메뉴 건너뛰기




Volumn 60, Issue 1, 2012, Pages 29-38

Unified framework to regularized covariance estimation in scaled Gaussian models

Author keywords

Covariance estimation; hidden convexity; optimization on manifolds; regularization; robust statistics

Indexed keywords

COVARIANCE ESTIMATION; HIDDEN CONVEXITY; OPTIMIZATION ON MANIFOLDS; REGULARIZATION; ROBUST STATISTICS;

EID: 84555190425     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2011.2170685     Document Type: Article
Times cited : (92)

References (46)
  • 1
    • 0030193445 scopus 로고    scopus 로고
    • Two decades of array signal processing research: The parametric approach
    • Jul.
    • H. Krim and M. Viberg, "Two decades of array signal processing research: The parametric approach," IEEE Signal Process. Mag., vol. 13, no. 4, pp. 67-94, Jul. 1996.
    • (1996) IEEE Signal Process. Mag. , vol.13 , Issue.4 , pp. 67-94
    • Krim, H.1    Viberg, M.2
  • 2
    • 85032751504 scopus 로고    scopus 로고
    • Research issues in genomic signal processing
    • Nov
    • E. R. Dougherty, A. Datta, and C. Sima, "Research issues in genomic signal processing," IEEE Signal Process. Mag., vol. 22, no. 6, pp. 46-68, Nov. 2005.
    • (2005) IEEE Signal Process. Mag. , vol.22 , Issue.6 , pp. 46-68
    • Dougherty, E.R.1    Datta, A.2    Sima, C.3
  • 3
    • 0000406169 scopus 로고
    • Empirical bayes estimation of the multivariate normal covariance matrix
    • L. R. Haff, "Empirical Bayes estimation of the multivariate normal covariance matrix," Ann. Statist., vol. 8, no. 3, pp. 586-597, 1980.
    • (1980) Ann. Statist. , vol.8 , Issue.3 , pp. 586-597
    • Haff, L.R.1
  • 5
    • 0346961488 scopus 로고    scopus 로고
    • A well-conditioned estimator for large-dimensional covariance matrices
    • Feb.
    • O. Ledoit and M. Wolf, "A well-conditioned estimator for large-dimensional covariance matrices," J. Multivar. Anal., vol. 88, no. 2, pp. 365-411, Feb. 2004.
    • (2004) J. Multivar. Anal. , vol.88 , Issue.2 , pp. 365-411
    • Ledoit, O.1    Wolf, M.2
  • 6
    • 77956726241 scopus 로고    scopus 로고
    • Shrinkage algorithms forMMSEcovariance estimation
    • Y. Chen, A. Wiesel, Y. C. Eldar, and A. O. Hero, "Shrinkage algorithms forMMSEcovariance estimation," IEEE Trans. Signal Process., vol. 58, no. 10, pp. 5016-5029, 2010.
    • (2010) IEEE Trans. Signal Process. , vol.58 , Issue.10 , pp. 5016-5029
    • Chen, Y.1    Wiesel, A.2    Eldar, Y.C.3    Hero, A.O.4
  • 7
    • 27844521293 scopus 로고    scopus 로고
    • A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics
    • J. Schafer and K. Strimmer, "A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics," Statist. Appl. Genetics Mol. Biol., vol. 4, no. 1, pp. 1175-, 2005.
    • (2005) Statist. Appl. Genetics Mol. Biol. , vol.4 , Issue.1 , pp. 1175
    • Schafer, J.1    Strimmer, K.2
  • 8
    • 44849087294 scopus 로고    scopus 로고
    • On using a priori knowledge in space-time adaptive processing
    • P. Stoica, L. Jian, Z. Xumin, and J. R. Guerci, "On using a priori knowledge in space-time adaptive processing," IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2598-2602, 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.6 , pp. 2598-2602
    • Stoica, P.1    Jian, L.2    Xumin, Z.3    Guerci, J.R.4
  • 9
    • 79959893120 scopus 로고    scopus 로고
    • Knowledge-aided covariance matrix estimation and adaptive detection in compound-gaussian noise
    • Oct.
    • F. Bandiera, O. Besson, and G. Ricci, "Knowledge-aided covariance matrix estimation and adaptive detection in compound-Gaussian noise," IEEE Trans. Signal Process., vol. 58, no. 10, pp. 5391-5396, Oct. 2010.
    • (2010) IEEE Trans. Signal Process. , vol.58 , Issue.10 , pp. 5391-5396
    • Bandiera, F.1    Besson, O.2    Ricci, G.3
  • 13
    • 20544451350 scopus 로고    scopus 로고
    • Statistical analysis of the nonhomogeneity detector for non-gaussian interference backgrounds
    • M. Rangaswamy, "Statistical analysis of the nonhomogeneity detector for non-Gaussian interference backgrounds," IEEE Trans. Signal Process., vol. 53, no. 6, pp. 2101-2111, 2005.
    • (2005) IEEE Trans. Signal Process. , vol.53 , Issue.6 , pp. 2101-2111
    • Rangaswamy, M.1
  • 14
    • 33749376774 scopus 로고    scopus 로고
    • Maximum likelihood estimation of compound-gaussian clutter and target parameters
    • J.Wang, A. Dogandzic, and A. Nehorai, "Maximum likelihood estimation of compound-Gaussian clutter and target parameters," IEEE Trans. Signal Process., vol. 54, no. 10, pp. 3884-3898, 2006.
    • (2006) IEEE Trans. Signal Process. , vol.54 , Issue.10 , pp. 3884-3898
    • Wang, J.1    Dogandzic, A.2    Nehorai, A.3
  • 15
    • 0036887912 scopus 로고    scopus 로고
    • Covariance matrix estimation for CFAR detection in correlated heavy tailed clutter
    • F. Gini and M. Greco, "Covariance matrix estimation for CFAR detection in correlated heavy tailed clutter," Signal Process., vol. 82, no. 12, pp. 1847-1859, 2002.
    • (2002) Signal Process. , vol.82 , Issue.12 , pp. 1847-1859
    • Gini, F.1    Greco, M.2
  • 16
    • 0036821858 scopus 로고    scopus 로고
    • Vector subspace detection in compound- gaussian clutter part i: Survey and new results
    • F. Gini and A. Farina, "Vector subspace detection in compound- Gaussian clutter. Part I: Survey and new results," IEEE Trans. Aerosp. Electron. Syst., , vol. 38, no. 4, pp. 1295-1311, 2002.
    • (2002) IEEE Trans. Aerosp. Electron. Syst. , vol.38 , Issue.4 , pp. 1295-1311
    • Gini, F.1    Farina, A.2
  • 17
    • 44849115615 scopus 로고    scopus 로고
    • Performance analysis of covariance matrix estimates in impulsive noise
    • F. Pascal, P. Forster, J. P. Ovarlez, and P. Larzabal, "Performance analysis of covariance matrix estimates in impulsive noise," IEEE Trans. Signal Process., vol. 56, no. 6, pp. 2206-2217, 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.6 , pp. 2206-2217
    • Pascal, F.1    Forster, P.2    Ovarlez, J.P.3    Larzabal, P.4
  • 18
    • 78650862100 scopus 로고    scopus 로고
    • Coherency matrix estimation of heterogeneous clutter in high-resolution polarimetric SAR images
    • G. Vasile, J. P. Ovarlez, F. Pascal, and C. Tison, "Coherency matrix estimation of heterogeneous clutter in high-resolution polarimetric SAR images," IEEE Trans. Geosci. Remote Sens., vol. 48, no. 4, pp. 1809-1826, 2010.
    • (2010) IEEE Trans. Geosci. Remote Sens. , vol.48 , Issue.4 , pp. 1809-1826
    • Vasile, G.1    Ovarlez, J.P.2    Pascal, F.3    Tison, C.4
  • 19
    • 0031069693 scopus 로고    scopus 로고
    • Sub-optimum coherent radar detection in a mixture of k-distributed and gaussian clutter
    • F. Gini, "Sub-optimum coherent radar detection in a mixture of K-distributed and Gaussian clutter," in Proc. Inst. Elect. Eng.-Radar, Sonar, Navig.-IET, 2002, vol. 144, pp. 39-48.
    • (2002) Proc. Inst. Elect. Eng.-Radar Sonar Navig.-IET , vol.144 , pp. 39-48
    • Gini, F.1
  • 20
    • 0029291208 scopus 로고    scopus 로고
    • Asymptotically optimum radar detection in compound-gaussian clutter
    • E. Conte, M. Lops, and G. Ricci, "Asymptotically optimum radar detection in compound-Gaussian clutter," IEEE Trans. Aerosp. Electron. Syst., vol. 31, no. 2, pp. 617-625, 2002.
    • (2002) IEEE Trans. Aerosp. Electron. Syst. , vol.31 , Issue.2 , pp. 617-625
    • Conte, E.1    Lops, M.2    Ricci, G.3
  • 21
    • 0000342767 scopus 로고
    • A distribution-free M-estimator of multivariate scatter
    • D. E. Tyler, "A distribution-free M-estimator of multivariate scatter," Ann. Statist., vol. 15, no. 1, pp. 234-251, 1987.
    • (1987) Ann. Statist. , vol.15 , Issue.1 , pp. 234-251
    • Tyler, D.E.1
  • 22
    • 0036683911 scopus 로고    scopus 로고
    • Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection
    • E. Conte, A. De'Maio, and G. Ricci, "Recursive estimation of the covariance matrix of a compound-Gaussian process and its application to adaptive CFAR detection," IEEE Trans. Signal Process., vol. 50, no. 8, pp. 1908-1915, 2002.
    • (2002) IEEE Trans. Signal Process. , vol.50 , Issue.8 , pp. 1908-1915
    • Conte, E.1    Demaio, A.2    Ricci, G.3
  • 23
    • 37749041370 scopus 로고    scopus 로고
    • Covariance structure maximum-likelihood estimates in compound Gaussian noise: Existence and algorithm analysis
    • Jan.
    • F. Pascal, Y. Chitour, J.-P. Ovarlez, P. Forster, and P. Larzabal, "Covariance structure maximum-likelihood estimates in compound Gaussian noise: Existence and algorithm analysis," IEEE Trans. Signal Process., vol. 56, no. 1, pp. 34-48, Jan. 2008.
    • (2008) IEEE Trans. Signal Process. , vol.56 , Issue.1 , pp. 34-48
    • Pascal, F.1    Chitour, Y.2    Ovarlez, J.-P.3    Forster, P.4    Larzabal, P.5
  • 24
    • 70350566064 scopus 로고    scopus 로고
    • A generalization of tylers-estimators to the case of incomplete data
    • G. Frahm and U. Jaekel, "A generalization of Tyler's estimators to the case of incomplete data," Comput. Statist. Data Anal., vol. 54, no. 2, pp. 374-393, 2010.
    • (2010) Comput. Statist. Data Anal. , vol.54 , Issue.2 , pp. 374-393
    • Frahm, G.1    Jaekel, U.2
  • 26
    • 7744247580 scopus 로고    scopus 로고
    • On tylers M -functional of scatter in high dimension
    • L. Dumbgen, "On Tyler's M -functional of scatter in high dimension," Ann. Inst. Statist. Math., vol. 50, no. 3, pp. 471-491, 1998.
    • (1998) Ann. Inst. Statist. Math. , vol.50 , Issue.3 , pp. 471-491
    • Dumbgen, L.1
  • 27
    • 34547511794 scopus 로고    scopus 로고
    • Diagonally loaded normalized sample matrix inversion LNSMI for outlier-resistant adaptive filtering
    • ICASSP), Apr. 15-20, 10.1109/ICASSP.2007.366877.
    • Y. I. Abramovich and N. K. Spencer, "Diagonally loaded normalized sample matrix inversion (LNSMI) for outlier-resistant adaptive filtering," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Process. (ICASSP), Apr. 15-20, 2007, vol. 3, pp. III-1105-III-1108, doi: 10.1109/ICASSP.2007.366877.
    • (2007) Proc. IEEE Int. Conf. Acoustics Speech Signal Process. , vol.3
    • Abramovich, Y.I.1    Spencer, N.K.2
  • 28
    • 78650161161 scopus 로고    scopus 로고
    • Robust Shrinkage estimation of high-dimensional covariance matrices
    • to be published.
    • Y. Chen, A. Wiesel, and A. O. Hero, III, "Robust Shrinkage estimation of high-dimensional covariance matrices," IEEE Trans. Signal Process., 2010, to be published.
    • (2010) IEEE Trans. Signal Process.
    • Chen, Y.1    Wiesel, A.2    Hero Iii, A.O.3
  • 29
    • 7044249783 scopus 로고    scopus 로고
    • Angular gaussian and cauchy estimation
    • C. Auderset, C. Mazza, and E. A. Ruh, "Angular Gaussian and Cauchy estimation," J. Multivar. Anal., vol. 93, no. 1, pp. 180-197, 2005.
    • (2005) J. Multivar. Anal. , vol.93 , Issue.1 , pp. 180-197
    • Auderset, C.1    Mazza, C.2    Ruh, E.A.3
  • 32
    • 36749072615 scopus 로고    scopus 로고
    • Majorization- Minimization algorithms for wavelet-based image restoration
    • M. A. T. Figueiredo, J. M. Bioucas-Dias, and R. D. Nowak, "Majorization- Minimization algorithms for wavelet-based image restoration," IEEE Trans. Image Process., vol. 16, no. 12, pp. 2980-2991, 2007.
    • (2007) IEEE Trans. Image Process. , vol.16 , Issue.12 , pp. 2980-2991
    • Figueiredo, M.A.T.1    Bioucas-Dias, J.M.2    Nowak, R.D.3
  • 33
    • 0036489046 scopus 로고    scopus 로고
    • Comparison of discrimination methods for the classification of tumors using gene expression data
    • S. Dudoit, J. Fridlyand, and T. P. Speed, "Comparison of discrimination methods for the classification of tumors using gene expression data," J. Amer. Statist. Assoc., vol. 97, no. 457, pp. 77-87, 2002.
    • (2002) J. Amer. Statist. Assoc. , vol.97 , Issue.457 , pp. 77-87
    • Dudoit, S.1    Fridlyand, J.2    Speed, T.P.3
  • 34
    • 34249812361 scopus 로고    scopus 로고
    • A tutorial on geometric programming
    • S. Boyd, S. J. Kim, L. Vandenberghe, and A. Hassibi, "A tutorial on geometric programming," Optim. Eng., vol. 8, no. 1, pp. 67-127, 2007.
    • (2007) Optim. Eng. , vol.8 , Issue.1 , pp. 67-127
    • Boyd, S.1    Kim, S.J.2    Vandenberghe, L.3    Hassibi, A.4
  • 36
    • 18844440455 scopus 로고    scopus 로고
    • Covariance subspace and intrinsic cramér-rao bounds
    • S. T. Smith, "Covariance, subspace, and intrinsic Cramér-Rao bounds," IEEE Trans. Signal Process., vol. 53, no. 5, pp. 1610-1630, 2005.
    • (2005) IEEE Trans. Signal Process. , vol.53 , Issue.5 , pp. 1610-1630
    • Smith, S.T.1
  • 37
    • 0026136793 scopus 로고
    • Geodesic convexity in nonlinear optimization
    • T. Rapcsak, "Geodesic convexity in nonlinear optimization," J. Optim. Theory Appl., vol. 69, no. 1, pp. 169-183, 1991.
    • (1991) J. Optim. Theory Appl. , vol.69 , Issue.1 , pp. 169-183
    • Rapcsak, T.1
  • 39
    • 22944439423 scopus 로고    scopus 로고
    • A differential geometric approach to the geometric mean of symmetric positive-definite matrices
    • M. Moakher, "A differential geometric approach to the geometric mean of symmetric positive-definite matrices," SIAM J. Matrix Anal. Appl., vol. 26, no. 3, pp. 735-747, 2005.
    • (2005) SIAM J. Matrix Anal. Appl. , vol.26 , Issue.3 , pp. 735-747
    • Moakher, M.1
  • 40
    • 61949083544 scopus 로고    scopus 로고
    • Innovative tools for radar signal processing based on cartans geometry of SPD matrices & information geometry
    • F. Barbaresco, "Innovative tools for radar signal processing based on Cartan's geometry of SPD matrices & information geometry," in Proc. IEEE Radar Conf. (RADAR), 2008, pp. 1-6.
    • (2008) Proc. IEEE Radar Conf. Radar , pp. 1-6
    • Barbaresco, F.1
  • 41
    • 78650181676 scopus 로고    scopus 로고
    • Differential feedback of MIMO channel gram matrices based on geodesic curves
    • Dec.
    • Sacristá, D. Murga, and A. Pascual-Iserte, "Differential feedback of MIMO channel Gram matrices based on geodesic curves," IEEE Trans. Wireless Commun., vol. 9, no. 12, pp. 3714-3727, Dec. 2010.
    • (2010) IEEE Trans. Wireless Commun. , vol.9 , Issue.12 , pp. 3714-3727
    • Murga, S.D.1    Pascual-Iserte, A.2
  • 42
    • 84555199186 scopus 로고    scopus 로고
    • On a class of nonconvex problems where all local minima are global
    • L. Liberti, "On a class of nonconvex problems where all local minima are global," Publications de l'Institut Mathematique, vol. 76, no. 90, pp. 101-109, 2004.
    • (2004) Publications de LInstitut Mathematique , vol.76 , Issue.90 , pp. 101-109
    • Liberti, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.