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Volumn 20, Issue 4, 2011, Pages 1094-1111

Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography in the presence of measurement noise

Author keywords

Adaptive meshing algorithms; error analysis; fluorescence diffuse optical tomography

Indexed keywords

ADAPTIVE FINITE ELEMENT METHODS; ADAPTIVE MESHING; BOUNDARY MEASUREMENTS; BOUNDED DOMAIN; COUPLED PARTIAL DIFFERENTIAL EQUATIONS; DETECTOR GEOMETRY; DIFFUSE OPTICAL; DISCRETIZATION ERRORS; DISCRETIZATIONS; ERROR BOUND; EXACT SOLUTION; FIGURE OF MERIT; FINITE-ELEMENT DISCRETIZATION; FLUORESCENCE DIFFUSE OPTICAL TOMOGRAPHY; FLUOROPHORE CONCENTRATION; MAXIMUM A POSTERIORI; MEASUREMENT NOISE; NOISE STATISTICS; NUMERICAL SIMULATION; NUMERICAL SOLUTION; OPTIMIZATION PROBLEMS; PRIORI INFORMATION; RECONSTRUCTED IMAGE; RECONSTRUCTION ACCURACY; TOMOGRAPHIC; UPPER BOUND;

EID: 79952968014     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2010.2083677     Document Type: Article
Times cited : (13)

References (41)
  • 1
    • 0037236238 scopus 로고    scopus 로고
    • Shedding light onto live molecular targets
    • DOI 10.1038/nm0103-123
    • R.Weissleder and V. Ntziachristos, "Shedding light onto live melecular targets," Nature Med., vol. 9, pp. 123-128, 2003. (Pubitemid 36098273)
    • (2003) Nature Medicine , vol.9 , Issue.1 , pp. 123-128
    • Weissleder, R.1    Ntziachristos, V.2
  • 2
    • 21444441373 scopus 로고    scopus 로고
    • Looking and listening to light: The evolution of whole-body photonic imaging
    • DOI 10.1038/nbt1074
    • V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, "Looking and listening to light: The evolution of whole-body photonic imaging," Nature Biotech., vol. 23, pp. 313-320, 2005. (Pubitemid 41094419)
    • (2005) Nature Biotechnology , vol.23 , Issue.3 , pp. 313-320
    • Ntziachristos, V.1    Ripoll, J.2    Wang, L.V.3    Weissleder, R.4
  • 4
    • 0141645572 scopus 로고    scopus 로고
    • Adaptive finite element approximation for distributed elliptic optimal control problems
    • R. Li, W. Liu, H. Ma, and T. Tang, "Adaptive finite element approximation for distributed elliptic optimal control problems," SIAM J. Control Optim., vol. 41, pp. 1321-1349, 2002.
    • (2002) SIAM J. Control Optim. , vol.41 , pp. 1321-1349
    • Li, R.1    Liu, W.2    Ma, H.3    Tang, T.4
  • 5
    • 0842325124 scopus 로고    scopus 로고
    • A posteriori error estimation for finite element discretization of parameter identification problems
    • R. Becker and B. Vexler, "A posteriori error estimation for finite element discretization of parameter identification problems," Numer. Math., vol. 96, pp. 435-459, 2003.
    • (2003) Numer. Math. , vol.96 , pp. 435-459
    • Becker, R.1    Vexler, B.2
  • 6
    • 39449084428 scopus 로고    scopus 로고
    • Adaptive space-time finite element methods for parabolic optimization problems
    • DOI 10.1137/060648994
    • D. Meidner and B.Vexler, "Adaptive space-time finite element methods for parabolic optimization problems," SIAM J. Control Optim., vol. 46, pp. 116-142, 2007. (Pubitemid 351271290)
    • (2007) SIAM Journal on Control and Optimization , vol.46 , Issue.1 , pp. 116-142
    • Meidner, D.1    Vexler, B.2
  • 7
    • 44449084080 scopus 로고    scopus 로고
    • Adaptive finite elements for elliptic optimization problems with control constraints
    • B. Vexler and W. Wollner, "Adaptive finite elements for elliptic optimization problems with control constraints," SIAM J. Control Optim., vol. 47, pp. 509-534, 2008.
    • (2008) SIAM J. Control Optim. , vol.47 , pp. 509-534
    • Vexler, B.1    Wollner, W.2
  • 8
    • 12144269436 scopus 로고    scopus 로고
    • A posteriori error estimation in computational inverse scattering
    • L. Beilina and C. Johnson, "A posteriori error estimation in computational inverse scattering," Math. Models Meth. Appl. Sci., vol. 15, pp. 23-37, 2005.
    • (2005) Math. Models Meth. Appl. Sci. , vol.15 , pp. 23-37
    • Beilina, L.1    Johnson, C.2
  • 9
    • 76249122188 scopus 로고    scopus 로고
    • Adaptive finite element/difference method for inverse elastic scattering waves
    • L. Beilina and C. Johnson, "Adaptive finite element/difference method for inverse elastic scattering waves," Appl. Comput. Math., vol. 2, pp. 158-174, 2003.
    • (2003) Appl. Comput. Math. , vol.2 , pp. 158-174
    • Beilina, L.1    Johnson, C.2
  • 10
    • 44449144860 scopus 로고    scopus 로고
    • Adaptive finite element methods for the solution of inverse problems in optical tomography
    • W. Bangerth and A. Joshi, "Adaptive finite element methods for the solution of inverse problems in optical tomography," Inverse Problems, vol. 24, p. 034011, 2008.
    • (2008) Inverse Problems , vol.24 , pp. 034011
    • Bangerth, W.1    Joshi, A.2
  • 11
    • 34249693085 scopus 로고    scopus 로고
    • Fully adaptive finite element based tomography using tetrahedral dual-meshing for fluorescence enhanced optical imaging in tissue
    • DOI 10.1364/OE.15.006955
    • J. Lee, A. Joshi, and E. Sevick-Muraca, "Fully adaptive finite element based tomography using tetrahedral dual-meshing for fluorescence enhanced optical imaging in tissue," Opt. Exp., vol. 15, no. 11, pp. 6955-6975, 2007. (Pubitemid 46827697)
    • (2007) Optics Express , vol.15 , Issue.11 , pp. 6955-6975
    • Lee, J.H.1    Joshi, A.2    Sevick-Muraca, E.M.3
  • 12
    • 42649093536 scopus 로고    scopus 로고
    • Fast intersections on nested tetrahedrons (fint): An algorithm for adaptive finite element based distributed parameter estimation
    • J. Lee, A. Joshi, and E. Sevick-Muraca, "Fast intersections on nested tetrahedrons (fint): An algorithm for adaptive finite element based distributed parameter estimation," J. Comput. Phys., vol. 227, pp. 5778-5798, 2008.
    • (2008) J. Comput. Phys. , vol.227 , pp. 5778-5798
    • Lee, J.1    Joshi, A.2    Sevick-Muraca, E.3
  • 13
    • 34249667125 scopus 로고    scopus 로고
    • Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging: I
    • DOI 10.1088/0266-5611/23/3/017, PII S0266561107234136, 017
    • M. Guven, B. Yazici, K. Kwon, E. Giladi, and X. Intes, "Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging: I," Inverse Problems, vol. 23, pp. 1115-1133, 2007. (Pubitemid 46838845)
    • (2007) Inverse Problems , vol.23 , Issue.3 , pp. 1115-1133
    • Guven, M.1    Yazici, B.2    Kwon, K.3    Giladi, E.4    Intes, X.5
  • 14
    • 34249720517 scopus 로고    scopus 로고
    • Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging: II
    • DOI 10.1088/0266-5611/23/3/018, PII S0266561107343955, 018
    • M. Guven, B. Yazici, K. Kwon, E. Giladi, and X. Intes, "Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging: II," Inverse Problems, vol. 23, pp. 1135-1160, 2007. (Pubitemid 46838846)
    • (2007) Inverse Problems , vol.23 , Issue.3 , pp. 1135-1160
    • Guven, M.1    Yazici, B.2    Kwon, K.3    Giladi, E.4    Intes, X.5
  • 15
    • 76249099563 scopus 로고    scopus 로고
    • Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography: Part I
    • Feb.
    • M. Guven, L. Reilly-Raska, L. Zhou, and B. Yazici, "Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography: Part I," IEEE Trans. Med. Imag., vol. 29, no. 2, pp. 217-229, Feb. 2010.
    • (2010) IEEE Trans. Med. Imag. , vol.29 , Issue.2 , pp. 217-229
    • Guven, M.1    Reilly-Raska, L.2    Zhou, L.3    Yazici, B.4
  • 16
    • 76249110272 scopus 로고    scopus 로고
    • Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography: Part II
    • Feb.
    • M. Guven, L. Zhou, L. Reilly-Raska, and B. Yazici, "Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography: Part II," IEEE Trans. Med. Imag., vol. 29, no. 2, pp. 230-245, Feb. 2010.
    • (2010) IEEE Trans. Med. Imag. , vol.29 , Issue.2 , pp. 230-245
    • Guven, M.1    Zhou, L.2    Reilly-Raska, L.3    Yazici, B.4
  • 17
    • 0042255750 scopus 로고
    • A unified approach to a posteriori error estimation using elemental residual methods
    • M. Ainsworth and J. T. Oden, "A unified approach to a posteriori error estimation using elemental residual methods," Numer. Math., vol. 65, pp. 23-50, 1993.
    • (1993) Numer. Math. , vol.65 , pp. 23-50
    • Ainsworth, M.1    Oden, J.T.2
  • 18
    • 0000613724 scopus 로고
    • Error estimates for adaptive finite element computations
    • I. Babuška and W. C. Rheinboldt, "Error estimates for adaptive finite element computations," SIAM J. Numer. Anal., vol. 15, pp. 736-754, 1978.
    • (1978) SIAM J. Numer. Anal. , vol.15 , pp. 736-754
    • Babuška, I.1    Rheinboldt, W.C.2
  • 20
    • 84966215690 scopus 로고
    • Some a posterior error estimators for elliptic partial differential equations
    • R. E. Bank and A. Weiser, "Some a posterior error estimators for elliptic partial differential equations," Math. Comput., vol. 44, pp. 283-301, 1985.
    • (1985) Math. Comput. , vol.44 , pp. 283-301
    • Bank, R.E.1    Weiser, A.2
  • 21
    • 0026876667 scopus 로고
    • Recent experiences with error estimation and adaptivity, part I: Review of error estimators for scalar elliptic problems
    • DOI 10.1016/0045-7825(92)90053-M
    • T. Strouboulis and K. A. Hague, "Recent experiences with error estimation and adaptivity, Part I: Review of error estimators for scalar elliptic problems," Comput. Meth. Appl. Mech. Eng., vol. 97, pp. 399-436, 1992. (Pubitemid 23590324)
    • (1992) Computer Methods in Applied Mechanics and Engineering , vol.97 , Issue.3 , pp. 399-436
    • Strouboulis, T.1    Haque, K.A.2
  • 23
    • 78549264453 scopus 로고    scopus 로고
    • Performance evaluation of adaptive meshing algorithms for fluorescence diffuse optical tomography using experimental data
    • L. Zhou, B. Yazici, A. B. F. Ale, and V. Ntziachristos, "Performance evaluation of adaptive meshing algorithms for fluorescence diffuse optical tomography using experimental data," Opt. Lett., vol. 35, pp. 3727-3729, 2010.
    • (2010) Opt. Lett. , vol.35 , pp. 3727-3729
    • Zhou, L.1    Yazici, B.2    Ale, A.B.F.3    Ntziachristos, V.4
  • 24
    • 0031183895 scopus 로고    scopus 로고
    • Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques
    • E. M. Sevick-Muraca, G. Lopez, J. S. Reynolds, T. L. Troy, and C. L. Hutchinson, "Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques," Photochem. Photobiol., vol. 66, pp. 56-64, 1997.
    • (1997) Photochem. Photobiol. , vol.66 , pp. 56-64
    • Sevick-Muraca, E.M.1    Lopez, G.2    Reynolds, J.S.3    Troy, T.L.4    Hutchinson, C.L.5
  • 25
    • 0032638277 scopus 로고    scopus 로고
    • Optical tomography in medical imaging
    • S. R. Arridge, "Optical tomography in medical imaging," Inverse Problems, vol. 15, pp. R41-R93, 1999.
    • (1999) Inverse Problems , vol.15
    • Arridge, S.R.1
  • 26
    • 0001273549 scopus 로고    scopus 로고
    • Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation
    • V. Ntziachristos and R. Weissleder, "Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized born approximation," Opt. Lett., vol. 26, no. 12, pp. 893-895, 2001. (Pubitemid 33693607)
    • (2001) Optics Letters , vol.26 , Issue.12 , pp. 893-895
    • Ntziachristos, V.1    Weissleder, R.2
  • 28
    • 0026898364 scopus 로고
    • Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation
    • Jul.
    • N. P. Galatsanos and A. K. Katsaggelos, "Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation," IEEE Trans. Image Process., vol. 1, no. 3, pp. 322-336, Jul. 1992.
    • (1992) IEEE Trans. Image Process. , vol.1 , Issue.3 , pp. 322-336
    • Galatsanos, N.P.1    Katsaggelos, A.K.2
  • 29
    • 0042208667 scopus 로고    scopus 로고
    • A general heuristic for choosing the regularization parameter in ill-posed problems
    • M. Hanke and T. Raus, "A general heuristic for choosing the regularization parameter in ill-posed problems," SIAM J. Sci. Comput., vol. 17, pp. 956-972, 1996. (Pubitemid 126621187)
    • (1996) SIAM Journal of Scientific Computing , vol.17 , Issue.4 , pp. 956-972
    • Hanke, M.1    Raus, T.2
  • 30
    • 0033078391 scopus 로고    scopus 로고
    • Bayesian and regularization methods for hyperparameter estimation in image restoration
    • Feb.
    • R. Molina, A. K. Katsaggelos, and J. Mateos, "Bayesian and regularization methods for hyperparameter estimation in image restoration," IEEE Trans. Image Process., vol. 8, no. 2, pp. 231-246, Feb. 1999.
    • (1999) IEEE Trans. Image Process. , vol.8 , Issue.2 , pp. 231-246
    • Molina, R.1    Katsaggelos, A.K.2    Mateos, J.3
  • 31
    • 32044449925 scopus 로고
    • Generalized cross-validation as a method for choosing a good ridge paramete
    • M. Heath, G. Golub, and G. Wahba, "Generalized cross-validation as a method for choosing a good ridge paramete," Technometrics, vol. 21, pp. 215-223, 1979.
    • (1979) Technometrics , vol.21 , pp. 215-223
    • Heath, M.1    Golub, G.2    Wahba, G.3
  • 32
    • 0001632418 scopus 로고
    • The use of the l-curve in the regularization of discrete ill-posed problems
    • P. Hansen and D. O'Learly, "The use of the l-curve in the regularization of discrete ill-posed problems," SIAM J. Comput., vol. 14, pp. 1487-1503, 1993.
    • (1993) SIAM J. Comput. , vol.14 , pp. 1487-1503
    • Hansen, P.1    O'Learly, D.2
  • 36
    • 34548277425 scopus 로고    scopus 로고
    • Deal.II-A general-purpose object-oriented finite element library
    • W. Bangerth, R. Hartmann, and G. Kanschat, "deal.II-A general-purpose object-oriented finite element library," ACM Trans. Math. Softw., vol. 33, no. 4, 2007.
    • (2007) ACM Trans. Math. Softw. , vol.33 , Issue.4
    • Bangerth, W.1    Hartmann, R.2    Kanschat, G.3
  • 37
    • 0026898364 scopus 로고
    • Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation
    • Jul.
    • N. P. Galatsanos and A. K. Katsaggelos, "Methods for choosing the regularization parameter and estimating the noise variance in image restoration and their relation," IEEE Trans. Image Process., vol. 1, no. 3, pp. 322-336, Jul. 1992.
    • (1992) IEEE Trans. Image Process. , vol.1 , Issue.3 , pp. 322-336
    • Galatsanos, N.P.1    Katsaggelos, A.K.2
  • 38
    • 0033078391 scopus 로고    scopus 로고
    • Bayesian and regularization methods for hyperparameter estimation in image restoration
    • Feb.
    • R. Molina, A. K. Katsaggelos, and J. Mateos, "Bayesian and regularization methods for hyperparameter estimation in image restoration," IEEE Trans. Image Process., vol. 8, no. 2, pp. 231-246, Feb. 1999.
    • (1999) IEEE Trans. Image Process. , vol.8 , Issue.2 , pp. 231-246
    • Molina, R.1    Katsaggelos, A.K.2    Mateos, J.3
  • 39
    • 18444416128 scopus 로고
    • Sugli integrali multipli
    • G. Fubini, "Sugli integrali multipli," Opere scelte, vol. 2, pp. 243-249, 1958.
    • (1958) Opere Scelte , vol.2 , pp. 243-249
    • Fubini, G.1
  • 41
    • 0004151494 scopus 로고
    • Cambridge, U.K.: Cambridge Univ. Press
    • R. A. Horn, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press, 1985.
    • (1985) Matrix Analysis
    • Horn, R.A.1


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