An integral equation method for the inverse conductivity problem

Physics Letters, Section A: General, Atomic and Solid State Physics

Volumn 325, Issue 3-4, 2004, Pages 253-267

  Ciulli, S ^a   Pidcock, M K ^b   Sebu, C ^a  

^a UNIV MONTPELLIER   (France)

^b OXFORD BROOKES UNIVERSITY   (United Kingdom)

Author keywords

Electrical impedance tomography; Inverse conductivity problem; Land mine detection; Nonlinear inverse problems

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ELECTRIC IMPEDANCE TOMOGRAPHY; IMAGE RECONSTRUCTION; INTEGRAL EQUATIONS; LANDMINE DETECTION;

CONDUCTIVITY DISTRIBUTIONS; ELECTRICAL IMPEDANCE TOMOGRAPHY; FIRST ORDER PARTIAL DIFFERENTIAL EQUATIONS; FREDHOLM INTEGRAL EQUATIONS; IMAGE RECONSTRUCTION ALGORITHM; INTEGRAL EQUATION METHODS; INVERSE CONDUCTIVITY PROBLEM; NON-LINEAR INVERSE PROBLEM;

INVERSE PROBLEMS;

ARTICLE; CALCULATION; CONDUCTANCE; ELECTRIC CURRENT; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; PHYSICS;

EID: 2342448528     PISSN: 03759601     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physleta.2004.03.060     Document Type: Article

References (24)

1. Calderón A.P. Seminar on Numerical Analysis and its Applications to Continuum Physics. 1980;Sociedade Brasileira de Matemàtica, Rio de Janeiro. pp. 65-73
2. Kohn R., Vogelius M. Commun. Pure Appl. Math. 38:1985;643
3. Sylvester J., Uhlmann G. Commun. Pure Appl. Math. 41:1988;197
4. Nachman A.I. Ann. Math. 142:1995;71
5. Cedio-Fenygya D.J., Moscow S., Vogelius M.S. Inverse Problems. 14:1998;553
6. Brühl M., Hanke M. Inverse Problems. 16:2000;1029
7. Brühl M., Hanke M., Vogelius M. Numer. Math. 93:2003;635
8. Siltanen S., Mueller J., Isaacson D. Inverse Problems. 16:2000;681
9. Ciulli S., Pidcock M., Spearman T.D., Stroian A. Phys. Lett. A. 271:2000;377
10. Ciulli S., Pidcock M., Sebu C. Z. Angew. Math. Mech. 83:(11):2003;755
11. Yeh W.W.-G. Water Resour. Res. 22:1986;95
12. Richter G.R. SIAM J. Appl. Math. 41:1981;210
13. Alessandrini G. Annu. Math. Pura Appl. 145:1986;265
14. Chavent G., Kunisch K. New results on the non-linearity and the sensitivity of the estimation of the diffusion coefficient in a 2D elliptic equation. Woodbury K. Inverse Problems in Engineering: Theory and Practice. 1999;91-96 ASME
15. Farcas A., Elliot L., Ingham D.B., Lesnic D. A DRM for solving the inverse problem of steady groundwater flow. Amini S. Proceedings of the Fourth UK Conference on Boundary Integral Methods. 2003;87-96 Salford University
16. de Rham G. Variétes Différentieles-Formes, Courants, Formes Harmoniques. 1973;Hermann
17. Milnor J.W. Morse Theory. 1963;Princeton Univ. Press, Princeton
18. Reeds M., Simon B. Methods of Modern Mathematical Physics I: Functional Analysis. second ed. 1980;Academic Press, San Diego, CA
19. Engl H.W., Hanke M., Neubauer A. Regularization of Inverse Problems. 2000;Kluwer Academic Publishers
20. Ciulli S., Pomponiu C., Sabba-Stefanescu I. Phys. Rep. C. 17:1975;133
21. Ciulli S., Pidcock M.K., Sebu C. An analytical solution for the inverse conductivity problem. Proceeding of the First Romanian Conference of Theoretical Physics, September 2002 Romanian J. Phys. 48:2003;50
22. Courant R., Hilbert D. Methods of Mathematical Physics, vol. I. 1989;John Wiley & Sons, New York
23. C. Sebu, Inverse problems in classical and quantum physics, PhD thesis, Université de Montpellier II, 2004
24. P.C. Hansen, Regularization Tools: A Matlab Package for Analysis and Solution of Discrete Ill-Posed Problems