메뉴 건너뛰기




Volumn 15, Issue 3, 2006, Pages 604-613

Kronecker product approximation for preconditioning in three-dimensional imaging applications

Author keywords

Image restoration; Iterative methods; Kronecker products; Orthogonal tensor decomposition; Preconditioning; Singular value decomposition (SVD)

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ITERATIVE METHODS; MATRIX ALGEBRA; TENSORS;

EID: 32944458698     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2005.863112     Document Type: Article
Times cited : (48)

References (35)
  • 5
    • 32944481714 scopus 로고    scopus 로고
    • National Research Council Institute of Medicine, Washington, DC: National Academy Press
    • National Research Council Institute of Medicine, Mathematics and Physics of Emerging Biomedical Imaging. Washington, DC: National Academy Press, 1997.
    • (1997) Mathematics and Physics of Emerging Biomedical Imaging
  • 12
    • 0002396233 scopus 로고
    • "Adaptive optics"
    • J. W. Hardy, "Adaptive optics," Sci. Amer., vol. 270, no. 6, pp. 60-65, 1994.
    • (1994) Sci. Amer. , vol.270 , Issue.6 , pp. 60-65
    • Hardy, J.W.1
  • 13
    • 6144257390 scopus 로고    scopus 로고
    • "Two-photon excitation imaging based on a compact scanning head"
    • Sep./Oct
    • A. Diaspro, M. Corosu, P. Ramoino, and M. Robello, "Two-photon excitation imaging based on a compact scanning head," IEEE Eng. Med. Biol. Mag., no. 5, pp. 18-22, Sep./Oct. 1999.
    • (1999) IEEE Eng. Med. Biol. Mag. , Issue.5 , pp. 18-22
    • Diaspro, A.1    Corosu, M.2    Ramoino, P.3    Robello, M.4
  • 14
    • 0142148133 scopus 로고    scopus 로고
    • "Fast preconditioned conjugate gradient reconstruction for 2D SPECT"
    • Norfolk, Virginia
    • P. Khurd, Y. Xing, I. T. Hsiao, and G. Gindi, "Fast preconditioned conjugate gradient reconstruction for 2D SPECT," in Proc. IEEE NSS/MIC, Norfolk, Virginia, 2002, pp. 10-16.
    • (2002) Proc. IEEE NSS/MIC , pp. 10-16
    • Khurd, P.1    Xing, Y.2    Hsiao, I.T.3    Gindi, G.4
  • 15
    • 0031340730 scopus 로고    scopus 로고
    • "Preconditioning methods for shift-variant image reconstruction"
    • J. A. Fessler, "Preconditioning methods for shift-variant image reconstruction," in Proc. Int. Conf. Image Processing, vol. 1, 1997, pp. 185-188.
    • (1997) Proc. Int. Conf. Image Processing , vol.1 , pp. 185-188
    • Fessler, J.A.1
  • 16
    • 4043135800 scopus 로고    scopus 로고
    • "Steepest descent, CG, and iterative regularization of ill-posed problems"
    • J. G. Nagy and K. M. Palmer, "Steepest descent, CG, and iterative regularization of ill-posed problems," BIT, vol. 43, pp. 1003-1017, 2003.
    • (2003) BIT , vol.43 , pp. 1003-1017
    • Nagy, J.G.1    Palmer, K.M.2
  • 17
    • 0033632948 scopus 로고    scopus 로고
    • "Iterative regularization and MINRES"
    • M. Kilmer and G. W. Stewart, "Iterative regularization and MINRES," SIAM J. Matrix Anal. Appl., vol. 21, pp. 613-628, 1999.
    • (1999) SIAM J. Matrix Anal. Appl. , vol.21 , pp. 613-628
    • Kilmer, M.1    Stewart, G.W.2
  • 19
    • 0027607776 scopus 로고
    • "Maximum likelihood, least squares, and penalized least squares for PET"
    • Feb
    • L. Kaufman, "Maximum likelihood, least squares, and penalized least squares for PET," IEEE Trans. Med. Imag., vol. 12, no. 2, pp. 200-214, Feb. 1993.
    • (1993) IEEE Trans. Med. Imag. , vol.12 , Issue.2 , pp. 200-214
    • Kaufman, L.1
  • 20
    • 0033661265 scopus 로고    scopus 로고
    • "Enforcing nonnegativity in image reconstruction algorithms"
    • E. A. D. C. Wilson, Ed. Bellingham, WA: SPIE
    • J. G. Nagy and Z. Strakoš, "Enforcing nonnegativity in image reconstruction algorithms," in Mathematical Modeling, Estimation, and Imaging, E. A. D. C. Wilson, Ed. Bellingham, WA: SPIE, 2000, vol. 3461, pp. 182-190.
    • (2000) Mathematical Modeling, Estimation, and Imaging , vol.3461 , pp. 182-190
    • Nagy, J.G.1    Strakoš, Z.2
  • 21
    • 0033295054 scopus 로고    scopus 로고
    • "Pivoted cauchy-like preconditioners for the regularized solution of ill-posed problems"
    • M. E. Kilmer and D. P. O'Leary, "Pivoted cauchy-like preconditioners for the regularized solution of ill-posed problems," SIAM J. Sci. Comput., vol. 21, no. 1, 1999.
    • (1999) SIAM J. Sci. Comput. , vol.21 , Issue.1
    • Kilmer, M.E.1    O'Leary, D.P.2
  • 22
    • 0033239811 scopus 로고    scopus 로고
    • "Cauchy-like preconditioners for 2-dimensional ill-posed problems"
    • M. E. Kilmer, "Cauchy-like preconditioners for 2-dimensional ill-posed problems," SIAM J. Matrix Anal. Appl., vol. 20, no. 3, 1999.
    • (1999) SIAM J. Matrix Anal. Appl. , vol.20 , Issue.3
    • Kilmer, M.E.1
  • 23
    • 0000137080 scopus 로고    scopus 로고
    • "Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques"
    • M. Hanke and J. G. Nagy, "Restoration of atmospherically blurred images by symmetric indefinite conjugate gradient techniques," Inv. Prob., vol. 12, pp. 157-173, 1996.
    • (1996) Inv. Prob. , vol.12 , pp. 157-173
    • Hanke, M.1    Nagy, J.G.2
  • 24
    • 0000333315 scopus 로고
    • "Preconditioned iterative regularization"
    • L. Reichel, A. Ruttan, and R. S. Varga, Eds. Berlin, Germany: de Gruyter
    • M. Hanke, J. G. Nagy, and R. J. Plemmons, "Preconditioned iterative regularization," in Numerical Linear Algebra, L. Reichel, A. Ruttan, and R. S. Varga, Eds. Berlin, Germany: De Gruyter, 1993, pp. 141-163.
    • (1993) Numerical Linear Algebra , pp. 141-163
    • Hanke, M.1    Nagy, J.G.2    Plemmons, R.J.3
  • 26
    • 0034353666 scopus 로고    scopus 로고
    • "Optimal Kronecker product approximation of block Toeplitz matrices"
    • J. Kamm and J. G. Nagy, "Optimal Kronecker product approximation of block Toeplitz matrices," SIAM J. Matrix Anal. Appl., vol. 22, pp. 155-172, 2000.
    • (2000) SIAM J. Matrix Anal. Appl. , vol.22 , pp. 155-172
    • Kamm, J.1    Nagy, J.G.2
  • 27
    • 3142661848 scopus 로고    scopus 로고
    • "Kronecker product approximation for image restoration with reflexive boundary conditions"
    • J. G. Nagy, M. K. Ng, and L. C. Perrone, "Kronecker product approximation for image restoration with reflexive boundary conditions," SIAM J. Matrix Anal. Appl., vol. 25, pp. 829-841, 2004.
    • (2004) SIAM J. Matrix Anal. Appl. , vol.25 , pp. 829-841
    • Nagy, J.G.1    Ng, M.K.2    Perrone, L.C.3
  • 28
    • 0036055687 scopus 로고    scopus 로고
    • "Orthogonal tensor decompositions"
    • T. G. Kolda, "Orthogonal tensor decompositions," SIAM J. Matrix Anal. Appl., vol. 23, pp. 243-255, 2001.
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 243-255
    • Kolda, T.G.1
  • 31
    • 0036056838 scopus 로고    scopus 로고
    • "Rank-one approximation to high order tensors"
    • T. Zhang and G. H. Golub, "Rank-one approximation to high order tensors," SIAM J. Matrix Anal. Appl., vol. 23, pp. 534-550, 2001.
    • (2001) SIAM J. Matrix Anal. Appl. , vol.23 , pp. 534-550
    • Zhang, T.1    Golub, G.H.2
  • 33
    • 32944470461 scopus 로고    scopus 로고
    • "Exploiting residual information in the parameter choice for discrete ill-posed problems"
    • to be published
    • P. C. Hansen, M. E. Kilmer, and R. Kjeldsen, "Exploiting residual information in the parameter choice for discrete ill-posed problems," BIT, to be published.
    • BIT
    • Hansen, P.C.1    Kilmer, M.E.2    Kjeldsen, R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.