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Volumn 49, Issue 2, 2003, Pages 411-424

A generalized Levinson algorithm for covariance extension with application to multiscale autoregressive modeling

Author keywords

Chordal graphs; Covariance completion; Covariance extension; Levinson's algorithm; Maximum entropy; Multiscale autoregressive (MAR) models; Reflection coefficients

Indexed keywords

COMPUTATIONAL COMPLEXITY; GRAPH THEORY; REGRESSION ANALYSIS; TIME SERIES ANALYSIS;

EID: 0037321011     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2002.807315     Document Type: Article
Times cited : (8)

References (52)
  • 3
    • 0004147631 scopus 로고
    • Ph.D. dissertation, Stanford Univ., Stanford, CA
    • _, "Maximum entropy spectral analysis," Ph.D. dissertation, Stanford Univ., Stanford, CA, 1975.
    • (1975) Maximum Entropy Spectral Analysis
  • 4
    • 0028398860 scopus 로고
    • Multiscale recursive estimation, data fusion, and regularization
    • Mar.
    • K. Chou, A. Willsky, and A. Benveniste, "Multiscale recursive estimation, data fusion, and regularization," IEEE Trans. Automat. Contr., vol. 39, pp. 464-478, Mar. 1994.
    • (1994) IEEE Trans. Automat. Contr. , vol.39 , pp. 464-478
    • Chou, K.1    Willsky, A.2    Benveniste, A.3
  • 5
    • 0028400404 scopus 로고
    • Multiscale systems, Kalman filters, and Riccati equations
    • Mar.
    • K. Chou, A. Willsky, and R. Nikoukhah, "Multiscale systems, Kalman filters, and Riccati equations," IEEE Trans. Automat. Contr., vol. 39, pp. 479-492, Mar. 1994.
    • (1994) IEEE Trans. Automat. Contr. , vol.39 , pp. 479-492
    • Chou, K.1    Willsky, A.2    Nikoukhah, R.3
  • 8
    • 0030734976 scopus 로고    scopus 로고
    • A multiresolution methodology for signal-level fusion and data assimilation with applications to remote sensing
    • Jan.
    • M. Daniel and A. Willsky, "A multiresolution methodology for signal-level fusion and data assimilation with applications to remote sensing," Proc. IEEE, vol. 85, pp. 164-180, Jan. 1997.
    • (1997) Proc. IEEE , vol.85 , pp. 164-180
    • Daniel, M.1    Willsky, A.2
  • 9
    • 0013258141 scopus 로고    scopus 로고
    • Travel time estimation using a multiscale stochastic framework
    • May
    • M. Daniel, A. Willsky, and D. McLaughlin, "Travel time estimation using a multiscale stochastic framework," Adv. Water Resources, vol. 23, no. 6, pp. 571-665, May 2000.
    • (2000) Adv. Water Resources , vol.23 , Issue.6 , pp. 571-665
    • Daniel, M.1    Willsky, A.2    McLaughlin, D.3
  • 10
    • 0032623730 scopus 로고    scopus 로고
    • Multiscale autoregressive models and wavelets
    • Apr.
    • K. Daoudi, A. Frakt, and A. Willsky, "Multiscale autoregressive models and wavelets," IEEE Trans. Inform. Theory, vol. 45, pp. 828-845, Apr. 1999.
    • (1999) IEEE Trans. Inform. Theory , vol.45 , pp. 828-845
    • Daoudi, K.1    Frakt, A.2    Willsky, A.3
  • 11
    • 0001637134 scopus 로고
    • Markov fields and log-linear interaction models for contingency tables
    • J. Darroch, S. Lauritzen, and T. Speed, "Markov fields and log-linear interaction models for contingency tables," Ann. Statist., vol. 8, no. 3, pp. 522-539, 1980.
    • (1980) Ann. Statist. , vol.8 , Issue.3 , pp. 522-539
    • Darroch, J.1    Lauritzen, S.2    Speed, T.3
  • 13
    • 0029271212 scopus 로고
    • Multiresolution optimal interpolation and statistical analysis of TOPEX/POSEIDON satellite altimetry
    • Mar.
    • P. Fieguth, W. Karl, A. Willsky, and C. Wunsch, "Multiresolution optimal interpolation and statistical analysis of TOPEX/POSEIDON satellite altimetry," IEEE Trans. Geosci. Remote Sensing, vol. 33, pp. 280-292, Mar. 1995.
    • (1995) IEEE Trans. Geosci. Remote Sensing , vol.33 , pp. 280-292
    • Fieguth, P.1    Karl, W.2    Willsky, A.3    Wunsch, C.4
  • 14
    • 0000363684 scopus 로고    scopus 로고
    • Mapping Mediterranean altimeter data with a multiresolution optimal interpolation algorithm
    • Apr.
    • P. Fieguth, D. Menemenlis, T. Ho, A. Willsky, and C. Wunsch, "Mapping Mediterranean altimeter data with a multiresolution optimal interpolation algorithm," J. Atmosph. Ocean. Technol., vol. 15, pp. 535-546, Apr. 1998.
    • (1998) J. Atmosph. Ocean. Technol. , vol.15 , pp. 535-546
    • Fieguth, P.1    Menemenlis, D.2    Ho, T.3    Willsky, A.4    Wunsch, C.5
  • 15
    • 0030144705 scopus 로고    scopus 로고
    • Fractal estimation using models on multiscale trees
    • May
    • P. Fieguth and A. Willsky, "Fractal estimation using models on multiscale trees," IEEE Trans. Signal Processing, vol. 44, pp. 1297-1300, May 1996.
    • (1996) IEEE Trans. Signal Processing , vol.44 , pp. 1297-1300
    • Fieguth, P.1    Willsky, A.2
  • 16
    • 0032070632 scopus 로고    scopus 로고
    • Efficient multiresolution counter-paris to variational methods for surface reconstruction
    • May
    • P. Fieguth, A. Willsky, and W. Karl, "Efficient multiresolution counter-paris to variational methods for surface reconstruction," Comput. Vision Image Understand., vol. 70, no. 2, pp. 157-176, May 1998.
    • (1998) Comput. Vision Image Understand. , vol.70 , Issue.2 , pp. 157-176
    • Fieguth, P.1    Willsky, A.2    Karl, W.3
  • 17
    • 0030779419 scopus 로고    scopus 로고
    • Multiscale segmentation and anomaly enhancement of SAR imagery
    • Jan.
    • C. Fosgate, H. Krim, W. Irving, and A. Willsky, "Multiscale segmentation and anomaly enhancement of SAR imagery," IEEE Trans. Image Processing, vol. 6, pp. 7-20, Jan. 1997.
    • (1997) IEEE Trans. Image Processing , vol.6 , pp. 7-20
    • Fosgate, C.1    Krim, H.2    Irving, W.3    Willsky, A.4
  • 19
    • 0035304538 scopus 로고    scopus 로고
    • Computationally efficient stochastic realization for internal multiscale autoregressive models
    • A. Frakt and A. Willsky, "Computationally efficient stochastic realization for internal multiscale autoregressive models," Multidim. Syst. Signal Processing, vol. 12, pp. 109-142, 2001.
    • (2001) Multidim. Syst. Signal Processing , vol.12 , pp. 109-142
    • Frakt, A.1    Willsky, A.2
  • 20
    • 0020187982 scopus 로고
    • Lattice methods for spectral estimation
    • Sept.
    • B. Friedlander, "Lattice methods for spectral estimation," Proc. IEEE, vol. 70, pp. 990-1017, Sept. 1982.
    • (1982) Proc. IEEE , vol.70 , pp. 990-1017
    • Friedlander, B.1
  • 21
    • 0039627862 scopus 로고    scopus 로고
    • Positive definite completions and determinant maximization
    • W. Glunt, T. Hayden, C. Johnson, and P. Tarazaga, "Positive definite completions and determinant maximization," Linear Alg. Its Applic., vol. 288, pp. 1-10, 1999.
    • (1999) Linear Alg. Its Applic. , vol.288 , pp. 1-10
    • Glunt, W.1    Hayden, T.2    Johnson, C.3    Tarazaga, P.4
  • 24
    • 0013208135 scopus 로고
    • A remark on the correspondence between the maximum-entropy method and the autoregressive model
    • Nov.
    • J. Grandell, M. Hamrud, and P. Toll, "A remark on the correspondence between the maximum-entropy method and the autoregressive model," IEEE Trans. Inform. Theory, vol. IT-26, pp. 750-751, Nov. 1980.
    • (1980) IEEE Trans. Inform. Theory , vol.IT-26 , pp. 750-751
    • Grandell, J.1    Hamrud, M.2    Toll, P.3
  • 25
    • 47849109874 scopus 로고
    • Positive definite completions of partial Hermitian matrices
    • R. Grone, C. Johnson, E. Sa, and H. Wolkowicz, "Positive definite completions of partial Hermitian matrices," Linear Alg. Its Applic., vol. 58, pp. 109-124, 1984.
    • (1984) Linear Alg. Its Applic. , vol.58 , pp. 109-124
    • Grone, R.1    Johnson, C.2    Sa, E.3    Wolkowicz, H.4
  • 27
    • 0029750985 scopus 로고    scopus 로고
    • Multiresolution stochastic models for the efficient solution of large-scale space-time estimation problems
    • Atlanta, GA, May
    • T. Ho, P. Fieguth, and A. Willsky, "Multiresolution stochastic models for the efficient solution of large-scale space-time estimation problems," in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, vol. 6, Atlanta, GA, May 1996, pp. 3097-3100.
    • (1996) Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing , vol.6 , pp. 3097-3100
    • Ho, T.1    Fieguth, P.2    Willsky, A.3
  • 28
    • 0004151494 scopus 로고
    • Cambridge, U.K.: Cambridge Univ. Press
    • R. Horn and C. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.
    • (1985) Matrix Analysis
    • Horn, R.1    Johnson, C.2
  • 29
    • 0003335420 scopus 로고
    • Maximum entropy spectral analysis and ARMA processes
    • Mar.
    • S. Ihara, "Maximum entropy spectral analysis and ARMA processes," IEEE Trans. Inform. Theory, vol. IT-30, pp. 377-380, Mar. 1984.
    • (1984) IEEE Trans. Inform. Theory , vol.IT-30 , pp. 377-380
    • Ihara, S.1
  • 30
    • 0031258567 scopus 로고    scopus 로고
    • A multiresolution approach to discriminating targets from clutter in SAR imagery
    • Oct.
    • W. Irving, L. Novak, and A. Willsky, "A multiresolution approach to discriminating targets from clutter in SAR imagery," IEEE Trans. Aerosp. Electron. Syst., vol. 33, pp. 1157-1169, Oct. 1997.
    • (1997) IEEE Trans. Aerosp. Electron. Syst. , vol.33 , pp. 1157-1169
    • Irving, W.1    Novak, L.2    Willsky, A.3
  • 31
    • 0035471665 scopus 로고    scopus 로고
    • A canonical correlations approach to multiscale stochastic realization
    • Oct.
    • W. Irving and A. Willsky, "A canonical correlations approach to multiscale stochastic realization," IEEE Trans. Automat. Contr., vol. 46, pp. 1514-1528, Oct. 2001.
    • (2001) IEEE Trans. Automat. Contr. , vol.46 , pp. 1514-1528
    • Irving, W.1    Willsky, A.2
  • 32
    • 0020187981 scopus 로고
    • On the rationale of maximum-entropy methods
    • Sept.
    • E. Jaynes, "On the rationale of maximum-entropy methods," Proc. IEEE, vol. 70, pp. 939-952, Sept. 1982.
    • (1982) Proc. IEEE , vol.70 , pp. 939-952
    • Jaynes, E.1
  • 33
    • 0000374855 scopus 로고
    • Matrix completion problems: A survey
    • Matrix Theory and Applications, Providence, RI
    • C. Johnson, "Matrix completion problems: A survey," in Matrix Theory and Applications, Proceedings of Symposia in Applied Mathematics. Providence, RI, 1990.
    • (1990) Proceedings of Symposia in Applied Mathematics
    • Johnson, C.1
  • 35
    • 0032653576 scopus 로고    scopus 로고
    • Tree-structured models of parameter dependence for rapid adaptation in large vocabulary conversational speech recognition
    • Phoenix, AZ
    • A. Kannan and S. Khudanpur, "Tree-structured models of parameter dependence for rapid adaptation in large vocabulary conversational speech recognition," in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing, Phoenix, AZ, 1999.
    • (1999) Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing
    • Kannan, A.1    Khudanpur, S.2
  • 36
    • 0013208309 scopus 로고    scopus 로고
    • Modeling dependence in adaptation of acoustic models using multiscale tree processes
    • A. Kannan and M. Ostendorf, "Modeling dependence in adaptation of acoustic models using multiscale tree processes," in Proc. EUROSPEECH, 1997, pp. 1863-1866.
    • (1997) Proc. EUROSPEECH , pp. 1863-1866
    • Kannan, A.1    Ostendorf, M.2
  • 37
    • 0033079988 scopus 로고    scopus 로고
    • Hierarchical stochastic modeling of SAR imagery for segmentation/compression
    • Feb.
    • A. Kim and H. Krim, "Hierarchical stochastic modeling of SAR imagery for segmentation/compression," IEEE Trans. Signal Processing, vol. 47, pp. 458-468, Feb. 1999.
    • (1999) IEEE Trans. Signal Processing , vol.47 , pp. 458-468
    • Kim, A.1    Krim, H.2
  • 38
    • 0032757960 scopus 로고    scopus 로고
    • A multiple scale state-space model for characterizing subgrid scale variability of near-surface soil moisture
    • Jan.
    • P. Kumar, "A multiple scale state-space model for characterizing subgrid scale variability of near-surface soil moisture," IEEE Trans. Geosci. Remote Sensing, vol. 37, pp. 182-197, Jan. 1999.
    • (1999) IEEE Trans. Geosci. Remote Sensing , vol.37 , pp. 182-197
    • Kumar, P.1
  • 41
    • 0024667926 scopus 로고
    • Multidimensional maximum-entropy covariance extension
    • May
    • H. Lev-Ari, S. Parker, and T. Kailath, "Multidimensional maximum-entropy covariance extension," IEEE Trans. Inform. Theory, vol. 35, pp. 497-508, May 1989.
    • (1989) IEEE Trans. Inform. Theory , vol.35 , pp. 497-508
    • Lev-Ari, H.1    Parker, S.2    Kailath, T.3
  • 42
    • 0028204562 scopus 로고
    • Efficient multiscale regularization with applications to the computation of optical flow
    • Jan.
    • M. Luettgen, W. Karl, and A. Willsky, "Efficient multiscale regularization with applications to the computation of optical flow," IEEE Trans. Image Processing, vol. 3, pp. 41-64, Jan. 1994.
    • (1994) IEEE Trans. Image Processing , vol.3 , pp. 41-64
    • Luettgen, M.1    Karl, W.2    Willsky, A.3
  • 44
    • 0029253301 scopus 로고
    • Likelihood calculation for a class of multiscale stochastic models, with application to texture discrimination
    • Feb.
    • M. Luettgen and A. Willsky, "Likelihood calculation for a class of multiscale stochastic models, with application to texture discrimination," IEEE Trans. Image Processing, vol. 4, pp. 194-207, Feb. 1995.
    • (1995) IEEE Trans. Image Processing , vol.4 , pp. 194-207
    • Luettgen, M.1    Willsky, A.2
  • 45
    • 0013304879 scopus 로고
    • Linearly constrained positive definite completions
    • M. Lundquist and C. Johnson, "Linearly constrained positive definite completions," Linear Alg. Its Applic., vol. 150, pp. 195-208, 1991.
    • (1991) Linear Alg. Its Applic. , vol.150 , pp. 195-208
    • Lundquist, M.1    Johnson, C.2
  • 46
    • 0019701695 scopus 로고
    • Maximum entropy and spectral estimation: A review
    • Dec.
    • A. Papoulis, "Maximum entropy and spectral estimation: A review," IEEE Trans. Acoust., Speech, Signal Processing, vol. ASSP-29, pp. 1176-1186, Dec. 1981.
    • (1981) IEEE Trans. Acoust., Speech, Signal Processing , vol.ASSP-29 , pp. 1176-1186
    • Papoulis, A.1
  • 47
    • 0001580189 scopus 로고
    • Algorithmic aspects of vertex elimination on graphs
    • June
    • D. Rose, R. Tarjan, and G. Lueker, "Algorithmic aspects of vertex elimination on graphs," SIAM J. Comput., vol. 5, no. 2, pp. 266-283, June 1976.
    • (1976) SIAM J. Comput. , vol.5 , Issue.2 , pp. 266-283
    • Rose, D.1    Tarjan, R.2    Lueker, G.3
  • 50
    • 0001568882 scopus 로고
    • Ganssian Markov distributions of finite graphs
    • T. Speed and H. Kiiveri, "Ganssian Markov distributions of finite graphs," Ann. Statist., vol. 14, no. 1, pp. 138-150, 1986.
    • (1986) Ann. Statist. , vol.14 , Issue.1 , pp. 138-150
    • Speed, T.1    Kiiveri, H.2
  • 52
    • 0021473698 scopus 로고
    • Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs
    • R. Tarjan and M. Yannakakis, "Simple linear-time algorithms to test chordality of graphs, test acyclicity of hypergraphs, and selectively reduce acyclic hypergraphs," SIAM J. Comput., vol. 13, no. 3, pp. 566-579, 1984.
    • (1984) SIAM J. Comput. , vol.13 , Issue.3 , pp. 566-579
    • Tarjan, R.1    Yannakakis, M.2


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