Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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By M. Goharian, M. Soleimani, and G. R. Moran

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Image reconstruction in electrical impedance tomography (EIT) is an ill-posed nonlinear inverse problem. Regularization methods are needed to solve this problem. The results of the ill-posed EIT problem strongly depends on noise level in measured data as well as regularization parameter. In this paper we present trust region subproblem (TRS), with the use of Lcurve maximum curvature criteria to find a regularization parameter. Currently Krylov subspace methods especially conjugate gradient least squares (CGLS) are used for large scale 3D problem. CGLS is an efficient technique when the norm of measured noise is exactly known. This paper demonstrates that CGLS and TRS converge to the same point on the L-curve with the same noise level. TRS can be implemented efficiently for large scale inverse EIT problem as CGLS with no need a priori knowledge of the noise level.

M. Goharian, M. Soleimani, and G. R. Moran, "A trust region subproblem for 3D electrical impedance tomography inverse problem using experimental data," Progress In Electromagnetics Research, Vol. 94, 19-32, 2009.

1. Eldén, L., "Algorithms for the regularization of ill-conditioned least squares problems," BIT, Vol. 17, 134-145, 1977.

2. Björck, A., "Numerical methods for least squares problems," SIAM, Philadelphia, 1996.

3. Rojas, M., "A large-scale trust-region approach to the regularization of discrete ill-posed problems,", Ph.D. Thesis, Technical Report TR98-19, Department of Computational and Applied Mathematics, Rice University, Houston, 1998.

4. Grodzevich, O., "Regularization using a parameterized Trust-Region subproblem,", M.Sc. Thesis, Department of Combinatorics and Optimization, University of Waterloo, Canada, 2004.

5. Hansen, P. C., "Analysis of discrete ill-posed problems by means of the L-curve," SIAM Rev., Vol. 34, No. 2, 561-580, 1992.

6. Sorensen, D. C., "Minimization of a large-scale quadratic function subject to a spherical constraint," SIAM Journal on Optimization, Vol. 7, No. 1, 141-161, 1997.

7. Stern, R. J. and W. Hlkowicz, "Indefinite trust region subproblems and nonsymmetric eigenvalue perturbations," SIAM Journal on Optimization, Vol. 5, No. 2, 286-313, 1995.

8. Boone, K., D. Barber, and B. Brown, "Imaging with electricity: Report of the european concerted action on impedance tomography," Journal of Medical Engineering & Technology, Vol. 21, No. 4, 201-232, 1997.

9. Metherall, P., D. C. Barber, R. H. Smallwood, and B. H. Brown, "Three-dimensional electrical impedance tomography," Nature, Vol. 380, No. 6574, 509-512, 1996.

10. Vauhkonen, M., "Electrical impedance tomography and prior information,", Thesis, Univeristy of Kuopio, 1997.

11. Goharian, M., G. R. Moran, K. Wilson, C. Seymour, A. Jegatheesan, M. Hill, R. T. Thompson, and G. Campbe, "Modifying the MRI, elastic stiffness and electrical properties of polyvinyl alcohol cryogel using irradiation," Nucl. Instr. and Meth. B, 2007.

12. Mori, Y., H. Tokura, and M. Yoshikawa, "Properties of hydrogels synthesized by freezing and thawing aqueous polyvinyl alcohol solutions and their applications," Journal of Materials Science, Vol. 32, No. 2, 491-496, 1997.

13. Surry, K. J. M., H. J. B. Austin, A. Fenster, and T. M. Peters, "Poly (vinyl alcohol) cryogel phantoms for use in ultrasound and MR imaging," Physics in Medicine and Biology, Vol. 49, No. 24, 5529-5546, 2004.

14. Goharian, M., A. Jegatheesan, and G. R. Moran, "Dogleg trustregion application in electrical impedance tomography," Physiol. Meas., Vol. 28, 555-572, 2007.

15. Soleimani, M., C. N. Mitchell, R. Banasiak, R. Wajman, and A. Adler, "Four-dimensional electrical capacitance tomography imaging using experimental data," Progress In Electromagnetics Research, Vol. 90, 171-186, 2009.

16. Soleimani, M., "Simultaneous reconstruction of permeability and conductivity in magnetic induction tomography," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 5--6, 785-798, 2009.

17. Zacharopoulos, A. and S. Arridge, "3D shape reconstruction in optical tomography using spherical harmonics and BEM," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 13, 1827-1836, 2006.

18. Zhang, H., S. Y. Tan, and H. S. Tan, "A novel method for microwave breast cancer detection," Progress In Electromagnetics Research, Vol. 83, 413-434, 2008.

19. Chen, G. P., W. B. Yu, Z. Q. Zhao, Z. P. Nie, and Q. H. Liu, "The prototype of microwave-induced thermo-acoustic tomography imaging by time reversal mirror," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 11--12, 1565-1574, 2008.

20. Giamalaki, M. I., I. S. Karanasiou, and N. K. Uzunoglu, "Electromagnetic analysis of a non invasive microwave radiometry imaging system emphasizing on the focusing sensitivity optimization," Progress In Electromagnetics Research, Vol. 90, 385-407, 2009.

21. Polydorides, N., "Linearization error in electrical impedance tomography," Progress In Electromagnetics Research, Vol. 93, 323-337, 2009.

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