Eddy current tomography using a binary Markov model

Signal Processing

Volumn 49, Issue 2, 1996, Pages 119-132

  Nikolova, Mila ^a   Mohammad Djafari, Ali ^a  

^a UNIV PARIS SUD   (France)

Author keywords

Bayesian estimation; Binary Markov random field; Eddy current tomography; Fourier Laplace transform; Global optimization; Graduated non convexity; Ill posed inverse problem; Image reconstruction; Non destructive evaluation; Regularization

Indexed keywords

ADAPTIVE ALGORITHMS; COMBINATORIAL MATHEMATICS; CONDUCTIVE MATERIALS; EDDY CURRENTS; ELECTRIC FIELD MEASUREMENT; IMAGING TECHNIQUES; INVERSE PROBLEMS; MARKOV PROCESSES; MATHEMATICAL MODELS; NONDESTRUCTIVE EXAMINATION; OPTIMIZATION; SPURIOUS SIGNAL NOISE;

BINARY IMAGE; EDDY CURRENT TOMOGRAPHY; MARKOV RANDOM FIELD; MONOCHROMATIC ELECTRIC FIELD; NONCONVEXITY ALGORITHM; OBSERVATION OPERATOR;

IMAGE PROCESSING;

EID: 0030101036     PISSN: 01651684     EISSN: None     Source Type: Journal    
DOI: 10.1016/0165-1684(95)00151-4     Document Type: Article

References (16)

1. J.E. Besag, "On the statistical analysis of dirty pictures (with discussion)", J. Roy. Statist. Soc. B, Vol. 48, No. 3, 1986, pp. 259-302.
2. J. Besag, "Digital image processing: Towards Bayesian image analysis", J. Appl. Statist., Vol. 16, No. 3, 1989, pp. 395-407.
3. A. Blake, "Comparison of the efficiency of deterministic and stochastic algorithms for visual reconstruction", IEEE Trans. Pattern Anal. Machine Intell., Vol. PAMI-11, No. 1, 1989, pp. 2-12.
4. A. Blake and A. Zisserman, Visual Reconstruction, MIT Press, Cambridge, MA, 1987.
5. G. Box and G. Tiao, Bayesian Inference in Statistical Analysis, Addison-Wesley, Reading, MA, 1972.
6. G. Demoment, "Image reconstruction and restoration: Overview of common estimation structure and problems", IEEE Trans. Acoust. Speech Signal Process., Vol. ASSP-37, No. 12, 1989, pp. 2024-2036.
7. D. Geiger and F. Girosi, "Parallel and deterministic algorithms from MRF's: Surface reconstruction", IEEE Trans. Pattern Anal. Machine Intell., Vol. PAMI-13, No. 5, 1991, pp. 401-412.
8. D.M. Grieg, B.T. Porteous and A.H. Seheult, "Exact maximum a posteriori estimation for binary images", J. Roy. Statist. Soc. B, Vol. 51, No. 2, 1989, pp. 271-279.
9. Y. Leclerc, "Constructing simple stable description for image partitioning", Internat. J. Comput. Vision, Vol. 3, 1989, pp. 73-102.
10. M. Nikolova, "Markovian reconstruction in computed imaging and Fourier synthesis", Proc. IEEE ICIP, Vol. 2, 1994, pp. 690-694.
11. M. Nikolova, J. Idier and A. Mohammad-Djafari, Inversion of large-support ill-posed operators using a piecewise Gaussian MRF, Tech. Rep., GPI-LSS, 1995.
12. M. Nikolova and A. Mohammad-Djafari, "Maximum entropy image reconstruction in eddy current tomography, in: A. Mohammad-Djafari and G. Demoment, eds., Maximum Entropy and Bayesian Methods, Kluwer Academic Publishers, Paris, 1992, pp. 273-278.
13. I. Richards and Y. Heekyung, Theory of Distributions: A Non-technical Introduction, Cambridge University Press, Cambridge, 1990.
14. H. Sabbagh, "An eddy-current model for three-dimensional inversion", IEEE Trans. Magn., Vol. MAG-22, No. 4 1986, pp. 282-292.
15. R. Zorgati, B. Duchene, D. Lesselier and F. Pons, "Eddy current testing of anomalies in conductive materials, Part I: Qualitative imaging via diffraction tomography techniques", IEEE Trans. Magn., Vol. M-27, No. 6, 1991, pp. 4416-4437.
16. R. Zorgati, B. Duchene, D. Lesselier and F. Pons, "Eddy current testing of anomalies in conductive materials, Part II: Quantitative imaging via deterministic and stochastic inversion techniques", IEEE Trans. Magn., Vol. M-28, No. 3, 1992, pp. 1850-1862.