Speeding up the Tikhonov regularization iterative procedure in solving the inverse problem of electrical impedance tomography

Irina A. Sushko; A. I. Rybin

doi:10.3103/S0735272715090058

Authors

Irina A. Sushko National Technical University of Ukraine "Kyiv Polytechnic Institute", Ukraine https://orcid.org/0000-0002-3018-2875
A. I. Rybin National Technical University of Ukraine "Kyiv Polytechnic Institute", Ukraine https://orcid.org/0000-0003-4443-1075

DOI:

https://doi.org/10.3103/S0735272715090058

Keywords:

electrical impedance tomography, conductivity zones, regularization, inverse problem, matrix conditionality, phantom, finite elements method, correction of surface conductivities

Abstract

Algorithms of enhancing the speed of Tikhonov regularization algorithm for the conductivity zones method have been proposed; these algorithms make it possible to organize an iterative procedure with logarithmic step and evaluate the result of such iterative procedure through a single inversion of the matrix generated from the matrices of derivatives of phantom contour-edge voltages with respect to the surface conductivities of zones.

References

BROWN, B.H.; BARBER, D.C. Electrical Impedance Tomography. Clinical Physics and Physiological Measurement, v.13, Sappl. A, 207 p.

WEBB, S. The Physics of Medical Imaging. CRC Press, 1988.

PEKKER, Y.S.; BRAZOVSKII, K.S.; USOV, V.Y.; PLOTNIKOV, M.P.; UMANSKII, O.S. Electrical Impedance Tomography. Tomsk: NTL, 2004 [in Russian].

RYBINA, I.A. Solution of direct task of impedance tomography by the methods of theory of circuits. Visnyk NTUU KPI. Ser. Radiotekhnika. Radioaparatobuduvannya, 2010, n.43, p.4-13.

SUSHKO, I.A. Algorithm for solving the Electrical Impedance Tomography forward problem by the modification method. Visnyk NTUU KPI. Ser. Radiotekhnika. Radioaparatobuduvannya, 2011, n.47, p.165-175.

SILVESTER, P.P.; FERRARI, R.F. Finite Elements for Electrical Engineers. Cambridge: CUP, 1983.

MURAI, TADAKUNI; KAGAWA, YUKIO. Electrical impedance computed tomography based on a finite element model. IEEE Trans. Biomed. Eng., Mar. 1985, v.BME-32, n.3, p.177-184, DOI: http://dx.doi.org/10.1109/TBME.1985.325526.

RYBIN, A.I. Numerical-and-Symbolic Analysis of Electric Networks by the Generalized Modification Method. Pratsi Instytutu Elektrodynamiky NAN Ukrainy, IED NANU, 2002, n.1, p.28-30.

RYBINA, I.O.; RYBIN, A.I.; SHARPAN, O.B. Solving the Electrical Impedance Tomography (EIT) inverse problem by the conductivity and back projection methods. Visnyk NTUU KPI. Ser. Radiotekhnika. Radioaparatobuduvannya, 2011, n.45, p.33-45, http://radap.kpi.ua/radiotechnique/article/view/166.

SUSHKO, IRINA A. Visualization of surface conductivity distributions of tomography cross-section using conductivity zones method. Izv. Vyssh. Uchebn. Zaved., Radioelektron., 2013, v.56, n.7, p.60-68, http://radio.kpi.ua/article/view/S0021347013070078 [Radioelectron. Commun. Syst., 2013, v.56, n.7, p.377-383, DOI: http://dx.doi.org/10.3103/S0735272713070078].

SUSHKO, I.A.; GAYDAYENKO, E.V.; YAKUBENKO, A.A. Electrical Impedance Tomography potential sensitivity. Visnyk NTUU KPI. Ser. Radiotekhnika. Radioaparatobuduvannya, 2012, n.50, p.92-104, http://radap.kpi.ua/radiotechnique/article/view/237.

DOSTAL, T.; SUSHKO, I.A.; MATSAI, A.; GAYDAYENKO, E.V.; RYBIN, A.I. Sensitivity of phantom contour voltage to complex impedance changes of inhomogeneities in Electrical Impedance Tomography. Visnyk NTUU KPI. Ser. Radiotekhnika. Radioaparatobuduvannya, 2014, n.56, p.152-164, http://radap.kpi.ua/radiotechnique/article/view/756.

RYBIN, A.I.; GAYDAYENKO, E.V.; SUSHKO, I.A.; GAMANENKO, A.I. The sensitivity in Electrical Impedance Tomography. Visnyk NTUU KPI. Ser. Radiotekhnika. Radioaparatobuduvannya, 2013, n.55, p.107-117, http://radap.kpi.ua/radiotechnique/article/view/677.

VAUHKONEN, M.; VADASZ, D.; KARJALAINEN, P.A.; SOMERSALO, E.; KAIPIO, J.P. Tikhonov regularization and prior information in electrical impedance tomography. IEEE Trans. Med. Imaging, Apr. 1998, v.17, n.2, p.285-293, DOI: http://dx.doi.org/10.1109/42.700740.

TIKHONOV, A.N.; ARSENIN, V.Y. Methods for Solving the Ill-Conditioned Problems. Moscow: Nauka, 1979 [in Russian].

SUSHKO, I.A.; RYBIN, A.I. Peculiarities of using the regularization method in solving the inverse problem of impedance tomography by the conductivity zones method. Research Bulletin of NTUU KPI, 2013, n.56, p.14-24.