Discrete tomography with a very few views, using Gibbs priors and a Marginal Posterior Mode approach

Electronic Notes in Discrete Mathematics

Volumn 20, Issue , 2005, Pages 399-418

  Liao, Hstau Y ^a   Herman, Gabor T ^a  

^a CITY UNIVERSITY OF NEW YORK   (United States)

Author keywords

discrete tomography; few projections; Gibbs distribution; marginal posterior mode; stochastic optimization

Indexed keywords

EID: 33746462225     PISSN: 15710653     EISSN: 15710653     Source Type: Journal    
DOI: 10.1016/j.endm.2005.05.075     Document Type: Article

References (20)

1. Besag J. Efficiency of pseudo-likelihood estimation for simple Gaussian fields. Biometrika 64 (1977) 616-618
2. Besag J. On the statistical analysis of dirty pictures. J. Roy. Statist. Soc. Ser. B 48 (1986) 259-302
3. Carazo J.M., Sorzano C.O., Rietzel E., Schröder R., and Marabini R. Discrete tomography in electron microscopy. In: Herman G.T., and Kuba A. (Eds). Discrete Tomography: Foundations, Algorithms and Applications (1999), Birkhäuser, Boston 405-416
4. Carvalho B.M., Herman G.T., Matej S., Salzberg C., and Vardi E. Binary tomography for triplane cardiography. In: Kuba A., Smal M., and Todd-Pokropek A. (Eds). Information Processing in Medical Imaging (1999), Springer-Verlag, Berlin 29-41
5. Fox C., and Nicholls G.K. Exact MAP states and expectations from perfect sampling: Greig, Porteous and Seheult revisited. In: Mohammad-Djafari A. (Ed). Bayesian Inference and Maximum Entropy Methods in Science and Engineering (2001), AIP, Melville, NY 252-263
6. Geman S., and Geman D. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6 (1984) 721-741
7. Hastings W.K. Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57 (1970) 97-109
8. Herman G.T. Geometry of Digital Spaces (1998), Birkhäuser, Boston, MA
9. Herman G.T., De Pierro A.R., and Gai N. On methods for maximum a posteriori image reconstruction with a normal prior. J. Visual Comm. Image Represent. 3 (1992) 316-324
10. In: Herman G.T., and Kuba A. (Eds). Discrete Tomography: Foundations, Algorithms and Applications (1999), Birkhäuser, Boston
11. Herman G., and Meyer L. Algebraic reconstruction techniques can be made computationally efficient. IEEE Trans. Med. Imag. 12 (1993) 600-609
12. Liao H.Y., and Herman G.T. Automated estimation of the parameters of Gibbs priors to be used in binary tomography. Discrete Appl. Math. 139 (2004) 149-170
13. Metropolis N., Rosenbluth A.W., Rosenbluth M.N., Teller A.H., and Teller E. Equation of state calculations by fast computing machines. J. Chem. Phys. 21 (1953) 1087-1092
14. Papoulis A. Probability and Statistics (1990), Prentice-Hall, Inc., New Jersey, USA
15. Sahoo P.K., Soltani S., Wong A.K.C., and Chen Y.C. A survey of thresholding techniques. Computer Vision, Graphics, and Image Processing 41 (1996) 233-260
16. Shepp L.A., and Vardi Y. Maximum likelihood reconstruction in positron emission tomography. IEEE Trans. Med. Imag. 1 (1982) 113-122
17. Sotthivirat S., and Fessler J.A. Image recovery using partitioned-separable paraboloidal surrogate coordinate ascent algorithms. IEEE Trans. Image Process. 11 (2002) 306-317
18. Tjelmeland H., and Besag J. Markov random fields with higher-order interactions. Scand. J. Statist. 25 (1998) 415-433
19. Vardi E., Herman G.T., and Kong T.Y. Speeding up stochastic reconstructions of binary images from limited projection directions. Linear Algebra Appl. 339 (2001) 75-89
20. Winkler G. Image Analysis, Random Fields and Dynamic Monte Carlo Methods. second edition (2003), Springer, Berlin