Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography: Part II

IEEE Transactions on Medical Imaging

Volumn 29, Issue 2, 2010, Pages 230-245

  Guven, Murat ^a   Zhou, Lu ^b   Reilly Raska, Laurel ^c   Yazici, Birsen ^b  

^a INTEL CORPORATION   (United States)

^b RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Adaptive meshing algorithms; Error analysis; Fluorescence diffuse optical tomography

Indexed keywords

ADAPTIVE MESH GENERATION; ADAPTIVE MESHING; ADAPTIVE MESHING ALGORITHMS; DETECTABILITY; DISCRETIZATION ERRORS; DISCRETIZATIONS; ERROR ESTIMATES; ERROR REDUCTION; FLUORESCENCE DIFFUSE OPTICAL TOMOGRAPHY; FLUOROPHORE CONCENTRATION; NUMERICAL SOLUTION; OPTICAL IMAGE; RECONSTRUCTED IMAGE; THREE-DIMENSIONAL NUMERICAL SIMULATIONS;

DIFFERENTIAL EQUATIONS; ERROR ANALYSIS; FLUORESCENCE; GEOMETRICAL OPTICS; INVERSE PROBLEMS; MESH GENERATION; OPTICAL TOMOGRAPHY; THREE DIMENSIONAL;

ADAPTIVE ALGORITHMS;

ALGORITHM; ARTICLE; COMPUTER SIMULATION; FINITE ELEMENT ANALYSIS; FLUORESCENCE; IMAGE PROCESSING; METHODOLOGY; OPTICAL TOMOGRAPHY; REPRODUCIBILITY; THEORETICAL MODEL;

ALGORITHMS; COMPUTER SIMULATION; FINITE ELEMENT ANALYSIS; FLUORESCENCE; IMAGE PROCESSING, COMPUTER-ASSISTED; MODELS, THEORETICAL; REPRODUCIBILITY OF RESULTS; TOMOGRAPHY, OPTICAL;

EID: 76249110272     PISSN: 02780062     EISSN: None     Source Type: Journal    
DOI: 10.1109/TMI.2009.2029855     Document Type: Article

References (32)

1. 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. Medical Imaging, to be published.
2. M. Ainsworth and J. T. Oden, "A unified approach to a posteriori error estimation using elemental residual methods, " Numerische Mathematik, vol.65, pp. 23-50, 1993.
3. I. Babu?ska and W. C. Rheinboldt, "Error estimates for adaptive finite element computations, " SIAM Journal on Numerical Analysis, vol.15, pp. 736-754, 1978.
4. I. Babuska, O.C. Zienkiewicz, J. Gago, and E. R. de A. Oliveira, Accuracy Estimates and Adaptive Refinements in Finite Element Computations.: John Wiley and Sons 1986.
5. R. E. Bank and A. Weiser, "Some a posterior error estimators for elliptic partial differential equations, " Mathematics of Computation, vol.44, pp. 283-301, 1985.
6. T. Strouboulis and K. A. Hague, "Recent experiences with error estimation and adaptivity, part I: Review of error estimators for scalar elliptic problems, " Computer Methods in Applied Mechanics and Engineering, vol.97, pp. 399-436, 1992.
7. R. Verfurth, A Review of A Posteriori Error Estimation and Adaptive Mesh Refinement Techniques.: Teubner-Wiley, 1996.
8. J. G. Brankov, Y. Yang, and M. N. Wernick, "Tomographic image reconstruction based on a content-adaptive mesh model, " IEEE Trans. Medical Imaging, vol.23, no.2, pp. 202-212, 2004.
9. M. Molinari, S. J. Cox, B. H. Blott, and G. J. Daniell, "Adaptive mesh refinement techniques for electrical impedance tomography, " Physiological Measurement, vol.22, pp. 91-96, 2001.
10. L. Beilina and C. Johnson, "A posteriori error estimation in computational inverse scattering, " Mathematical Models and Methods in Applied Sciences, vol.15, pp. 23-37, 2005.
11. L. Beilina and C. Johnson, "Adaptive finite element/difference method for inverse elastic scattering waves, "Applied and Computational Mathematics, vol.2, pp. 158-174, 2003.
12. M. Torregrossa, C. V. Zint, and P. Poulet, "Image reconstruction in optical tomography: Mesh influence, " in IV International Workshop, 2002, Computational Problems ofElectrical Engineering, pp. 183-186.
13. M. Guven, B. Yazici, X. Intes, and B. Chance, "An adaptive multigrid algorithm for region of interest diffuse optical tomography, " in International Conference in Image Processing, 2003, vol.2, Proc. of IEEE, pp. 823-826.
14. X. Gu, Y. Xu, and H. Jiang, "Mesh-based enhancement schemes in diffuse optical tomography, " Medical Physics, vol.30, no.5, pp. 861-869, 2003.
15. M. Huang and Q. Zhu, "Dual-mesh optical tomography reconstruction method with a depth correction that uses a priori ultrasound information, " Applied Optics, vol.43, no.8, pp. 1654-1662, 2004.
16. 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)
17. S. R. Arridge, J. P. Kaipio, V. Kolehmainen, M. Schweiger, E. Som-ersalo, T. Tarvainen, and M. Vauhkonen, "Approximation errors and model reduction with an application in optical diffusion tomography, " Inverse Problems, vol.22, pp. 175-195, 2006.
18. 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.
19. 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, " Optics Express, vol.15, no.11, p. 6955C6975, 2007.
20. W. Bangerth, "Adaptive Finite Element Methods for the Identification of Distributed Parameters in Partial Differential Equations, " Ph. D. dissertation, University of Heidelberg, 2002.
21. J. Lee, A. Joshi, and E. Sevick-Muraca, "Fast intersections on nested tetrahedrons (fint): An algorithm for adaptive finite element based distributed parameter estimation, " Journal of Computational Physics, vol.227, pp. 5778-5798, 2008.
22. 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)
23. S. C. Brenner and L. R. Scott, The Mathematical Theory of Finite Element Methods.: Springer Verlag, 2002.
24. O. Axelsson and V. Barker, Finite Element Solution of Boundary Value Problems, Theory and Computation. Orlando, FL: Academic Press, 1984.
25. M. C. Rivara, "Mesh refinement processes based on the generalized bisection of simplices, " SIAM Journal on Numerical Analysis, vol.21, no.3, pp. 604-613, 1984.
26. 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.
27. I. M. Smith and D. V. Griffiths, Programming the Finite Element Method, 4th ed.: John Wiley & Sons, 2004.
28. T. A. Johansen, "On tikhonov regularization, bias and variance in nonlinear system identification, " Automatica, vol.33, pp. 441-446, 1997.
29. N. P. Galatsanos and A. K. Katsaggelos, "Methods for choosing the regularization parameter and estimatingthe noise variance in image restoration and their relation, " IEEE Trans. Image Processing, vol.1, pp. 322-336, 1992.
30. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions.: Dover, 1968.
31. J. D. Jackson, Classical Electrodynamics.: John Wiley and Sons, 1962.
32. S. Walker, D. A. Boas, and E. Gratton, "Photon density waves scattered from cylindrical inhomogeneities: Theory and experiments, " Applied Optics, vol.37, no.10, pp. 1935-1944, 1998.