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Volumn 59, Issue 6, 2013, Pages 3434-3447

Reconstruction from anisotropic random measurements

Author keywords

1 minimization; Design matrices with uniformly bounded entries; restricted eigenvalue (RE) conditions; sparsity; sub Gaussian random matrices

Indexed keywords

COVARIANCE STRUCTURES; EIGEN-VALUE; LOW-DIMENSIONAL SUBSPACE; RANDOM MATRICES; REDUCTION PRINCIPLE; RESTRICTED ISOMETRIES; SPARSITY; UNIFORMLY BOUNDED;

EID: 84877881209     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2013.2243201     Document Type: Article
Times cited : (130)

References (33)
  • 1
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • DOI 10.1109/TIT.2005.858979
    • E. Candès and T. Tao, "Decoding by linear programming," IEEE Trans. Inf. Theory, vol. 51, no. 12, pp. 4203-4215, Dec. 2005. (Pubitemid 41800353)
    • (2005) IEEE Transactions on Information Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candes, E.J.1    Tao, T.2
  • 2
    • 33947416035 scopus 로고    scopus 로고
    • Near-optimal signal recovery from random projections: Universal encoding strategies?
    • DOI 10.1109/TIT.2006.885507
    • E. Candès and T. Tao, "Near optimal signal recovery from random projections: Universal encoding strategies?," IEEE Trans. Inf. Theory, vol. 52, no. 12, pp. 5406-5425, Dec. 2006. (Pubitemid 46445381)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candes, E.J.1    Tao, T.2
  • 3
    • 34548275795 scopus 로고    scopus 로고
    • The Dantzig selector: Statistical estimation when p is much larger than n
    • E. Candès and T. Tao, "The Dantzig selector: Statistical estimation when p is much larger than n," Ann. Statist., vol. 35, no. 6, pp. 2313-2351, 2007.
    • (2007) Ann. Statist. , vol.35 , Issue.6 , pp. 2313-2351
    • Candès, E.1    Tao, T.2
  • 5
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr.
    • D. Donoho, "Compressed sensing," IEEE Trans. Inf. Theory, vol. 52, no. 4, pp. 1289-1306, Apr. 2006.
    • (2006) IEEE Trans. Inf. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.1
  • 6
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • DOI 10.1002/cpa.20124
    • E. Candès, J. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol. 59, no. 8, pp. 1207-1223, Aug. 2006. (Pubitemid 43988295)
    • (2006) Communications on Pure and Applied Mathematics , vol.59 , Issue.8 , pp. 1207-1223
    • Candes, E.J.1    Romberg, J.K.2    Tao, T.3
  • 7
    • 33646365077 scopus 로고    scopus 로고
    • 1-norm solution is also the sparsest solution
    • DOI 10.1002/cpa.20132
    • D. Donoho, "For most large underdetermined systems of equations, the minimal-norm solution is also the sparsest solution," Commun. Pure Appl. Math., vol. 59, no. 6, pp. 797-829, 2006. (Pubitemid 43667226)
    • (2006) Communications on Pure and Applied Mathematics , vol.59 , Issue.6 , pp. 797-829
    • Donoho, D.L.1
  • 8
    • 44049083305 scopus 로고    scopus 로고
    • Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements
    • Mar.
    • M. Rudelson and R. Vershynin, "Sparse reconstruction by convex relaxation: Fourier and Gaussian measurements," in Proc. 40th Annu. Conf. Inf. Sci. Syst., Mar. 2006, pp. 207-212.
    • (2006) Proc. 40th Annu. Conf. Inf. Sci. Syst. , pp. 207-212
    • Rudelson, M.1    Vershynin, R.2
  • 9
    • 52349092455 scopus 로고    scopus 로고
    • On sparse reconstruction fromFourier and Gaussian measurements
    • M. Rudelson and R. Vershynin, "On sparse reconstruction fromFourier and Gaussian measurements," Commun. Pure Appl. Math., vol. 61, pp. 1025-1045, 2008.
    • (2008) Commun. Pure Appl. Math. , vol.61 , pp. 1025-1045
    • Rudelson, M.1    Vershynin, R.2
  • 10
    • 33746801607 scopus 로고    scopus 로고
    • Geometric approach to error-correcting codes and reconstruction of signals
    • DOI 10.1155/IMRN.2005.4019, PII S1073792805150922
    • 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. (Pubitemid 44178240)
    • (2005) International Mathematics Research Notices , Issue.64 , pp. 4019-4041
    • Rudelson, M.1    Vershynin, R.2
  • 11
    • 55649115527 scopus 로고    scopus 로고
    • A simple proof of the restricted isometry property for random matrices
    • R. G. Baraniuk, M. Davenport, R. A. DeVore, and M. B. Wakin, "A simple proof of the restricted isometry property for random matrices," Construct. Approx., vol. 28, no. 3, pp. 253-263, 2008.
    • (2008) Construct. Approx. , vol.28 , Issue.3 , pp. 253-263
    • Baraniuk, R.G.1    Davenport, M.2    Devore, R.A.3    Wakin, M.B.4
  • 12
    • 55649100730 scopus 로고    scopus 로고
    • Uniform uncertainty principle for Bernoulli and sub-Gaussian ensembles
    • S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, "Uniform uncertainty principle for Bernoulli and sub-Gaussian ensembles," Construct. Approx., vol. 28, no. 3, pp. 277-289, 2008.
    • (2008) Construct. Approx. , vol.28 , Issue.3 , pp. 277-289
    • Mendelson, S.1    Pajor, A.2    Tomczak-Jaegermann, N.3
  • 13
    • 84877887533 scopus 로고    scopus 로고
    • Restricted isometry property of matrices with independent columns and neighborly polytopes by
    • 0904.4723v1
    • R. Adamczak, A. E. Litvak, A. Pajor, and N. Tomczak-Jaegermann, Restricted Isometry Property of Matrices With Independent Columns and Neighborly Polytopes by Random Sampling 2009, 0904.4723v1.
    • (2009) Random Sampling
    • Adamczak, R.1    Litvak, A.E.2    Pajor, A.3    Tomczak-Jaegermann, N.4
  • 14
    • 68649086910 scopus 로고    scopus 로고
    • Simultaneous analysis of Lasso and Dantzig selector
    • P. Bickel, Y. Ritov, and A. Tsybakov, "Simultaneous analysis of Lasso and Dantzig selector," Ann. Statist., vol. 37, no. 4, pp. 1705-1732, 2009.
    • (2009) Ann. Statist. , vol.37 , Issue.4 , pp. 1705-1732
    • Bickel, P.1    Ritov, Y.2    Tsybakov, A.3
  • 15
    • 0001287271 scopus 로고    scopus 로고
    • Regression shrinkage and selection via the Lasso
    • R. Tibshirani, "Regression shrinkage and selection via the Lasso," J. Roy. Statist. Soc. Ser. B, vol. 58, no. 1, pp. 267-288, 1996.
    • (1996) J. Roy. Statist. Soc. Ser. B , vol.58 , Issue.1 , pp. 267-288
    • Tibshirani, R.1
  • 16
    • 77955054299 scopus 로고    scopus 로고
    • On the conditions used to prove oracle results for the Lasso
    • S. van de Geer and P. Buhlmann, "On the conditions used to prove oracle results for the Lasso," Electron. J. Statist., vol. 3, pp. 1360-1392, 2009.
    • (2009) Electron. J. Statist. , vol.3 , pp. 1360-1392
    • Geer De S.Van1    Buhlmann, P.2
  • 17
    • 77956925453 scopus 로고    scopus 로고
    • Restricted nullspace and eigenvalue properties for correlated Gaussian designs
    • G. Raskutti, M. Wainwright, and B. Yu, "Restricted nullspace and eigenvalue properties for correlated Gaussian designs," J. Mach. Learn. Res., vol. 11, pp. 2241-2259, 2010.
    • (2010) J. Mach. Learn. Res. , vol.11 , pp. 2241-2259
    • Raskutti, G.1    Wainwright, M.2    Yu, B.3
  • 19
    • 51249179500 scopus 로고
    • Some inequalities for Gaussian processes and applications
    • Y. Gordon, "Some inequalities for Gaussian processes and applications," Israel J. Math., vol. 50, no. 4, pp. 265-289, 1985.
    • (1985) Israel J. Math. , vol.50 , Issue.4 , pp. 265-289
    • Gordon, Y.1
  • 21
    • 38849196916 scopus 로고    scopus 로고
    • Reconstruction and subgaussian operators in asymptotic geometric analysis
    • S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann, "Reconstruction and subgaussian operators in asymptotic geometric analysis," Geometr. Funct. Anal., vol. 17, no. 4, pp. 1248-1282, 2007.
    • (2007) Geometr. Funct. Anal. , vol.17 , Issue.4 , pp. 1248-1282
    • Mendelson, S.1    Pajor, A.2    Tomczak-Jaegermann, N.3
  • 22
    • 80555145308 scopus 로고    scopus 로고
    • High-dimensional covariance estimation based on Gaussian graphical models
    • S. Zhou, P. Rütimann, M. Xu, and P. Bühlmann, "High-dimensional covariance estimation based on Gaussian graphical models," J. Mach. Learn. Res., vol. 12, pp. 2975-3026, 2011.
    • (2011) J. Mach. Learn. Res. , vol.12 , pp. 2975-3026
    • Zhou, S.1    Rütimann, P.2    Xu, M.3    Bühlmann, P.4
  • 23
    • 61349111475 scopus 로고    scopus 로고
    • Compressed and privacy sensitive sparse regression
    • Feb.
    • S. Zhou, J. Lafferty, and L.Wasserman, "Compressed and privacy sensitive sparse regression," IEEE Trans. Inf. Theory, vol. 55, no. 2, pp. 846-866, Feb. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.2 , pp. 846-866
    • Zhou, S.1    Lafferty, J.2    Wasserman, L.3
  • 24
    • 84972531331 scopus 로고
    • Enhancing access to microdata while protecting confidentiality: Prospects for the future
    • Aug.
    • G. Duncan and R. Pearson, "Enhancing access to microdata while protecting confidentiality: Prospects for the future," Statist. Sci., vol. 6, no. 3, pp. 219-232, Aug. 1991.
    • (1991) Statist. Sci. , vol.6 , Issue.3 , pp. 219-232
    • Duncan, G.1    Pearson, R.2
  • 25
    • 80051608696 scopus 로고    scopus 로고
    • Approximating the moments of marginals of high dimensional distributions
    • R. Vershynin, "Approximating the moments of marginals of high dimensional distributions," Ann. Probabil., vol. 39, pp. 1591-1606, 2011.
    • (2011) Ann. Probabil. , vol.39 , pp. 1591-1606
    • Vershynin, R.1
  • 26
    • 84865433010 scopus 로고    scopus 로고
    • How close is the sample covariance matrix to the actual covariance matrix?
    • R. Vershynin, "How close is the sample covariance matrix to the actual covariance matrix?," J. Theor. Probabil., vol. 25, pp. 655-686, 2012.
    • (2012) J. Theor. Probabil. , vol.25 , pp. 655-686
    • Vershynin, R.1
  • 28
    • 0003345901 scopus 로고
    • Remarques sur un résultat non publié de b.Maurey
    • Palaiseau
    • G. Pisier, "Remarques sur un résultat non publié de b.Maurey," Semin. Funct. Anal.,École Polytech., Palaiseau, vol. 5, 1981.
    • (1981) Semin. Funct. Anal.,École Polytech. , vol.5
    • Pisier, G.1
  • 29
    • 0030489977 scopus 로고    scopus 로고
    • New concentration inequalities in product spaces
    • M. Talagrand, "New concentration inequalities in product spaces," Invent. Math., vol. 126, pp. 505-563, 1996. (Pubitemid 126323770)
    • (1996) Inventiones Mathematicae , vol.126 , Issue.3 , pp. 505-563
    • Talagrand, M.1
  • 31
    • 0003270948 scopus 로고
    • Asymptotic theory of finite dimensional normed spaces ser
    • New York, NY, USA: Springer- Verlag
    • V. D.Milman and G. Schechtman, Asymptotic Theory of Finite Dimensional Normed Spaces, ser. LectureNotes in Mathematics 1200. New York, NY, USA: Springer-Verlag, 1986.
    • (1986) Lecture Notes in Mathematics , pp. 1200
    • Milman, V.D.1    Schechtman, G.2
  • 32
    • 0012942540 scopus 로고    scopus 로고
    • The concentration of measure phenomenon ser
    • Providence, RI, USA: Amer. Math. Soc.
    • M. Ledoux, The Concentration of Measure Phenomenon, ser. Mathematical Surveys and Monographs, 89. Providence, RI, USA: Amer. Math. Soc., 2001.
    • (2001) Mathematical Surveys and Monographs , pp. 89
    • Ledoux, M.1


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