LINEAR OVER RANGES ITERATIVE ALGORITHMS FOR IMAGE RECONSTRUCTION IN ELECTRICAL CAPACITANCE TOMOGRAPHY


Abstract

The paper concerns the non-linear algorithms for image reconstruction in electrical capacitance tomography for which Jacobi matrix computation time is very long. The paper presents the idea of an iterative linearization in nonlinear problems, which leads to a reduction in the number of steps calculating Jacobi matrix. The linear Landweber algorithm with sensitivity matrix updating and non-linear Levenberg-Marquardt algorithm with Jacobi matrix updating in selected steps only were presented.


Keywords

non-linear problem; iterative linearization; electrical tomography; image reconstruction from projections

Brandstatter B., Holler G., Watzenig, D.: Reconstruction of inhomogeneities in fluids by means of capacitance tomography. COMPEL—Int. J. Comput. Math. Electr. Electron. Eng., 22/2003, 508–19.

Brzeski P., Mirkowski J., Olszewski T., Pląskowski A., Smolik W., Szabatin R.: Multichannel capacitance tomograph for dynamic process imaging. Opto-Electronics Review, 11(3)/2003, 175–180.

Gomez S., Ono M., Gamio C., Fraguela A.: Reconstruction of capacitance tomography images of simulated two-phase flow regimes. Appl. Num. Math., 2003, 197–208.

Hansen P.C., O'leary D.P.: The use of the L-curve in the regularization of discrete ill-posed problems. SIAM J. Sci. Comput., 14/1993, 1487–1503.

Holler G., Watzenig D., Brandstatter B.: A fast Gauss–Newton based ECT algorithm with automatic adjustment of the regularization parameter. Proc. 3rd World Congress on Industrial Process Tomography, Banff, Alberta, Canada, 2003, 415–420.

Huang S.M., Plaskowski A.B., Xie C.G., Beck M.S.: Capacitance-based tomographic flow imaging system. Electron. Lett., 24/1988, 418–419.

Huang S.M., Plaskowski A., Xie C.G., Beck M.S.: Tomographic imaging of two-component flow using capacitance sensors. J.Phys. E:Sci. Instrum., 22/1989, 173–177.

Landweber L.: An Iterative Formula for Fredholm Integral Equations of the First Kind. Amer. J. Math., 73/1951, 615–624.

Li Y., Yang W.Q.: Image reconstruction by nonlinear Landweber iteration for complicated distributions. Meas. Sci. Technol., 19/2008, 1–8.

Lionheart W. R.: EIT reconstruction algorithms: pitfalls, challenges and recent developments. Physiol. Meas., 25/2004, 125–142.

Lionheart W., Polydordes N., Borsic A.: The reconstruction problem. In: Holder D.S. (ed.) Electrical Impedance Tomography: Methods, History and Applications. Institute of Physics, 2004.

Mirkowski J., Smolik W., Olszewski T., Radomski D., Szabatin R., Brzeski P.: Parameters Optimization For Model Based Image Reconstruction In Electrical Capacitance Tomography. Proc. 4th World Congress on Industrial Process Tomography, Aizu, Japan, 2005, 703–707.

Mirkowski J., Smolik W.T., Yang M., Olszewski T., Szabatin R., Radomski D.S., Yang W.Q.: A New Forward-Problem Solver Based on a Capacitor-Mesh Model for Electrical Capacitance Tomography. IEEE Trans. Instrumentation and Measurement, Vol. 57, No 5, 2008, 973–980.

Plaskowski, A., Beck, M., Thorn, R. & Dyakowski, T.: Imaging industrial flows. Applications of electrical process tomography, IOP Publishing Ltd., 1995.

Smolik W.: Reconstruction of complex objects in electrical capacitance tomography. IEEE International Workshop on Imaging Systems and Techniques (IST 2009), Shenzhen, China, 2009, 432–437.

Smolik W.T., Radomski D.: Performance evaluation of the iterative image reconstruction algorithm with sensitivity matrix updating based on real measurements for electrical capacitance tomography. Meas. Sci. Technol., 20/2009, 115502 (12pp).

Smolik W., Mirkowski J., Olszewski T., Szabatin R.: Verification of image reconstruction algorithm with sensitivity matrix updating for real data in electrical capacitance tomography. Proc. 4th International Symposium on Process Tomography in Poland, Warsaw, Poland, 2006.

Smolik W.T., Accelerated Levenberg-Marquardt Method With an Optimal Step Length in Electrical Capacitance Tomography, Proc. of IEEE International Conference on Imaging Systems and Techniques (IST 2010), Thessaloniki, Greece, 2010, 204–209.

Smolik W.: Forward Problem Solver for Image Reconstruction by Nonlinear Optimization in Electrical Capacitance Tomography. Flow Measurement and Instrumentation, 21/2010, 70–77.

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Published : 2017-03-03


Smolik, W., & Kryszyn, J. (2017). LINEAR OVER RANGES ITERATIVE ALGORITHMS FOR IMAGE RECONSTRUCTION IN ELECTRICAL CAPACITANCE TOMOGRAPHY. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 7(1), 115-120. https://doi.org/10.5604/01.3001.0010.4598

Waldemar Smolik  W.Smolik@ire.pw.edu.pl
Warsaw University of Technology, Faculty of Electronics and Information Technology, The Institute of Radioelectronics and Multimedia Technology, Nuclear and Medical Electronics Division  Poland
Jacek Kryszyn 
Warsaw University of Technology, Faculty of Electronics and Information Technology, The Institute of Radioelectronics and Multimedia Technology, Nuclear and Medical Electronics Division  Poland