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Progress In Electromagnetics Research
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TWO FFT SUBSPACE-BASED OPTIMIZATION METHODS FOR ELECTRICAL IMPEDANCE TOMOGRAPHY

By Z. Wei, R. Chen, H. Zhao, and X. Chen

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Abstract:
Two numerical methods are proposed to solve the electric impedance tomography (EIT) problem in a domain with arbitrary boundary shape. The rst is the new fast Fourier transform subspace-based optimization method (NFFT-SOM). Instead of implementing optimization within the subspace spanned by smaller singular vectors in subspace-based optimization method (SOM), a space spanned by complete Fourier bases is used in the proposed NFFT-SOM. We discuss the advantages and disadvantages of the proposed method through numerical simulations and comparisons with traditional SOM. The second is the low frequency subspace optimized method (LF-SOM), in which we replace the deterministic current and noise subspace in SOM with low frequency current and space spanned by discrete Fourier bases, respectively. We give a detailed analysis of strengths and weaknesses of LF-SOM through comparisons with mentioned SOM and NFFT-SOM in solving EIT problem in a domain with arbitrary boundary shape.

Citation:
Z. Wei, R. Chen, H. Zhao, and X. Chen, "Two FFT Subspace-Based Optimization Methods for Electrical Impedance Tomography," Progress In Electromagnetics Research, Vol. 157, 111-120, 2016.
doi:10.2528/PIER16082302
http://www.jpier.org/PIER/pier.php?paper=16082302

References:
1. Harrach, B., J. K. Seo, and E. J. Woo, "Factorization method and its physical justification in frequency-difference electrical impedance tomography," IEEE Transactions on Medical Imaging, Vol. 29, No. 11, 1918-1926, 2010.
doi:10.1109/TMI.2010.2053553

2. Goharian, M., 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.
doi:10.2528/PIER09052003

3. Polydorides, N., "Linearization error in electrical impedance tomography," Progress In Electromagnetics Research, Vol. 93, 323-337, 2009.
doi:10.2528/PIER09052503

4. Borcea, L., "Electrical impedance tomography," Inverse Problems, Vol. 18, No. 6, R99-R136, 2002.
doi:10.1088/0266-5611/18/6/201

5. Chaulet, N., S. Arridge, T. Betcke, and D. Holder, "The factorization method for three dimensional electrical impedance tomography," Inverse Problems, Vol. 30, No. 4, 2014.
doi:10.1088/0266-5611/30/4/045005

6. Borcea, L., G. A. Gray, and Y. Zhang, "Variationally constrained numerical solution of electrical impedance tomography," Inverse Problems, Vol. 19, No. 5, 1159-1184, 2003.
doi:10.1088/0266-5611/19/5/309

7. Abubakar, A. and P. M. van den Berg, "Nonlinear inversion in electrode logging in a highly deviated formation with invasion using an oblique coordinate system," IEEE Transactions on Geoscience and Remote Sensing, Vol. 38, No. 1, 25-38, 2000.
doi:10.1109/36.823898

8. Chen, X., "Subspace-based optimization method in electric impedance tomography," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 11-12, 1397-1406, 2009.
doi:10.1163/156939309789476301

9. Chen, X., "Subspace-based optimization method for solving inverse-scattering problems," IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 1, 42-49, 2010.
doi:10.1109/TGRS.2009.2025122

10. van den Berg, P.M., A. L. van Broekhoven, and A. Abubakar, "Extended contrast source inversion," Inverse Problems, Vol. 15, No. 5, 1325-1344, 1999.
doi:10.1088/0266-5611/15/5/315

11. Zhong, Y., X. Chen, and K. Agarwal, "An improved subspace-based optimization method and its implementation in solving three-dimensional inverse problems," IEEE Transactions on Geoscience and Remote Sensing, Vol. 48, No. 10, 3763-3768, 2010.
doi:10.1109/TGRS.2010.2049744

12. Zhong, Y. and X. Chen, "An FFT twofold subspace-based optimization method for solving electromagnetic inverse scattering problems," IEEE Transactions on Antennas and Propagation, Vol. 59, No. 3, 914-927, 2011.
doi:10.1109/TAP.2010.2103027

13. Gibson, W. C., The Method of Moments in Electromagnetics, CRC Press, 2014.

14. Lakhtakia, A. and G. W. Mulholland, "On two Numerical techniques for light scattering by dielectric agglomerated," Journal of Research of the National Institute of Standards and Technology, Vol. 98, No. 6, 699-716, 1993.
doi:10.6028/jres.098.046

15. Hansen, P., M. E. Kilmer, and R. H. Kjeldsen, "Exploiting residual information in the parameter choice for discrete ill-posed problems," Bit Numerical Mathematics, Vol. 46, No. 1, 41-59, 2006.
doi:10.1007/s10543-006-0042-7

16. Gil, A., J. Segura, and N. M. Temme, Numerical Methods for Special Functions, Society for Industrial and Applied Mathematics, Philadelphia, Pa, 2007.
doi:10.1137/1.9780898717822

17. Dehghani, H. and M. Soleimani, "Numerical modelling errors in electrical impedance tomography," Physiol. Meas., Vol. 28, No. 7, S45-S55, 2007.
doi:10.1088/0967-3334/28/7/S04

18. Stewart, G. W., Matrix Algorithms, Society for Industrial and Applied Mathematics, Philadelphia, 1998.
doi:10.1137/1.9781611971408

19. Dai, Y. H. and Y. Yuan, "A nonlinear conjugate gradient method with a strong global convergence property," SIAM Journal on Optimization, Vol. 10, No. 1, 177-182, 1999.
doi:10.1137/S1052623497318992


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