A Bayesian approach to crack detection in electrically conducting media

Inverse Problems

Volumn 17, Issue 1, 2001, Pages 121-136

  Andersen, Kim E ^a   Brooks, Stephen P ^b   Hansen, Martin B ^a  

^a AALBORG UNIVERSITY   (Denmark)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CRACKS; INVERSE PROBLEMS; MATHEMATICAL MODELS; SET THEORY; STATISTICAL METHODS;

BAYESIAN APPROACH;

ELECTRIC CONDUCTORS;

EID: 0034832060     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/17/1/310     Document Type: Article

References (32)

1. Atkinson K E 1976 A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind (Philadelphia, PA: SIAM)
2. Barber D and Brown B 1986 Recent developments in applied potential tomography - APT Information Processing in Medical Imaging ed S Bacharach (Amsterdam: Nijhoff) pp 106-21
3. Bernado J M and Smith A F M 2000 Bayesian Theory (New York: Wiley)
4. Brooks S P 1998 Markov chain Monte Carlo method and its application Statistician 47 69-100
5. Brooks S P and Gelman A 1998 General methods for monitoring convergence of iterative simulations J. Comput. Graph. Stat. 7 434-55
6. Brooks S P and Guidici P 2000 MCMC convergence assessment via two-way ANOVA J. Comput. Graph. Stat. 9 266-85
7. Brooks S P and Roberts G O 1998 Assessing convergence of Markov chain Monte Carlo algorithms Stat. Comput. 8 319-35
8. Bryan K and Vogelius M 1994 A computational algorithm to determine crack locations from electrostatic boundary measurements. The case of multiple cracks Int. J. Eng. Sci. 32 579-603
9. Cheney M, Isaacson D and Newell J C 1993 Electrical impedance tomography SIAM Rev. 41 85-101
10. Dahl-Jensen D, Mosegaard K, Gundestrup N, Clow G D, Johnsen S J, Jensen A W and Balling N 1998 Past temperatures directly from the Greenland ice sheet Science 282 268-71
11. Daley D J and Vere-Jones D 1988 An Introduction to the Theory of Point Processes (New York: Springer)
12. Efromovich S 1999 Nonparametric Curve Estimation (New York: Springer)
13. Fox C and Nicholls G 1997 Sampling conductivity images via MCMC The Art and Science of Bayesian Image Analysis, Proc. Leeds Annual Statistics Research Workshop ed K V Mardia, C A Gill and R G Aykroyd (Leeds: Leeds University Press) pp 91-100
14. Gelfand A E and Smith AFM 1990 Sampling-based approaches to calculating marginal densities J. Am. Stat. Assoc. 85 398-409
15. Gelman A and Rubin D B 1992 Inference from iterative simulation using multiple sequence Stat. Sci. 7 457-72
16. Geman S and Geman D 1984 Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images IEEE Trans. Pattern Anal. Mach. Intell. 6 721-41
17. Geyer C J and Møller J 1994 Simulation procedures and likelihood inference for spatial point processes Scand. J. Stat. 21 359-73
18. Geyer C J and Thompson E A 1995 Annealing Markov chain Monte Carlo with applications to ancestral inference J. Am. Stat. Assoc. 90 909-20
19. Green P 1995 Reversible jump Markov chain Monte Carlo computation and Bayesian model determination Biometrika 82 711-32
20. Hadamard J 1923 Lectures on the Cauchy Problem in Linear Partial Differential Equations (New Haven, CT: Yale University Press)
21. Hastings W K 1970 Monte Carlo sampling methods using Markov chains and their applications Biometrika 57 97-109
22. Kaipio J P, Kolehmainen V, Somersalo E and Vauhkonen M 2000 Statistical inversion and Monte Carlo sampling methods in electrical impedance tomography Inverse Problems 16 1487-522
23. Marini E and Parisi G 1992 Simulated tempering: a new Monte Carlo scheme Europhys. Lett. 19 451-8
24. Metropolis N, Rosenbluth A W, Rosenbluth M N, Teller A H and Teller E 1953 Equations of state calculations by fast computing machines J. Chem. Phys. 21 1087-92
25. Mosegaard K 1998 Resolution analysis of general inverse problems through inverse Monte Carlo sampling Inverse Problems 14 405-26
26. Mosegaard K and Rygaard-Hjalsted C 1999 Probabilistic analysis of implicit inverse problems Inverse Problems 15 573-83
27. Mosegaard K and Tarantola A 1995 Monte Carlo sampling of solutions to inverse problems J. Geophys. Res. B 100 12 431-47
28. Robert C P and Casella G 1999 Monte Carlo Statistical Methods (New York: Springer)
29. Santosa F and Vogelius M 1990 A backprojection algorithm for electrical impedance imaging SIAM J. Appl. Math. 50 216-43
30. Tarantola A 1987 Inverse Problem Theory (Amsterdam: Elsevier)
31. Tikhonov A N 1963a Regularization of incorrectly posed problems Sov. Dokl. 4 1624-7
32. 1963b Solution of incorrectly formulated problems and the regularization method Sov. Dokl. 4 1035-8