Electrical impedance tomography (EIT) is a technique for reconstructing the conductivity distribution by injecting currents at the boundary of a subject and measuring the resulting changes in voltage. Many algorithms have been proposed for two-dimensional EIT reconstruction. However, since the human thorax has the characteristic of three-dimensions, EIT is a truly three-dimensional imaging problem. In this paper, we propose a three-dimensional imaging method using tensors for EIT. A tensor EIT model is established by EIT data and the Tucker decomposition is used to obtain the tensor basis. The tensor basis can form a new way to reconstruct image in three-dimensional space. Experiment results revealed that the data structural information of image can be fully used by the tensor method. A comparison of the peak signal to noise ratio (PSNR) shows that the newly proposed method performs better than other methods, i.e. the Dynamic Group Sparse TV algorithm and Tikhonov algorithm. The newly proposed method is closer to the ground truth, thus it can more accurately reflect the state of a lung than two-dimensional EIT. Finally, the EIT experiment is carried out to evaluate the proposed method. The experimental results show that the accuracy of reconstruction based on the new method is efficiently improved.
2. Yu, Y., J. Jin, F. Liu, and S. Crozier, "Multidimensional compressed sensing MRI using tensor decomposition-based sparsifying transform," PLoS ONE, Vol. 9, No. 6, e98441, 2014.
3. Fu, H.-S. and B. Han, "Tikhonov regularization-homotopy method for electrical impedance tomography," Journal of Natural Science of Heilongjiang University, Vol. 3, 319-323, 2011.
4. Wang, Q., et al., "Image reconstruction based on L1 regularization and projection methods for electrical impedance tomography," Review of Scientific Instruments, Vol. 83, No. 10, 104707, 2012.
5. Zhao, B., H. X. Wang, X. Y. Chen, X. L. Shi, and W. Q. Yang, "Linearized solution to electrical impedance tomography based on the Schur conjugate gradient method," Measurement Science and Technology, Vol. 18, No. 11, 3373-3383, 2007.
6. Morucii, J., M. Granie, M. Lei, M. Chebett, and W. Dai, "Direct sensitivity matrix in electrical impedance imaging," International Conference of the IEEE Engineering in Medicine and Biology Society, 538-539, 1994.
7. Barber, D. C., "A sensitivity method for electrical impedance tomography," Clinicial Phyiscs and Physiological Measurement, Vol. 10, No. 4, 368-371, 1989.
8. Semenov, S. Y., et al., "Iterative algorithm for 3D EIT," Engineering in Medicine and Biology Society, 10, 1997.
9. Wang, M., "Inverse solutions for electrical impedance tomography based on conjugate gradients methods," Measurement Science and Technology, Vol. 13, 101-117, 2002.
10. Borsic, A., et al., "In vivo impedance imaging with total variation regularization," IEEE Transactions on Medical Imaging, Vol. 29, No. 1, 44-53, 2010.
11. Lukaschewitsch, M., P. Maass, and M. Pidcock, "Tikhonov regularization for electrical impedance tomography on unbounded domains," Inverse Problems, Vol. 19, 585-610, 2003.
12. Fan, W., et al., "An image reconstruction algorithm based on preconditioned LSQR for 3D EIT," IEEE International Instrumentation and Measurement Technology Conference, 10, 2011.
13. Jacobsen, M., P. C. Hansen, and M. A. Saunders, "Subspace preconditioned LSQR for discrete ill-posed problems," BIT Numerical Mathematics, Vol. 43, 975-989, 2003.
14. Wang, H. X., L. Tang, and Y. Yan, "Total variation regularization algorithm for electrical capacitance tomography," Chinese Journal of Scientific Instrument, Vol. 28, No. 11, 2014-2018, 2007.
15. Chambelle, A., et al., "An algorithm for total variation minimization and applications," Journal of Mathematical Imaging and Vision, Vol. 20, 89-97, 2004.
16. Yang, Y., et al., "Image reconstruction for electrical impedance tomography using enhanced adaptive group sparsity with total variation," IEEE Sensors Journal, Vol. 17, No. 17, 5589-5598, 2017.
17. Hemming, B., A. Fagerlund, and A. Lassila, "Linearized solution to electrical impedance tomography based on the schur conjugate gradient method," Measurement Science & Technology, Vol. 18, No. 11, 3373, 2007.
18. Li, X., et al., "Electrical-impedance-tomography imaging based on a new three-dimensional thorax model for assessing the extent of lung injury," AIP Advances, Vol. 10, 9000000, 2019.
19. Kolda, T. and B. Bader, "Tensor decompositions and applications," SIAM Rev., Vol. 51, No. 3, 455-500, 2009.
20. De Lathauwer, L., B. De Moor, and J. Vandewalle, "A multilinear singular value decomposition," SIAM J. Matrix Anal. Appl., Vol. 21, 1253-1278, 2000.
21. Wang, Q., et al., "Patch-based sparse reconstruction for electrical impedance tomography," Sensor Review, Vol. 37, No. 3, 257-269, 2017.
22. Caiafa, C. F. and A. Cichocki, "Fast and stable recovery of approximatelly low multilinear rank tensors from multi-way compressive measurements," IEEE Int. Conf. Acoust. Speech, Signal., 6790-6794, 2014.
23. Caiafa, C. F. and A. Cichocki, "Multidimensional compressed sensing and their applications," Wiley Interdisciplinary Rev.: Data Mining Knowledge Discovery, Vol. 3, No. 6, 355-380, 2013.
24. Hansen, P. C., "Rank-deficient and discrete Ill-posed problems," American Mathematical Monthly, Vol. 10, No. 3, 215-247, 1998.
25. Caiafa, C. F. and A. Cichocki, "Stable, robust, and super fast reconstruction of tensors using multi-way projections," IEEE Transactions on Signal Processing, Vol. 63, No. 3, 780-793, 2015.
26. Schullcke, B., Z. S. Krueger, and B. Gong, "Ventilation inhomogeneity in obstructive lung diseases measured by electrical impedance tomography: A simulation study," J. Clin. Monit. Comput., Vol. 32, No. 4, 753-761, 2018.
27. Schullcke, B., Z. S. Krueger, and B. Gong, "A simulation study on the ventilation inhomogeneity measured with electrical impedance tomography," IFAC Papers on Line, Vol. 50, 8781-8785, 2017.
28. Wang, Q., et al., "Image reconstruction based on L1 regularization and projection methods for electrical impedance tomography," Review of Scientific Instruments, Vol. 83, No. 10, 104707, 2012.