메뉴 건너뛰기




Volumn 5, Issue 5, 2011, Pages 1032-1047

Near-oracle performance of greedy block-sparse estimation techniques from noisy measurements

Author keywords

Block sparsity; Gaussian noise; orthogonal matching pursuit; performance guarantees; thresholding

Indexed keywords

BLOCK SPARSITY; CONSTANT FACTORS; ESTIMATION TECHNIQUES; GAUSSIAN NOISE MODEL; GREEDY ALGORITHMS; HIGH SIGNAL-TO-NOISE RATIO; NOISE POWER; NOISY MEASUREMENTS; ORTHOGONAL MATCHING PURSUIT; PARAMETER VECTORS; PERFORMANCE GUARANTEES; SPARSE METHODS; THRESHOLDING; THRESHOLDING ALGORITHMS;

EID: 80051713661     PISSN: 19324553     EISSN: None     Source Type: Journal    
DOI: 10.1109/JSTSP.2011.2160250     Document Type: Article
Times cited : (52)

References (41)
  • 1
    • 33645712892 scopus 로고    scopus 로고
    • Compressed sensing
    • Apr.
    • D. L. 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.L.1
  • 2
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • DOI 10.1002/cpa.20124
    • E. J. Candès, J. K. Romberg, and T. Tao, "Stable signal recovery from incomplete and inaccurate measurements," Commun. Pure Appl. Math., vol. LIX, pp. 1207-1223, 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
  • 3
    • 33645712308 scopus 로고    scopus 로고
    • Just relax: Convex programming methods for identifying sparse signals in noise
    • DOI 10.1109/TIT.2005.864420
    • J. A. Tropp, "Just relax: Convex programming methods for identifying sparse signals in noise," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 1030-1051, Mar. 2006. (Pubitemid 46444890)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.3 , pp. 1030-1051
    • Tropp, J.A.1
  • 4
    • 33144483155 scopus 로고    scopus 로고
    • Stable recovery of sparse overcomplete representations in the presence of noise
    • DOI 10.1109/TIT.2005.860430
    • D. L. Donoho, M. Elad, and V. N. Temlyakov, "Stable recovery of sparse overcomplete representations in the presence of noise," IEEE Trans. Inf. Theory, vol. 52, no. 1, pp. 6-18, Jan. 2006. (Pubitemid 43263116)
    • (2006) IEEE Transactions on Information Theory , vol.52 , Issue.1 , pp. 6-18
    • Donoho, D.L.1    Elad, M.2    Temlyakov, V.N.3
  • 5
    • 20444411101 scopus 로고    scopus 로고
    • Blind deconvolution of images using optimal sparse representations
    • DOI 10.1109/TIP.2005.847322
    • M. M. Bronstein, A. M. Bronstein, M. Zibulevsky, and Y. Y. Zeevi, "Blind deconvolution of images using optimal sparse representations," IEEE Trans. Image Process., vol. 14, no. 6, pp. 726-736, Jun. 2005. (Pubitemid 40794805)
    • (2005) IEEE Transactions on Image Processing , vol.14 , Issue.6 , pp. 726-736
    • Bronstein, M.M.1    Bronstein, A.M.2    Zibulevsky, M.3    Zeevi, Y.Y.4
  • 6
    • 60649102899 scopus 로고    scopus 로고
    • Inpainting and zooming using sparse representations
    • M. J. Fadili, J.-L. Starck, and F. Murtagh, "Inpainting and zooming using sparse representations," Comput. J., vol. 52, no. 1, pp. 64-79, 2009.
    • (2009) Comput. J. , vol.52 , Issue.1 , pp. 64-79
    • Fadili, M.J.1    Starck, J.-L.2    Murtagh, F.3
  • 7
    • 44849115269 scopus 로고    scopus 로고
    • A theory for sampling signals from a union of subspaces
    • DOI 10.1109/TSP.2007.914346
    • Y. M. Lu and M. N. Do, "A theory for sampling signals from a union of subspaces," IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2334-2345, Jun. 2008. (Pubitemid 351795887)
    • (2008) IEEE Transactions on Signal Processing , vol.56 , Issue.6 , pp. 2334-2345
    • Lu, Y.M.1    Do, M.N.2
  • 8
    • 70350743173 scopus 로고    scopus 로고
    • Robust recovery of signals from a structured union of subspaces
    • Nov.
    • Y. C. Eldar and M. Mishali, "Robust recovery of signals from a structured union of subspaces," IEEE Trans. Inf. Theory, vol. 55, no. 11, pp. 5302-5316, Nov. 2009.
    • (2009) IEEE Trans. Inf. Theory , vol.55 , Issue.11 , pp. 5302-5316
    • Eldar, Y.C.1    Mishali, M.2
  • 9
    • 0036612082 scopus 로고    scopus 로고
    • Sampling signals with finite rate of innovation
    • DOI 10.1109/TSP.2002.1003065, PII S1053587X02043921
    • M. Vetterli, P. Marziliano, and T. Blu, "Sampling signals with finite rate of innovation," IEEE Trans. Signal Process., vol. 50, no. 6, pp. 1417-1428, Jun. 2002. (Pubitemid 34822552)
    • (2002) IEEE Transactions on Signal Processing , vol.50 , Issue.6 , pp. 1417-1428
    • Vetterli, M.1    Marziliano, P.2    Blu, T.3
  • 10
    • 34247887411 scopus 로고    scopus 로고
    • Sampling moments and reconstructing signals of finite rate of innovation: Shannon meets strang-fix
    • DOI 10.1109/TSP.2006.890907
    • P. L. Dragotti, M. Vetterli, and T. Blu, "Sampling moments and reconstructing signals of finite rate of innovation: Shannon meets Strang-Fix," IEEE Trans. Signal Process., vol. 55, no. 7, pp. 1741-1757, Jul. 2007. (Pubitemid 46691625)
    • (2007) IEEE Transactions on Signal Processing , vol.55 , Issue.5 , pp. 1741-1757
    • Dragotti, P.L.1    Vetterli, M.2    Blu, T.3
  • 11
    • 77951180022 scopus 로고    scopus 로고
    • Time delay estimation from low rate samples:Aunion of subspaces approach
    • Jun
    • K. Gedalyahu and Y. C. Eldar, "Time delay estimation from low rate samples:Aunion of subspaces approach," IEEE Trans. Signal Process., vol. 58, no. 6, pp. 3017-3031, Jun. 2010.
    • (2010) IEEE Trans. Signal Process. , vol.58 , Issue.6 , pp. 3017-3031
    • Gedalyahu, K.1    Eldar, Y.C.2
  • 12
    • 79952686739 scopus 로고    scopus 로고
    • Multichannel sampling of pulse streams at the rate of innovation
    • Apr
    • K. Gedalyahu, R. Tur, and Y. C. Eldar, "Multichannel sampling of pulse streams at the rate of innovation," IEEE Trans. Signal Process., vol. 59, no. 4, pp. 1491-1504, Apr. 2011.
    • (2011) IEEE Trans. Signal Process. , vol.59 , Issue.4 , pp. 1491-1504
    • Gedalyahu, K.1    Tur, R.2    Eldar, Y.C.3
  • 13
    • 77949662812 scopus 로고    scopus 로고
    • From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals
    • Apr
    • M. Mishali and Y. C. Eldar, "From theory to practice: Sub-Nyquist sampling of sparse wideband analog signals," IEEE J. Sel. Topics Signal Process., vol. 4, no. 2, pp. 375-391, Apr. 2010.
    • (2010) IEEE J. Sel. Topics Signal Process. , vol.4 , Issue.2 , pp. 375-391
    • Mishali, M.1    Eldar, Y.C.2
  • 14
    • 61549103040 scopus 로고    scopus 로고
    • Blind multi-band signal reconstruction: Compressed sensing for analog signals
    • Mar.
    • M. Mishali and Y. C. Eldar, "Blind multi-band signal reconstruction: Compressed sensing for analog signals," IEEE Trans. Signal Process., vol. 57, no. 3, pp. 993-1009, Mar. 2009.
    • (2009) IEEE Trans. Signal Process. , vol.57 , Issue.3 , pp. 993-1009
    • Mishali, M.1    Eldar, Y.C.2
  • 17
    • 68249141421 scopus 로고    scopus 로고
    • On the reconstruction of block-sparse signals with an optimal number of measurements
    • Aug.
    • M. Stojnic, F. Parvaresh, and B. Hassibi, "On the reconstruction of block-sparse signals with an optimal number of measurements," IEEE Trans. Signal Process., vol. 57, no. 8, pp. 3075-3085, Aug. 2009.
    • (2009) IEEE Trans. Signal Process. , vol.57 , Issue.8 , pp. 3075-3085
    • Stojnic, M.1    Parvaresh, F.2    Hassibi, B.3
  • 18
    • 77952576986 scopus 로고    scopus 로고
    • Block-sparse signals: Uncertainty relations and efficient recovery
    • Jun
    • Y. C. Eldar, P. Kuppinger, and H. Bölcskei, "Block-sparse signals: Uncertainty relations and efficient recovery," IEEE Trans. Signal Process., vol. 58, no. 6, pp. 3042-3054, Jun. 2010.
    • (2010) IEEE Trans. Signal Process. , vol.58 , Issue.6 , pp. 3042-3054
    • Eldar, Y.C.1    Kuppinger, P.2    Bölcskei, H.3
  • 20
    • 80051715867 scopus 로고    scopus 로고
    • Group orthogonal matching pursuit for variable selection and prediction
    • Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams, and A. Culotta, Eds.
    • A. C. Lozano, G.Ś wirszcz, and N. Abe, "Group orthogonal matching pursuit for variable selection and prediction," in Adv. Neural Inf. Process. Syst. 22, Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams, and A. Culotta, Eds., 2009, pp. 1150-1158.
    • (2009) Adv. Neural Inf. Process. Syst. , vol.22 , pp. 1150-1158
    • Lozano, A.C.1    Wirszcz, G.Ś.2    Abe, N.3
  • 21
    • 34548275795 scopus 로고    scopus 로고
    • The Dantzig selector: Statistical estimation when is much larger than
    • E. Candes and T. Tao, "The Dantzig selector: Statistical estimation when is much larger than," Ann. Statist., vol. 35, no. 6, pp. 2313-2351, 2007, with discussion.
    • (2007) Ann. Statist. , vol.35 , Issue.6 , pp. 2313-2351
    • Candes, E.1    Tao, T.2
  • 22
    • 77956742050 scopus 로고    scopus 로고
    • Coherence-based performance guarantees for estimating a sparse vector under random noise
    • Oct
    • Z. Ben-Haim, Y. C. Eldar, and M. Elad, "Coherence-based performance guarantees for estimating a sparse vector under random noise," IEEE Trans. Signal Process., vol. 58, no. 10, pp. 5030-5043, Oct. 2010.
    • (2010) IEEE Trans. Signal Process. , vol.58 , Issue.10 , pp. 5030-5043
    • Ben-Haim, Z.1    Eldar, Y.C.2    Elad, M.3
  • 23
    • 84857213851 scopus 로고    scopus 로고
    • RIP-based near-oracle performance guarantees for SP, CoSaMP, and IHT
    • [Online] submitted for publication
    • R. Giryes and M. Elad, "RIP-based near-oracle performance guarantees for SP, CoSaMP, and IHT," IEEE Trans. Signal Process. [Online]. Available: http://www.cs.technion.ac.il/-elad/publications/journals/2011/NearOracle- IEEETSP.pdf, submitted for publication
    • IEEE Trans. Signal Process.
    • Giryes, R.1    Elad, M.2
  • 24
    • 36249017221 scopus 로고    scopus 로고
    • Average performance analysis for thresholding
    • DOI 10.1109/LSP.2007.903248
    • K. Schnass and P. Vandergheynst, "Average performance analysis for thresholding," IEEE Signal Process. Lett., vol. 14, no. 11, pp. 828-831, Nov. 2007. (Pubitemid 350130772)
    • (2007) IEEE Signal Processing Letters , vol.14 , Issue.11 , pp. 828-831
    • Schnass, K.1    Vandergheynst, P.2
  • 25
    • 73849109362 scopus 로고    scopus 로고
    • Average case analysis of multichannel sparse recovery using convex relaxation
    • Jan
    • Y. C. Eldar and H. Rauhut, "Average case analysis of multichannel sparse recovery using convex relaxation," IEEE Trans. Inf. Theory, vol. 56, no. 1, pp. 505-519, Jan. 2010.
    • (2010) IEEE Trans. Inf. Theory , vol.56 , Issue.1 , pp. 505-519
    • Eldar, Y.C.1    Rauhut, H.2
  • 26
    • 69049120308 scopus 로고    scopus 로고
    • Near-ideal model selection by minimization
    • Oct.
    • E. J. Candès and Y. Plan, "Near-ideal model selection by-minimization," Ann. Statist., vol. 37, no. 5A, pp. 2145-2177, Oct. 2009.
    • (2009) Ann. Statist. , vol.37 , Issue.5 A , pp. 2145-2177
    • Candès, E.J.1    Plan, Y.2
  • 27
    • 77952566605 scopus 로고    scopus 로고
    • Some theoretical results on the grouped variables lasso
    • C. Chesneau and M. Hebiri, "Some theoretical results on the grouped variables lasso," Math. Methods Statist., vol. 17, pp. 317-326, 2008.
    • (2008) Math. Methods Statist. , vol.17 , pp. 317-326
    • Chesneau, C.1    Hebiri, M.2
  • 28
    • 46249088758 scopus 로고    scopus 로고
    • Consistency of the group lasso and multiple kernel learning
    • F. R. Bach, "Consistency of the group lasso and multiple kernel learning," J. Mach. Learn. Res., vol. 9, pp. 1179-1225, 2008.
    • (2008) J. Mach. Learn. Res. , vol.9 , pp. 1179-1225
    • Bach, F.R.1
  • 29
    • 30844445842 scopus 로고    scopus 로고
    • Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit
    • DOI 10.1016/j.sigpro.2005.05.030, PII S0165168405002227, Sparse Approximations in Signal and Image Processing
    • J. A. Tropp, A. C. Gilbert, and M. J. Strauss, "Algorithms for simultaneous sparse approximation. Part I: Greedy pursuit," Signal Process., vol. 86, no. 3, pp. 572-588, 2006. (Pubitemid 43106572)
    • (2006) Signal Processing , vol.86 , Issue.3 , pp. 572-588
    • Tropp, J.A.1    Gilbert, A.C.2    Strauss, M.J.3
  • 30
    • 0027814133 scopus 로고
    • Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition
    • Nov.
    • Y. C. Pati, R. Rezaiifar, and P. S. Krishnaprasad, "Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition," in Proc. 27th Asilomar Conf. Signals, Syst., Comput., Nov. 1993, pp. 40-44.
    • (1993) Proc. 27th Asilomar Conf. Signals, Syst., Comput. , pp. 40-44
    • Pati, Y.C.1    Rezaiifar, R.2    Krishnaprasad, P.S.3
  • 32
    • 0025517126 scopus 로고
    • Lower bounds for parametric estimation with constraints
    • Nov.
    • J. D. Gorman and A. O. Hero, "Lower bounds for parametric estimation with constraints," IEEE Trans. Inf. Theory, vol. 26, no. 6, pp. 1285-1301, Nov. 1990.
    • (1990) IEEE Trans. Inf. Theory , vol.26 , Issue.6 , pp. 1285-1301
    • Gorman, J.D.1    Hero, A.O.2
  • 33
    • 0032123107 scopus 로고    scopus 로고
    • On the Cramér-Rao bound under parametric constraints
    • Jul.
    • P. Stoica and B. C. Ng, "On the Cramér-Rao bound under parametric constraints," IEEE Signal Process. Lett., vol. 5, no. 7, pp. 177-179, Jul. 1998.
    • (1998) IEEE Signal Process. Lett. , vol.5 , Issue.7 , pp. 177-179
    • Stoica, P.1    Ng, B.C.2
  • 34
    • 65649106479 scopus 로고    scopus 로고
    • On the constrained Cramér-Rao bound with a singular Fisher information matrix
    • Jun.
    • Z. Ben-Haim and Y. C. Eldar, "On the constrained Cramér-Rao bound with a singular Fisher information matrix," IEEE Signal Process. Lett., vol. 16, no. 6, pp. 453-456, Jun. 2009.
    • (2009) IEEE Signal Process. Lett. , vol.16 , Issue.6 , pp. 453-456
    • Ben-Haim, Z.1    Eldar, Y.C.2
  • 35
    • 77952570699 scopus 로고    scopus 로고
    • The Cramér-Rao bound for estimating a sparse parameter vector
    • Jun
    • Z. Ben-Haim and Y. C. Eldar, "The Cramér-Rao bound for estimating a sparse parameter vector," IEEE Trans. Signal Process., vol. 58, no. 6, pp. 3384-3389, Jun. 2010.
    • (2010) IEEE Trans. Signal Process. , vol.58 , Issue.6 , pp. 3384-3389
    • Ben-Haim, Z.1    Eldar, Y.C.2
  • 36
  • 37
    • 84972535723 scopus 로고
    • Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem
    • D. G. Feingold and R. S. Varga, "Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem," Pacific J. Math., vol. 12, no. 4, pp. 1241-1250, 1962.
    • (1962) Pacific J. Math. , vol.12 , Issue.4 , pp. 1241-1250
    • Feingold, D.G.1    Varga, R.S.2
  • 38
    • 84947402121 scopus 로고
    • Rectangular confidence regions for the means of multivariate normal distributions
    • Jun.
    • Z. Sidák, "Rectangular confidence regions for the means of multivariate normal distributions," J. Amer. Statist. Assoc., vol. 62, no. 318, pp. 626-633, Jun. 1967.
    • (1967) J. Amer. Statist. Assoc. , vol.62 , Issue.318 , pp. 626-633
    • Sidák, Z.1
  • 39
    • 84968476146 scopus 로고
    • The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities
    • T. W. Anderson, "The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities," in Proc. Amer. Math. Soc., 1955, vol. 6, pp. 170-176.
    • (1955) Proc. Amer. Math. Soc. , vol.6 , pp. 170-176
    • Anderson, T.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.