Abstract
A tomographic reconstruction method based on Monte Carlo random searching guided by the information contained in the projections of radiographed objects is presented. In order to solve the optimization problem, a multiscale algorithm is proposed to reduce computation. The reconstruction is performed in a coarse-to-fine multigrid scale that initializes each resolution level with the reconstruction of the previous coarser level, which substantially improves the performance. The method was applied to a real case reconstructing the internal structure of a small metallic object with internal components, showing excellent results.
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References
A. Aho, J. Ullman, Foundations of Computer Science (Computer Science Press, New York 1995)
T. Chan, G. Herman, E. Levitan, in Discrete Tomography: Foundation, Algorithms and Application, ed. by G.T. Herman, A. Kuba (Birkhäuser, Boston, 1999), pp. 214–233
D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, New York, 1987)
T. Frese, C.A. Bouman, K. Sauer, in Discrete Tomography: Foundation, Algorithms and Application, ed. by G.T. Herman, A. Kuba (Birkhäuser, Boston, 1999), pp. 237–264
B. Frieden, in Topics in Applied Physics, vol. 6 (Springer, Berlin, 1975), pp. 177–249
S. Geman, D. Geman, IEEE Trans. Pattern Anal. Mach. Intell. 6, 721–741 (1984)
S. Geman, D. McClure, in Proc. Stat. Comput. Sect. Am. Stat. Assoc. (Washington, DC, 1985), pp. 12–18
G. Glover, N. Pelc, Med. Phys. 8, 799–807 (1981)
R. Gordon, G. Herman, Commun. ACM 14(12), 759–764 (1971)
P. Green, IEEE Trans. Med. Imaging 9, 84–93 (1990)
J. Hammersley, D. Handscomb, Monte Carlo Methods (Chapman and Hall, New York, 1964)
T. Hebert, R. Leahy, IEEE Trans. Med. Imaging 8, 194–202 (1989)
G.T. Herman, Image Reconstruction from Projection (Wiley, New York, 1980)
B. Hunt, IEEE Trans. Comput. C-26, 219–229 (1977)
T. Inouye, IEEE Trans. Nucl. Sci. NS-26, 2666–2684 (1979)
K. Kearfott, E. Scott, IEEE Trans. Med. Imaging 9(2), 128–143 (1990)
S. Kirkpatrick, C. Gelatt, M. Vecchi, Science 220(4598), 671–679 (1983)
S. Matej, A. Vardi, G. Herman, E. Vardi, in Discrete Tomography: Foundation, Algorithms and Application, ed. by G.T. Herman, A. Kuba (Birkhäuser, Boston, 1999), pp. 191–211
G. McKinnon, R. Bates, IEEE Trans. Biomed. Eng. 28, 123–127 (1981)
N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A. Teller, E. Teller, J. Chem. Phys. 21, 1087–1092 (1953)
J. Sanderson, IEEE Trans. Nucl. Sci. 26, 2685–2688 (1979)
K. Sauer, C. Bouman, IEEE Trans. Signal Process. 41, 534–548 (1993)
M. Vénere, C. Moreno, A. Clausse, R. Barbuzza, M. del Fresno, Nukleonica 46(1), 5–6 (2001)
G. Winkler, Image Analysis, Random Fields and Markov Chain Monte Carlo Methods, A Matematical Introduction, 2nd edn. (Springer, Berlin, 2003)
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Barbuzza, R., Vénere, M. & Clausse, A. Tomographic reconstruction using heuristic Monte Carlo methods. J Heuristics 13, 227–242 (2007). https://doi.org/10.1007/s10732-007-9017-3
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DOI: https://doi.org/10.1007/s10732-007-9017-3