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Volumn 56, Issue 4, 2010, Pages 2002-2016

Exponential bounds implying construction of compressed sensing matrices, error-correcting codes, and neighborly polytopes by random sampling

Author keywords

1 minimization; Compressed sensing; Error correction by linear programming; Neighborly polytopes; Random matrices

Indexed keywords

ASYMPTOTIC RATE; ASYMPTOTICS; CHECKSUM; COMPRESSED SENSING; ERROR CORRECTING CODE; ERROR PATTERNS; EXPONENTIAL BOUNDS; GEOMETRIC OBJECTS; HIGH PROBABILITY; POLYTOPES; RANDOM MATRICES; RANDOM MEASUREMENT; RANDOM SAMPLING; SAMPLING THEOREMS; SPARSE SIGNALS;

EID: 77950233813     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2010.2040892     Document Type: Article
Times cited : (60)

References (19)
  • 1
    • 77950276420 scopus 로고    scopus 로고
    • [Online]. Available:
    • [Online]. Available: http://ecos.maths.ed.ac.uk
  • 4
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • E. J. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, vol.52, no.2, pp. 489-509, 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.2 , pp. 489-509
    • Candès, E.J.1    Romberg, J.2    Tao, T.3
  • 5
    • 29144439194 scopus 로고    scopus 로고
    • Decoding via linear programming
    • E. J. Candès and T. Tao, "Decoding via linear programming," IEEE Trans. Inf. Theory, vol.51, no.12, pp. 4203-4215, 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candès, E.J.1    Tao, T.2
  • 6
    • 33947416035 scopus 로고    scopus 로고
    • Near optimal signal recovery from random projections and universal encoding strategies
    • E. J. Candès, "Near optimal signal recovery from random projections and universal encoding strategies," IEEE. Trans. Inf. Theory, vol.52, no.12, pp. 5406-5425, 2006.
    • (2006) IEEE. Trans. Inf. Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candès, E.J.1
  • 8
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • D. L. Donoho, "Compressed sensing," IEEE. Trans. Info. Thry., vol.52, no.4, pp. 1289-1306, 2006.
    • (2006) IEEE. Trans. Info. Thry. , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.L.1
  • 9
    • 33646479497 scopus 로고    scopus 로고
    • High-dimensional centrally-symmetric polytopes with neighborliness proportional to dimension
    • D. L. Donoho, "High-dimensional centrally-symmetric polytopes with neighborliness proportional to dimension," Disc. Comput. Geometry, vol.35, no.4, pp. 617-652, 2006.
    • (2006) Disc. Comput. Geometry , vol.35 , Issue.4 , pp. 617-652
    • Donoho, D.L.1
  • 10
    • 58149133580 scopus 로고    scopus 로고
    • 15 years of reproducible research in computational harmonic analysis
    • D. L. Donoho, A. Maleki, I. Rahman, M. Shahram, and V. Strodden, "15 years of reproducible research in computational harmonic analysis," Comput. Sci. Eng., vol.11, pp. 8-18, 2009.
    • (2009) Comput. Sci. Eng. , vol.11 , pp. 8-18
    • Donoho, D.L.1    Maleki, A.2    Rahman, I.3    Shahram, M.4    Strodden, V.5
  • 11
    • 22144471532 scopus 로고    scopus 로고
    • Neighborliness of randomly-projected simplices in high dimensions
    • D. L. Donoho and J. Tanner, "Neighborliness of randomly-projected simplices in high dimensions," Proc. Nat. Acad. Sci. USA, vol.102, no.27, pp. 9452-9457, 2005.
    • (2005) Proc. Nat. Acad. Sci. USA , vol.102 , Issue.27 , pp. 9452-9457
    • Donoho, D.L.1    Tanner, J.2
  • 12
    • 22144488449 scopus 로고    scopus 로고
    • Sparse nonnegative solutions of underdetermined linear equations by linear programming
    • D. L. Donoho, "Sparse nonnegative solutions of underdetermined linear equations by linear programming," Proc. Nat. Acad. Sci. USA, vol.102, no.27, pp. 9446-9451, 2005.
    • (2005) Proc. Nat. Acad. Sci. USA , vol.102 , Issue.27 , pp. 9446-9451
    • Donoho, D.L.1
  • 13
    • 57349138185 scopus 로고    scopus 로고
    • Counting faces of randomly projected polytopes when the projection radically lowers dimension
    • D. L. Donoho, "Counting faces of randomly projected polytopes when the projection radically lowers dimension," J. AMS, vol.22, no.1, pp. 1-53, 2009.
    • (2009) J. AMS , vol.22 , Issue.1 , pp. 1-53
    • Donoho, D.L.1
  • 14
    • 73149095252 scopus 로고    scopus 로고
    • Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing
    • D. L. Donoho, "Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing," Phil. Trans. Royal Soc. A, vol.367, no.1906, pp. 4273-4293, 2009.
    • (2009) Phil. Trans. Royal Soc. A , vol.367 , Issue.1906 , pp. 4273-4293
    • Donoho, D.L.1
  • 16
    • 33746923055 scopus 로고    scopus 로고
    • How neighborly can a centrally symmetric polytope be?
    • N. Linial and I. Novik, "How neighborly can a centrally symmetric polytope be?," Disc. Comput. Geometry, vol.36, no.2, pp. 273-281, 2006.
    • (2006) Disc. Comput. Geometry , vol.36 , Issue.2 , pp. 273-281
    • Linial, N.1    Novik, I.2
  • 17
    • 51249195097 scopus 로고
    • On the geometrical moments of skew-regular simplices in hyperspherical space, with some applications in geometry and mathematical statistics
    • H. Ruben, "On the geometrical moments of skew-regular simplices in hyperspherical space, with some applications in geometry and mathematical statistics," Acta Math., vol.103, pp. 1-23, 1960.
    • (1960) Acta Math. , vol.103 , pp. 1-23
    • Ruben, H.1
  • 18
    • 33746801607 scopus 로고    scopus 로고
    • Geometric approach to error-correcting codes and reconstruction of signals
    • M. Rudelson and R. Vershynin, "Geometric approach to error-correcting codes and reconstruction of signals," Int. Math. Res. Notices, vol.64, pp. 4019-4041, 2005.
    • (2005) Int. Math. Res. Notices , vol.64 , pp. 4019-4041
    • Rudelson, M.1    Vershynin, R.2
  • 19
    • 52349092455 scopus 로고    scopus 로고
    • On sparse reconstruction from fourier and gaussian measurements
    • M. Rudelson, "On sparse reconstruction from fourier and gaussian measurements," Commun. Pure and Appl. Math., vol.61, pp. 1025-1045, 2008.
    • (2008) Commun. Pure and Appl. Math. , vol.61 , pp. 1025-1045
    • Rudelson, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.