메뉴 건너뛰기




Volumn 67, Issue 11, 2014, Pages 1877-1904

Suprema of chaos processes and the restricted isometry property

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84908338179     PISSN: 00103640     EISSN: 10970312     Source Type: Journal    
DOI: 10.1002/cpa.21504     Document Type: Article
Times cited : (197)

References (48)
  • 1
    • 0000874693 scopus 로고
    • On decoupling, series expansions, and tail behavior of chaos processes
    • Arcones, M. A.; Giné, E. On decoupling, series expansions, and tail behavior of chaos processes. J. Theoret. Probab. 6 (1993), no. 1, 101-122. doi:10.1007/BF01046771
    • (1993) J. Theoret. Probab. , vol.6 , Issue.1 , pp. 101-122
    • Arcones, M.A.1    Giné, E.2
  • 2
    • 77952743265 scopus 로고    scopus 로고
    • Compressed channel sensing: a new approach to estimating sparse multipath channels
    • Bajwa, W. U.; Haupt, J.; Sayeed, A. M.; Nowak, R. Compressed channel sensing: a new approach to estimating sparse multipath channels. Proc. IEEE 98 (2010), no. 5, 1058-1076. doi:10.1109/JPROC.2010.2042415
    • (2010) Proc. IEEE , vol.98 , Issue.5 , pp. 1058-1076
    • Bajwa, W.U.1    Haupt, J.2    Sayeed, A.M.3    Nowak, R.4
  • 3
    • 55649115527 scopus 로고    scopus 로고
    • A simple proof of the restricted isometry property for random matrices
    • Baraniuk, R.; Davenport, M.; DeVore, R.; Wakin, M. A simple proof of the restricted isometry property for random matrices. Constr. Approx. 28 (2008), no. 3, 253-263. doi:10.1007/s00365-007-9003-x
    • (2008) Constr. Approx. , vol.28 , Issue.3 , pp. 253-263
    • Baraniuk, R.1    Davenport, M.2    DeVore, R.3    Wakin, M.4
  • 4
    • 69949164527 scopus 로고    scopus 로고
    • Iterative hard thresholding for compressed sensing
    • Blumensath, T.; Davies, M. E. Iterative hard thresholding for compressed sensing. Appl. Comput. Harmon. Anal. 27 (2009), no. 3, 265-274. doi:10.1016/j.acha.2009.04.002
    • (2009) Appl. Comput. Harmon. Anal. , vol.27 , Issue.3 , pp. 265-274
    • Blumensath, T.1    Davies, M.E.2
  • 5
    • 0038373013 scopus 로고    scopus 로고
    • Concentration inequalities using the entropy method
    • Boucheron, S.; Lugosi, G.; Massart, P. Concentration inequalities using the entropy method. Ann. Probab. 31 (2003), no. 3, 1583-1614. doi:10.1214/aop/1055425791
    • (2003) Ann. Probab. , vol.31 , Issue.3 , pp. 1583-1614
    • Boucheron, S.1    Lugosi, G.2    Massart, P.3
  • 6
    • 51249179251 scopus 로고
    • Invertibility of "large" submatrices with applications to the geometry of Banach spaces and harmonic analysis
    • Bourgain, J.; Tzafriri, L. Invertibility of "large" submatrices with applications to the geometry of Banach spaces and harmonic analysis. Israel J. Math. 57 (1987), no. 2, 137-224. doi:10.1007/BF02772174
    • (1987) Israel J. Math. , vol.57 , Issue.2 , pp. 137-224
    • Bourgain, J.1    Tzafriri, L.2
  • 7
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
    • Candés, E. J.; Romberg, J.; Tao, T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52 (2006), no. 2, 489-509. doi:10.1109/TIT.2005.862083
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.2 , pp. 489-509
    • Candés, E.J.1    Romberg, J.2    Tao, T.3
  • 8
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • Candés, E. J.; Romberg, J. K.; Tao, T. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59 (2006), no. 8, 1207-1223. doi:10.1002/cpa.20124
    • (2006) Comm. Pure Appl. Math. , vol.59 , Issue.8 , pp. 1207-1223
    • Candés, E.J.1    Romberg, J.K.2    Tao, T.3
  • 9
    • 33947416035 scopus 로고    scopus 로고
    • Near-optimal signal recovery from random projections: universal encoding strategies?
    • Candes, E. J.; Tao, T. Near-optimal signal recovery from random projections: universal encoding strategies? IEEE Trans. Inform. Theory 52 (2006), no. 12, 5406-5425. doi:10.1109/TIT.2006.885507
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.12 , pp. 5406-5425
    • Candes, E.J.1    Tao, T.2
  • 10
    • 0001845750 scopus 로고
    • Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces
    • Carl, B. Inequalities of Bernstein-Jackson-type and the degree of compactness of operators in Banach spaces. Ann. Inst. Fourier (Grenoble) 35 (1985), no. 3, 79-118.
    • (1985) Ann. Inst. Fourier (Grenoble) , vol.35 , Issue.3 , pp. 79-118
    • Carl, B.1
  • 11
    • 0032131292 scopus 로고    scopus 로고
    • Atomic decomposition by basis pursuit
    • Chen, S. S.; Donoho, D. L.; Saunders, M. A. Atomic decomposition by basis pursuit. SIAM J. Sci. Comput. 20 (1998), no. 1, 33-61. doi:10.1137/S1064827596304010
    • (1998) SIAM J. Sci. Comput. , vol.20 , Issue.1 , pp. 33-61
    • Chen, S.S.1    Donoho, D.L.2    Saunders, M.A.3
  • 13
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Donoho, D. L. Compressed sensing. IEEE Trans. Inform. Theory 52 (2006), no. 4, 1289-1306. doi:10.1109/TIT.2006.871582
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.4 , pp. 1289-1306
    • Donoho, D.L.1
  • 14
    • 0000660999 scopus 로고
    • The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
    • Dudley, R. M. The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Functional Analysis 1 (1967), 290-330.
    • (1967) J. Functional Analysis , vol.1 , pp. 290-330
    • Dudley, R.M.1
  • 15
    • 0003989054 scopus 로고    scopus 로고
    • Cambridge Studies in Advanced Mathematics, 63. Cambridge University Press, Cambridge
    • Dudley, R. M. Uniform central limit theorems. Cambridge Studies in Advanced Mathematics, 63. Cambridge University Press, Cambridge, 1999. doi:10.1017/CBO9780511665622
    • (1999) Uniform central limit theorems
    • Dudley, R.M.1
  • 17
    • 0001783943 scopus 로고
    • Regularité des trajectoires des fonctions aléatoires gaussiennes
    • Lecture Notes in Mathematics, 480. Springer, Berlin
    • Fernique, X. Regularité des trajectoires des fonctions aléatoires gaussiennes. École d'Été de Probabilités de Saint-Flour, IV-1974, 1-96. Lecture Notes in Mathematics, 480. Springer, Berlin, 1975.
    • (1975) École d'Été de Probabilités de Saint-Flour, IV-1974 , pp. 1-96
    • Fernique, X.1
  • 19
    • 84856034474 scopus 로고    scopus 로고
    • Hard thresholding pursuit: an algorithm for compressive sensing
    • Foucart, S. Hard thresholding pursuit: an algorithm for compressive sensing. SIAM J. Numer. Anal. 49 (2011), no. 6, 2543-2563. doi:10.1137/100806278
    • (2011) SIAM J. Numer. Anal. , vol.49 , Issue.6 , pp. 2543-2563
    • Foucart, S.1
  • 20
    • 84870050604 scopus 로고    scopus 로고
    • Sparse recovery algorithms: sufficient conditions in terms of restricted isometry constants
    • Springer, New York
    • Foucart, S. Sparse recovery algorithms: sufficient conditions in terms of restricted isometry constants. Approximation Theory XIII: San Antonio 2010, 65-77. Springer, New York, 2012. doi:10.1007/978-1-4614-0772-0_5
    • (2012) Approximation Theory XIII: San Antonio 2010 , pp. 65-77
    • Foucart, S.1
  • 22
    • 77956563404 scopus 로고    scopus 로고
    • Toeplitz compressed sensing matrices with applications to sparse channel estimation
    • Haupt, J.; Bajwa, W.; Raz, G.; Nowak, R. Toeplitz compressed sensing matrices with applications to sparse channel estimation. IEEE Trans. Inform. Theory 56 (2010), no. 11, 5862-5875. doi:10.1109/TIT.2010.2070191
    • (2010) IEEE Trans. Inform. Theory , vol.56 , Issue.11 , pp. 5862-5875
    • Haupt, J.1    Bajwa, W.2    Raz, G.3    Nowak, R.4
  • 23
    • 66849132093 scopus 로고    scopus 로고
    • High-resolution radar via compressed sensing
    • Herman, M.; Strohmer, T. High-resolution radar via compressed sensing. IEEE Trans. Signal Process. 57 (2009), no. 6, 2275-2284. doi:10.1109/TSP.2009.2014277
    • (2009) IEEE Trans. Signal Process. , vol.57 , Issue.6 , pp. 2275-2284
    • Herman, M.1    Strohmer, T.2
  • 24
    • 80052034277 scopus 로고    scopus 로고
    • Johnson-Lindenstrauss lemma for circulant matrices
    • Hinrichs, A.; Vybíral, J. Johnson-Lindenstrauss lemma for circulant matrices. Random Structures Algorithms 39 (2011), no. 3, 391-398. doi:10.1002/rsa.20360
    • (2011) Random Structures Algorithms , vol.39 , Issue.3 , pp. 391-398
    • Hinrichs, A.1    Vybíral, J.2
  • 25
    • 48349105627 scopus 로고    scopus 로고
    • Uncertainty in time-frequency representations on finite abelian groups and applications
    • Krahmer, F.; Pfander, G. E.; Rashkov, P. Uncertainty in time-frequency representations on finite abelian groups and applications. Appl. Comput. Harmon. Anal. 25 (2008), no. 2, 209-225. doi:10.1016/j.acha.2007.09.008
    • (2008) Appl. Comput. Harmon. Anal. , vol.25 , Issue.2 , pp. 209-225
    • Krahmer, F.1    Pfander, G.E.2    Rashkov, P.3
  • 26
    • 79960436599 scopus 로고    scopus 로고
    • New and improved Johnson-Lindenstrauss embeddings via the restricted isometry property
    • Krahmer, F.; Ward, R. New and improved Johnson-Lindenstrauss embeddings via the restricted isometry property. SIAM J. Math. Anal. 43 (2011), no. 3, 1269-1281. doi:10.1137/100810447
    • (2011) SIAM J. Math. Anal. , vol.43 , Issue.3 , pp. 1269-1281
    • Krahmer, F.1    Ward, R.2
  • 29
    • 0000426206 scopus 로고
    • Noncommutative Khintchine and Paley inequalities
    • Lust-Piquard, F.; Pisier, G. Noncommutative Khintchine and Paley inequalities. Ark. Mat. 29 (1991), no. 2, 241-260. doi:10.1007/BF02384340
    • (1991) Ark. Mat. , vol.29 , Issue.2 , pp. 241-260
    • Lust-Piquard, F.1    Pisier, G.2
  • 30
    • 38849196916 scopus 로고    scopus 로고
    • Reconstruction and subgaussian operators in asymptotic geometric analysis
    • Mendelson, S.; Pajor, A.; Tomczak-Jaegermann, N. Reconstruction and subgaussian operators in asymptotic geometric analysis. Geom. Funct. Anal. 17 (2007), no. 4, 1248-1282. doi:10.1007/s00039-007-0618-7
    • (2007) Geom. Funct. Anal. , vol.17 , Issue.4 , pp. 1248-1282
    • Mendelson, S.1    Pajor, A.2    Tomczak-Jaegermann, N.3
  • 32
    • 62749175137 scopus 로고    scopus 로고
    • CoSaMP: iterative signal recovery from incomplete and inaccurate samples
    • Needell, D.; Tropp, J. A. CoSaMP: iterative signal recovery from incomplete and inaccurate samples. Appl. Comput. Harmon. Anal. 26 (2009), no. 3, 301-321. doi:10.1016/j.acha.2008.07.002
    • (2009) Appl. Comput. Harmon. Anal. , vol.26 , Issue.3 , pp. 301-321
    • Needell, D.1    Tropp, J.A.2
  • 33
    • 77952098309 scopus 로고    scopus 로고
    • Sparsity in time-frequency representations
    • Pfander, G. E.; Rauhut, H. Sparsity in time-frequency representations. J. Fourier Anal. Appl. 16 (2010), no. 2, 233-260. doi:10.1007/s00041-009-9086-9
    • (2010) J. Fourier Anal. Appl. , vol.16 , Issue.2 , pp. 233-260
    • Pfander, G.E.1    Rauhut, H.2
  • 34
    • 54949110579 scopus 로고    scopus 로고
    • Identification of matrices having a sparse representation
    • Pfander, G. E.; Rauhut, H.; Tanner, J. Identification of matrices having a sparse representation. IEEE Trans. Signal Process. 56 (2008), no. 11, 5376-5388. doi:10.1109/TSP.2008.928503
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.11 , pp. 5376-5388
    • Pfander, G.E.1    Rauhut, H.2    Tanner, J.3
  • 35
    • 84880604098 scopus 로고    scopus 로고
    • The restricted isometry property for time-frequency structured random matrices
    • Pfander, G. E.; Rauhut, H.; Tropp, J. A. The restricted isometry property for time-frequency structured random matrices. Probab. Theory Relat. Fields 156 (2013), no. 3-4, 707-737. doi:10.1007/s00440-012-0441-4
    • (2013) Probab. Theory Relat. Fields , vol.156 , Issue.3-4 , pp. 707-737
    • Pfander, G.E.1    Rauhut, H.2    Tropp, J.A.3
  • 36
    • 0000065961 scopus 로고
    • Some applications of the metric entropy condition to harmonic analysis
    • Lecture Notes in Mathematics, 995. Springer, Berlin
    • Pisier, G. Some applications of the metric entropy condition to harmonic analysis. Banach spaces, harmonic analysis, and probability theory (Storrs, Conn., 1980/1981), 123-154. Lecture Notes in Mathematics, 995. Springer, Berlin, 1983. doi:10.1007/BFb0061891
    • (1983) Banach spaces, harmonic analysis, and probability theory (Storrs, Conn., 1980/1981) , pp. 123-154
    • Pisier, G.1
  • 37
  • 38
    • 78349246612 scopus 로고    scopus 로고
    • Compressive sensing and structured random matrices
    • Radon Series on Computational and Applied Mathematics, 9. Walter de Gruyter, Berlin
    • Rauhut, H. Compressive sensing and structured random matrices. Theoretical foundations and numerical methods for sparse recovery, 1-92. Radon Series on Computational and Applied Mathematics, 9. Walter de Gruyter, Berlin, 2010. doi:10.1515/9783110226157.1
    • (2010) Theoretical foundations and numerical methods for sparse recovery , pp. 1-92
    • Rauhut, H.1
  • 39
    • 84856471680 scopus 로고    scopus 로고
    • Restricted isometries for partial random circulant matrices
    • Rauhut, H.; Romberg, J.; Tropp, J. A. Restricted isometries for partial random circulant matrices. Appl. Comput. Harmon. Anal. 32 (2012), no. 2, 242-254. doi:10.1016/j.acha.2011.05.001
    • (2012) Appl. Comput. Harmon. Anal. , vol.32 , Issue.2 , pp. 242-254
    • Rauhut, H.1    Romberg, J.2    Tropp, J.A.3
  • 40
    • 84907737173 scopus 로고    scopus 로고
    • Compressive sensing by random convolution
    • Romberg, J. Compressive sensing by random convolution. SIAM J. Imaging Sci. 2 (2009), no. 4, 1098-1128. doi:10.1137/08072975X
    • (2009) SIAM J. Imaging Sci. , vol.2 , Issue.4 , pp. 1098-1128
    • Romberg, J.1
  • 41
    • 0033541884 scopus 로고    scopus 로고
    • Random vectors in the isotropic position
    • Rudelson, M. Random vectors in the isotropic position. J. Funct. Anal. 164 (1999), no. 1, 60-72. doi:10.1006/jfan.1998.3384
    • (1999) J. Funct. Anal. , vol.164 , Issue.1 , pp. 60-72
    • Rudelson, M.1
  • 42
    • 52349092455 scopus 로고    scopus 로고
    • On sparse reconstruction from Fourier and Gaussian measurements
    • Rudelson, M.; Vershynin, R. On sparse reconstruction from Fourier and Gaussian measurements. Comm. Pure Appl. Math. 61 (2008), no. 8, 1025-1045. doi:10.1002/cpa.20227
    • (2008) Comm. Pure Appl. Math. , vol.61 , Issue.8 , pp. 1025-1045
    • Rudelson, M.1    Vershynin, R.2
  • 43
    • 0002662601 scopus 로고
    • Regularity of Gaussian processes
    • Talagrand, M. Regularity of Gaussian processes. Acta Math. 159 (1987), no. 1-2, 99-149. doi:10.1007/BF02392556
    • (1987) Acta Math. , vol.159 , Issue.1-2 , pp. 99-149
    • Talagrand, M.1
  • 44
    • 0030489977 scopus 로고    scopus 로고
    • New concentration inequalities in product spaces
    • Talagrand, M. New concentration inequalities in product spaces. Invent. Math. 126 (1996), no. 3, 505-563. doi:10.1007/s002220050108
    • (1996) Invent. Math. , vol.126 , Issue.3 , pp. 505-563
    • Talagrand, M.1
  • 46
    • 84938533326 scopus 로고    scopus 로고
    • Introduction to the non-asymptotic analysis of random matrices
    • Cambridge University Press, Cambridge
    • Vershynin, R. Introduction to the non-asymptotic analysis of random matrices. Compressed sensing, 210-268. Cambridge University Press, Cambridge, 2012.
    • (2012) Compressed sensing , pp. 210-268
    • Vershynin, R.1
  • 47
    • 78650311155 scopus 로고    scopus 로고
    • A variant of the Johnson-Lindenstrauss lemma for circulant matrices
    • Vybíral, J. A variant of the Johnson-Lindenstrauss lemma for circulant matrices. J. Funct. Anal. 260 (2011), no. 4, 1096-1105. doi:10.1016/j.jfa.2010.11.014
    • (2011) J. Funct. Anal. , vol.260 , Issue.4 , pp. 1096-1105
    • Vybíral, J.1
  • 48
    • 80052353493 scopus 로고    scopus 로고
    • Sparse recovery with orthogonal matching pursuit under RIP
    • Zhang, T. Sparse recovery with orthogonal matching pursuit under RIP. IEEE Trans. Inform. Theory 57 (2011), no. 9, 6215-6221. doi:10.1109/TIT.2011.2162263
    • (2011) IEEE Trans. Inform. Theory , vol.57 , Issue.9 , pp. 6215-6221
    • Zhang, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.