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Volumn 27, Issue 3, 2009, Pages 275-288

Instance-optimality in probability with an ℓ1-minimization decoder

Author keywords

1 minimization decoder; Compressed sensing; Instance optimality in probability

Indexed keywords

BERNOULLI RANDOM VARIABLES; COMPRESSED SENSING; EQUAL PROBABILITY; GAUSSIAN MEASUREMENTS; GAUSSIAN RANDOM VARIABLE; GEOMETRIC MAPPING; HIGH PROBABILITY; INSTANCE-OPTIMALITY IN PROBABILITY; MATRIX; OPTIMALITY; RANDOM MATRICES; RANDOM POLYTOPES; SINGULAR VALUES;

EID: 69949141924     PISSN: 10635203     EISSN: 1096603X     Source Type: Journal    
DOI: 10.1016/j.acha.2009.05.001     Document Type: Article
Times cited : (56)

References (20)
  • 2
    • 55649115527 scopus 로고    scopus 로고
    • A simple proof of the restricted isometry property for random matrices
    • Baraniuk R., Davenport M., DeVore R., and Wakin M. A simple proof of the restricted isometry property for random matrices. Constr. Approx. 28 (2008) 253-263
    • (2008) Constr. Approx. , vol.28 , pp. 253-263
    • Baraniuk, R.1    Davenport, M.2    DeVore, R.3    Wakin, M.4
  • 3
    • 42649140570 scopus 로고    scopus 로고
    • The restricted isometry property and its implications for compressed sensing
    • Candés E. The restricted isometry property and its implications for compressed sensing. C. R. Acad. Sci. Paris Ser. I 346 (2008) 589-592
    • (2008) C. R. Acad. Sci. Paris Ser. I , vol.346 , pp. 589-592
    • Candés, E.1
  • 4
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • Candès E.J., Romberg J., and Tao T. Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52 (2006) 489-509
    • (2006) IEEE Trans. Inform. Theory , vol.52 , pp. 489-509
    • Candès, E.J.1    Romberg, J.2    Tao, T.3
  • 5
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • Candès E., Romberg J., and Tao T. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59 (2006) 1207-1223
    • (2006) Comm. Pure Appl. Math. , vol.59 , pp. 1207-1223
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 6
  • 7
    • 57349181932 scopus 로고    scopus 로고
    • Compressed sensing and best k-term approximation
    • Cohen A., Dahmen W., and DeVore R. Compressed sensing and best k-term approximation. J. Amer. Math. Soc. 22 (2009) 211-245
    • (2009) J. Amer. Math. Soc. , vol.22 , pp. 211-245
    • Cohen, A.1    Dahmen, W.2    DeVore, R.3
  • 8
    • 36248929865 scopus 로고    scopus 로고
    • Deterministic constructions of compressed sensing matrices
    • DeVore R. Deterministic constructions of compressed sensing matrices. J. Complexity 23 (2007) 918-925
    • (2007) J. Complexity , vol.23 , pp. 918-925
    • DeVore, R.1
  • 9
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Donoho D. Compressed sensing. IEEE Trans. Inform. Theory 52 4 (2006) 1289-1306
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.1
  • 10
    • 0000286901 scopus 로고
    • The widths of a Euclidean ball
    • Garnaev A., and Gluskin E. The widths of a Euclidean ball. Dokl. AN SSSR 277 (1984) 1048-1052
    • (1984) Dokl. AN SSSR , vol.277 , pp. 1048-1052
    • Garnaev, A.1    Gluskin, E.2
  • 13
    • 0001387808 scopus 로고
    • The widths of certain finite dimensional sets and classes of smooth functions
    • Kashin B. The widths of certain finite dimensional sets and classes of smooth functions. Izvestia 41 (1977) 334-351
    • (1977) Izvestia , vol.41 , pp. 334-351
    • Kashin, B.1
  • 14
    • 18644382839 scopus 로고    scopus 로고
    • Smallest singular value of random matrices and geometry of random polytopes
    • Litvak A., Pajor A., Rudelson M., and Tomczak-Jaegermann N. Smallest singular value of random matrices and geometry of random polytopes. Adv. Math. 195 (2005) 491-523
    • (2005) Adv. Math. , vol.195 , pp. 491-523
    • Litvak, A.1    Pajor, A.2    Rudelson, M.3    Tomczak-Jaegermann, N.4
  • 15
    • 0141473384 scopus 로고    scopus 로고
    • Constructive Approximation: Advanced Problems
    • Springer-Verlag, Berlin
    • Lorentz G., von Golitschek M., and Makovoz Yu. Constructive Approximation: Advanced Problems. Grundlehren Math. Wiss. vol. 304 (1996), Springer-Verlag, Berlin
    • (1996) Grundlehren Math. Wiss. , vol.304
    • Lorentz, G.1    von Golitschek, M.2    Makovoz, Yu.3
  • 16
    • 84966228950 scopus 로고
    • The distribution of Rademacher sums
    • Montgomery-Smith S. The distribution of Rademacher sums. Proc. Amer. Math. Soc. 109 (1990) 517-522
    • (1990) Proc. Amer. Math. Soc. , vol.109 , pp. 517-522
    • Montgomery-Smith, S.1
  • 19
    • 0010027220 scopus 로고
    • Subgaussian techniques in proving strong laws of large numbers
    • Taylor R., and Hu T.-C. Subgaussian techniques in proving strong laws of large numbers. Amer. Math. Monthly 9 (1987) 295-299
    • (1987) Amer. Math. Monthly , vol.9 , pp. 295-299
    • Taylor, R.1    Hu, T.-C.2
  • 20
    • 75849163827 scopus 로고    scopus 로고
    • Stability and instance optimality for Gaussian measurements in compressed sensing
    • in press
    • P. Wojtaszczyk, Stability and instance optimality for Gaussian measurements in compressed sensing, Found. Comput. Math., in press
    • Found. Comput. Math
    • Wojtaszczyk, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.