메뉴 건너뛰기




Volumn 52, Issue 12, 2006, Pages 5406-5425

Near-optimal signal recovery from random projections: Universal encoding strategies?

Author keywords

Concentration of measure; Convex optimization; Duality in optimization; Linear programming; Random matrices; Random projections; Signal recovery; Singular values of random matrices; Sparsity; Trigonometric expansions; Uncertainty principle

Indexed keywords

IMAGE PROCESSING; LINEAR PROGRAMMING; OPTIMIZATION; RANDOM PROCESSES; SIGNAL ENCODING;

EID: 33947416035     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2006.885507     Document Type: Article
Times cited : (6239)

References (47)
  • 1
    • 0000778931 scopus 로고
    • Bounded orthogonal systems and the A(p)-set problem
    • J. Bourgain, "Bounded orthogonal systems and the A(p)-set problem," Acta Math., vol. 162, no. 3-4, pp. 227-245, 1989.
    • (1989) Acta Math , vol.162 , Issue.3-4 , pp. 227-245
    • Bourgain, J.1
  • 2
    • 33947376641 scopus 로고    scopus 로고
    • J. Bourgain, Remarks on Halasz-Montgomery type inequalities, in Geometric Aspects of Functional Analysis (Israel, 1992-1994), ser. Oper. Theory Adv. Appl., Cambridge, MA: Birkhäuser, 77, pp. 25-39.
    • J. Bourgain, "Remarks on Halasz-Montgomery type inequalities," in Geometric Aspects of Functional Analysis (Israel, 1992-1994), ser. Oper. Theory Adv. Appl., Cambridge, MA: Birkhäuser, vol. 77, pp. 25-39.
  • 3
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information
    • Feb
    • E. Candès, J. Romberg, and T. Tao, "Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information," IEEE Trans. Inf. Theory, no. 2, pp. 489-509, Feb. 2006.
    • (2006) IEEE Trans. Inf. Theory , Issue.2 , pp. 489-509
    • Candès, E.1    Romberg, J.2    Tao, T.3
  • 4
    • 21944453585 scopus 로고    scopus 로고
    • The Role of Sparsity and Incoherence for Exactly Reconstructing a Signal from Limited Measurements California Inst. Technol., Pasadena
    • Tech. Rep
    • E. J. Candès and J. Romberg, The Role of Sparsity and Incoherence for Exactly Reconstructing a Signal from Limited Measurements California Inst. Technol., Pasadena, Tech. Rep., 2004.
    • (2004)
    • Candès, E.J.1    Romberg, J.2
  • 5
    • 33646365077 scopus 로고    scopus 로고
    • 1-norm solution is also the sparsest solution
    • 1-norm solution is also the sparsest solution," Commun. Pure Appl. Math., vol. 59, no. 6, pp. 797-829, 2006.
    • (2006) Commun. Pure Appl. Math , vol.59 , Issue.6 , pp. 797-829
    • Donoho, D.L.1
  • 6
    • 85009724776 scopus 로고    scopus 로고
    • Nonlinear approximation
    • Acta Numerica, 1998. Cambridge, U.K, Cambridge Univ. Press
    • R. A. DeVore, "Nonlinear approximation," in Acta Numerica, 1998. Cambridge, U.K.: Cambridge Univ. Press, 1998, vol. 7, pp. 51-150, ser. Acta Numer.
    • (1998) ser. Acta Numer , vol.7 , pp. 51-150
    • DeVore, R.A.1
  • 10
    • 84881084569 scopus 로고
    • Atomic characterizations of modulation spaces through Gabor-type representations
    • H. G. Feichtinger, "Atomic characterizations of modulation spaces through Gabor-type representations," Rocky Mountain J. Math., vol. 19, no. 1, pp. 113-125, 1989.
    • (1989) Rocky Mountain J. Math , vol.19 , Issue.1 , pp. 113-125
    • Feichtinger, H.G.1
  • 12
    • 33947395814 scopus 로고
    • n-Widths in Approximation Theory
    • Ergebnisse der Mathematik und ihrer Grenzgebiete (3, Results in Mathematics and Related Areas 3, Berlin, Germany: Springer-Verlag
    • A. Pinkus, n-Widths in Approximation Theory, ser. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)]. Berlin, Germany: Springer-Verlag, 1985, vol. 7.
    • (1985) ser , vol.7
    • Pinkus, A.1
  • 13
    • 0001387808 scopus 로고
    • The widths of certain finite dimensional sets and classes of smooth functions
    • B. Kashin, "The widths of certain finite dimensional sets and classes of smooth functions," Izvestia, vol. 41, pp. 334-351, 1977.
    • (1977) Izvestia , vol.41 , pp. 334-351
    • Kashin, B.1
  • 14
    • 0000286901 scopus 로고
    • The widths of a Euclidean ball
    • in Russian
    • A. Garnaev and E. Gluskin, "The widths of a Euclidean ball," Dokl. A. N. USSR, vol. 277, pp. 1048-1052, 1984, in Russian.
    • (1984) Dokl. A. N. USSR , vol.277 , pp. 1048-1052
    • Garnaev, A.1    Gluskin, E.2
  • 15
    • 33947361723 scopus 로고    scopus 로고
    • K. Ball, An elementary introduction to modem convex geometry, in Flavors of Geometry, ser. Math. Sci. Res. Inst. Publ., Cambridge, U.K.: Cambridge Univ. Press, 1997, 31, pp. 1-58.
    • K. Ball, "An elementary introduction to modem convex geometry," in Flavors of Geometry, ser. Math. Sci. Res. Inst. Publ., Cambridge, U.K.: Cambridge Univ. Press, 1997, vol. 31, pp. 1-58.
  • 16
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • E. J. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-1215, 2005.
    • (2005) IEEE Trans. Inf. Theory , vol.51 , Issue.12 , pp. 4203-1215
    • Candès, E.J.1    Tao, T.2
  • 17
    • 0033077324 scopus 로고    scopus 로고
    • The space complexity of approximating the frequency moments
    • N. Alon, Y. Matias, and M. Szegedy, "The space complexity of approximating the frequency moments," J. Comput. Syst. Sci., vol. 58, no. 1, pt. 2, pp. 137-147, 1999.
    • (1999) J. Comput. Syst. Sci , vol.58 , Issue.1 PART. 2 , pp. 137-147
    • Alon, N.1    Matias, Y.2    Szegedy, M.3
  • 19
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • D. L. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.L.1
  • 20
    • 0001616908 scopus 로고
    • Uncertainty principles and signal recovery
    • D. L. Donoho and P. B. Stark, "Uncertainty principles and signal recovery," SIAM J. Appl. Math., vol. 49, no. 3, pp. 906-931, 1989.
    • (1989) SIAM J. Appl. Math , vol.49 , Issue.3 , pp. 906-931
    • Donoho, D.L.1    Stark, P.B.2
  • 21
    • 0001654702 scopus 로고
    • Extensions of Lipschitz mappings into a Hilbert space
    • Providence, RI
    • W. B. Johnson and J. Lindenstrauss, "Extensions of Lipschitz mappings into a Hilbert space," in Proc. Conf. Modern Anal. Prob., Providence, RI, 1984, vol. 26, pp. 189-206.
    • (1984) Proc. Conf. Modern Anal. Prob , vol.26 , pp. 189-206
    • Johnson, W.B.1    Lindenstrauss, J.2
  • 22
    • 2942640138 scopus 로고    scopus 로고
    • On sparse representations in arbitrary redundant bases
    • J.-J. Fuchs, "On sparse representations in arbitrary redundant bases," IEEE Trans. Inf. Theory, vol. 50, no. 6, pp. 1341-1344, 2004.
    • (2004) IEEE Trans. Inf. Theory , vol.50 , Issue.6 , pp. 1341-1344
    • Fuchs, J.-J.1
  • 23
    • 0008988926 scopus 로고
    • Linear inversion of band-limited reflection seismograms
    • F. Santosa and W. W. Symes, "Linear inversion of band-limited reflection seismograms," SIAM J. Sci. Statist. Comput., vol. 7, no. 4, pp. 1307-1330, 1986.
    • (1986) SIAM J. Sci. Statist. Comput , vol.7 , Issue.4 , pp. 1307-1330
    • Santosa, F.1    Symes, W.W.2
  • 24
    • 0030212858 scopus 로고    scopus 로고
    • Recovery of blocky images from noisy and blurred data
    • D. C. Dobson and F. Santosa, "Recovery of blocky images from noisy and blurred data," SIAM J. Appl. Math., vol. 56, no. 4, pp. 1181-1198, 1996.
    • (1996) SIAM J. Appl. Math , vol.56 , Issue.4 , pp. 1181-1198
    • Dobson, D.C.1    Santosa, F.2
  • 25
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithm
    • L. I. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithm," Physica D, pp. 259-268, 1992.
    • (1992) Physica D , pp. 259-268
    • Rudin, L.I.1    Osher, S.2    Fatemi, E.3
  • 26
    • 0032131292 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • S.S. Chen, D. L. Donoho, and M. A. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol. 20, no. 1, pp. 33-61, 1998.
    • (1998) SIAM J. Sci. Comput , vol.20 , Issue.1 , pp. 33-61
    • Chen, S.S.1    Donoho, D.L.2    Saunders, M.A.3
  • 27
    • 0003958737 scopus 로고
    • Basis Pursuit,
    • Ph.D. dissertation, Stanford University, Stanford, CA
    • S. S. Chen, "Basis Pursuit," Ph.D. dissertation, Stanford University, Stanford, CA, 1995.
    • (1995)
    • Chen, S.S.1
  • 28
    • 0035504028 scopus 로고    scopus 로고
    • Uncertainty principles and ideal atomic decomposition
    • D. L. Donoho and X. Huo, "Uncertainty principles and ideal atomic decomposition," IEEE Trans. Inf. Theory, vol. 47, no. 7, pp. 2845-2862, 2001.
    • (2001) IEEE Trans. Inf. Theory , vol.47 , Issue.7 , pp. 2845-2862
    • Donoho, D.L.1    Huo, X.2
  • 30
    • 0347968052 scopus 로고    scopus 로고
    • Sparse representations in unions of bases
    • R. Gribonval and M. Nielsen, "Sparse representations in unions of bases," IEEE Trans. Inf. Theory, vol. 49, no. 12, pp. 3320-3325, 2003.
    • (2003) IEEE Trans. Inf. Theory , vol.49 , Issue.12 , pp. 3320-3325
    • Gribonval, R.1    Nielsen, M.2
  • 31
    • 33744726904 scopus 로고    scopus 로고
    • Quantitative robust uncertainty principles and optimally sparse decompositions
    • E. J. Candès and J. Romberg, "Quantitative robust uncertainty principles and optimally sparse decompositions," Found. Comput. Math., vol. 6, no. 2, pp. 227-254, 2006.
    • (2006) Found. Comput. Math , vol.6 , Issue.2 , pp. 227-254
    • Candès, E.J.1    Romberg, J.2
  • 32
    • 0003690415 scopus 로고
    • Least Absolute Deviations
    • Cambridge, MA: Birkhäuser, theory, applications, and algorithms
    • P. Bloomfield and W. L. Steiger, Least Absolute Deviations. Cambridge, MA: Birkhäuser, 1983, vol. 6, ser. Progress in Probability and Statistics, theory, applications, and algorithms.
    • (1983) ser. Progress in Probability and Statistics , vol.6
    • Bloomfield, P.1    Steiger, W.L.2
  • 33
    • 0000263239 scopus 로고
    • Distribution of eigenvalues in certain sets of random matrices
    • V. A. Marcenko and L. A. Pastur, "Distribution of eigenvalues in certain sets of random matrices," Mat. Sb. (N.S.), vol. 72, no. 114, pp. 507-536, 1967.
    • (1967) Mat. Sb. (N.S.) , vol.72 , Issue.114 , pp. 507-536
    • Marcenko, V.A.1    Pastur, L.A.2
  • 34
    • 0001629248 scopus 로고
    • The smallest eigenvalue of a large-dimensional Wishart matrix
    • J. W. Silverstein, "The smallest eigenvalue of a large-dimensional Wishart matrix," Ann. Probab., vol. 13, no. 4, pp. 1364-1368, 1985.
    • (1985) Ann. Probab , vol.13 , Issue.4 , pp. 1364-1368
    • Silverstein, J.W.1
  • 35
    • 0035641726 scopus 로고    scopus 로고
    • On the distribution of the largest eigenvalue in principal components analysis
    • I. M. Johnstone, "On the distribution of the largest eigenvalue in principal components analysis," Ann. Statist., vol. 29, no. 2, pp. 295-327, 2001.
    • (2001) Ann. Statist , vol.29 , Issue.2 , pp. 295-327
    • Johnstone, I.M.1
  • 36
    • 0009400517 scopus 로고
    • Condition numbers of random matrices
    • S. J. Szarek, "Condition numbers of random matrices," J. Complexity, vol. 7, no. 2, pp. 131-149, 1991.
    • (1991) J. Complexity , vol.7 , Issue.2 , pp. 131-149
    • Szarek, S.J.1
  • 37
    • 33947431773 scopus 로고    scopus 로고
    • K. R. Davidson and S. J. Szarek, Addenda and corrigenda to: Local operator theory, random matrices and Banach spaces [in it Handbook of the geometry of Banach Spaces, I, 317-366, North-Holland, Amsterdam, 2001; MR 1863696 (2004f:47002a)], in Handbook of the Geometry of Banach spaces. Amsterdam, The Netherlands: North-Holland, 2003, 2, pp. 1819-1820.
    • K. R. Davidson and S. J. Szarek, "Addenda and corrigenda to: "Local operator theory, random matrices and Banach spaces" [in it Handbook of the geometry of Banach Spaces, vol. I, 317-366, North-Holland, Amsterdam, 2001; MR 1863696 (2004f:47002a)]," in Handbook of the Geometry of Banach spaces. Amsterdam, The Netherlands: North-Holland, 2003, vol. 2, pp. 1819-1820.
  • 38
    • 0012942540 scopus 로고    scopus 로고
    • The Concentration of Measure Phenomenon
    • Providence, RI: American Mathematical Society
    • M. Ledoux, The Concentration of Measure Phenomenon, ser. Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society, 2001, vol. 89.
    • (2001) ser. Mathematical Surveys and Monographs , vol.89
    • Ledoux, M.1
  • 39
    • 29144495343 scopus 로고    scopus 로고
    • New Results About Random Covariance Matrices and Statistical Applications,
    • Ph.D. dissertation, Stanford University, Stanford, CA
    • N. El Karoui, "New Results About Random Covariance Matrices and Statistical Applications," Ph.D. dissertation, Stanford University, Stanford, CA, 2004.
    • (2004)
    • El Karoui, N.1
  • 40
    • 0001758959 scopus 로고
    • Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix
    • Z. D. Bai and Y. Q. Yin, "Limit of the smallest eigenvalue of a large-dimensional sample covariance matrix," Ann. Probab., vol. 21, no. 3, pp. 1275-1294, 1993.
    • (1993) Ann. Probab , vol.21 , Issue.3 , pp. 1275-1294
    • Bai, Z.D.1    Yin, Y.Q.2
  • 41
    • 18644382839 scopus 로고    scopus 로고
    • Smallest singular value of random matrices and geometry of random polytopes
    • A. E. Litvak, A. Pajor, M. Rudelson, and N. Tomczak-Jaegermann, "Smallest singular value of random matrices and geometry of random polytopes," Adv. Math., vol. 195, no. 2, pp. 491-523, 2005.
    • (2005) Adv. Math , vol.195 , Issue.2 , pp. 491-523
    • Litvak, A.E.1    Pajor, A.2    Rudelson, M.3    Tomczak-Jaegermann, N.4
  • 43
    • 0034344120 scopus 로고    scopus 로고
    • A sharp concentration inequality with applications
    • S. Boucheron, G. Lugosi, and P. Massart, "A sharp concentration inequality with applications," Random Struct. Algor., vol. 16, no. 3, pp. 277-292, 2000.
    • (2000) Random Struct. Algor , vol.16 , Issue.3 , pp. 277-292
    • Boucheron, S.1    Lugosi, G.2    Massart, P.3
  • 46
    • 0000994356 scopus 로고
    • Subspaces of small codimension of finite-dimensional Banach spaces
    • A. Pajor and N. Tomczak-Jaegermann, "Subspaces of small codimension of finite-dimensional Banach spaces," in Proc. Amer. Math. Soc., 1986, vol. 97, no. 4, pp. 637-642.
    • (1986) Proc. Amer. Math. Soc , vol.97 , Issue.4 , pp. 637-642
    • Pajor, A.1    Tomczak-Jaegermann, N.2
  • 47
    • 0002195680 scopus 로고
    • Approximation of zonoids by zonotopes
    • J. Bourgain, J. Lindenstrauss, and V. Milman, "Approximation of zonoids by zonotopes," Acta Math., vol. 162, no. 1-2, pp. 73-141, 1989.
    • (1989) Acta Math , vol.162 , Issue.1-2 , pp. 73-141
    • Bourgain, J.1    Lindenstrauss, J.2    Milman, V.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.