Prior modeling and posterior sampling in impedance imaging

Proceedings of SPIE - The International Society for Optical Engineering

Volumn 3459, Issue , 1998, Pages 116-127

  Nicholls, Geoff K ^a   Fox, Colin ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Bayesian; Impedance tomography; Inverse problem; Langevin; Markov chain Monte Carlo

Indexed keywords

BAYESIAN NETWORKS; COMPUTER PROGRAMMING LANGUAGES; DIAGNOSTIC RADIOGRAPHY; DIFFERENTIAL EQUATIONS; IMAGE SEGMENTATION; INFERENCE ENGINES; MARKOV PROCESSES; MAXIMUM LIKELIHOOD ESTIMATION; MEDICAL IMAGING; MONTE CARLO METHODS; TOMOGRAPHY; UNCERTAIN SYSTEMS;

BAYESIAN; BAYESIAN INFERENCES; CONDUCTIVITY DISTRIBUTIONS; IMPEDANCE IMAGING; IMPEDANCE TOMOGRAPHY; LANGEVIN; LIKELIHOOD RATIOS; LINEAR PARTIAL DIFFERENTIAL EQUATIONS; LOCAL UPDATES; MARKOV CHAIN MONTE CARLO; POSTE-RIORS; SECOND ORDERS;

INVERSE PROBLEMS;

EID: 57649124200     PISSN: 0277786X     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1117/12.323791     Document Type: Conference Paper

References (21)

1. P. Metherall, D. C. Barber, R. H. Smallwood, and B. H. Brown, "Three-dimensional electrical impedance tomography," Nature 380, pp. 509-512, 1996.
2. C. Fox and G. K. Nicholls, "Sampling conductivity images via MCMC," in The Art and Science of Bayesian Image Analysis, K. Mardia, R. Ackroyd, and C. Gill, eds., Leeds Annual Statistics Research Workshop, pp. 91-100, University of Leeds, 1997.
3. J. Sylvester and G. Uhlman, "A global uniquness theorem for an inverse boundary value problem," Ann. Math. 125, pp. 643-667, 1987.
4. C. Fox, Conductance Imaging. PhD thesis, University of Cambridge, 1989.
5. D. C. Barber, "A review of image reconstruction techniques for electrical impedance tomography," Med. Phys 16(2), pp. 162-169, 1989.
6. A. P. Calderon, "On an inverse boundary value problem," in Seminar on Numerical Analysis and its Applications, W. H. Meyet and M. A. Ranpp, eds., Brazilian Math. Soc., (Rio de Janerio, Brazil), 1980.
7. T. J. Yorkey, Comparing reconstruction methods for electrical impedance tomography. PhD thesis, University of Wisconson, Madison, WI, 1986.
8. P. Hua, E. J. Woo, J. G. Webster, and W. J. Tompkins, "Iterative reconstruction methods using regularization and optimal current patterns in electrical impedance tomography," IEEE Transactions on Medical Imaging 10, pp. 621-628, 1991.
9. T. Martin and J. Idier, "A Bayesian non-linear approach for electrical impedance tomography," tech. rep., CNRS, martin@lss.supelec.fr, Lab. des Signaux at Systems, CNRS, Plateau de Moulon, 91192 Gif-sur-Yvette Cedex, France, 1997.
10. U. Grenander and M. Miller, "Representation of knowledge in complex systems (with discussion)," Journal of the Royal Statistical Society B 56, pp. 549-604, 1993.
11. G. K. Nicholls, "Bayesian image analysis with Markov chain Monte Carlo and colored continuum triangulation mosaics," Journal of the Royal Statistical Society B 60, pp. 643-659, 1998.
12. P. Green, "Reversible jump MCMC and Bayesian model determination," Biometrika 82, pp. 711-732, 1995.
13. L. Tierney, "Markov chains for exploring posterior distributions," Annals of Statistics 22, pp. 1701-1762, 1994.
14. G. O. Roberts and J. S. Rosenthal, "Optimal scaling of discrete approximations to langevin diffusions," Journal of the Royal Statistical Society B , p. to appear, 1998.
15. M. Creutz, "Microcanonical monte carlo simulation," Phys. Rev. Lett. 50, pp. 1411-1414, 1983.
16. E. Clark, "Bayesian impedance imaging." Seminar, Physics Department, Auckland University, November 1997.
17. G. K. Nicholls, "Modelling planar change-point problems using colored continuum triangulation models," in The art and science of Bayesian Image analysis, K. Mardia, R. Ackroyd, and C. Gill, eds., Leeds Annual Statistics Research Workshop, pp. 143-150, 1997.
18. R. M. West, "Image reconstruction for electrical resistance tomography by updating local parameters," tech. rep., Camborne School of Mines, University of Exeter, UK, 1998.
19. B. D. Ripley, Stochastic Simulation, Cambridge University Press, Cambridge, 1987.
20. W. K. Hastings, "Monte Carlo sampling methods using Markov chains and their applications," Biometrika 57, pp. 97-109, 1970.
21. P. J. Rossky, J. D. Doll, and H. L. Friedman, "Brownian dynamics as smart monte-carlo simulation," J. Chem. Phys 69, pp. 4628-4633, 1978.