.
    • (2003) Graduate Texts in Mathematics , vol.221
    • Grünbaum, B.1
  • 42
    • 22144488449 scopus 로고    scopus 로고
    • Sparse nonnegative solution of underdetermined linear equations by linear programming
    • Donoho DL, Tanner J (2005) Sparse nonnegative solution of underdetermined linear equations by linear programming. Proc Natl Acad Sci USA 102(27):9446-9451.
    • (2005) Proc Natl Acad Sci USA , vol.102 , Issue.27 , pp. 9446-9451
    • Donoho, D.L.1    Tanner, J.2
  • 44
    • 59649115633 scopus 로고    scopus 로고
    • Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery
    • Applebaum L, Howard S, Searle S, Calderbank R (2009) Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery. Appl Comput Harmon Anal 26(2):283-290.
    • (2009) Appl Comput Harmon Anal , vol.26 , Issue.2 , pp. 283-290
    • Applebaum, L.1    Howard, S.2    Searle, S.3    Calderbank, R.4
  • 45
    • 48249089642 scopus 로고    scopus 로고
    • The finite harmonic oscillator and its associated sequences
    • Gurevich S, Hadani R, Sochen N (2008) The finite harmonic oscillator and its associated sequences. Proc Natl Acad Sci USA 105(29):9869-9873.
    • (2008) Proc Natl Acad Sci USA , vol.105 , Issue.29 , pp. 9869-9873
    • Gurevich, S.1    Hadani, R.2    Sochen, N.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.