HYBRID TECHNIQUES TO SOLVE OPTIMIZATION PROBLEMS IN EIT
Tomasz Rymarczyk
tomasz.rymarczyk@netrix.com.plNetrix S.A., Research and Development Center (Poland)
Paweł Tchórzewski
Netrix S.A., Research and Development Center (Poland)
Abstract
This paper presents the hybrid algorithm for identification the unknown shape of an interface to solve the inverse problem in electrical impedance tomography. The conductivity values in different regions are determined by the finite element method. The numerical algorithm is a combination of the level set method, Gauss-Newton method and the finite element method. The representation of the shape of the boundary and its evolution during an iterative reconstruction process is achieved by the level set function. The cost of the numerical algorithm is enough effective. These algorithms are a relatively new procedure to overcome this problem.
Keywords:
Inverse Problem, Level Set Method, Electrical Impedance TomographyReferences
Chan T. and Vese L.: Active contours without edges, IEEE Transactions on Image Processing, vol. 10, 2001, 266–277.
Google Scholar
Ito K., Kunish K., Li Z.: The Level-Set Function Approach to an Inverse Interface Problem. Inverse Problems, 2001, Vol. 17, No. 5, 1225–1242.
Google Scholar
Lechleiter A., Rieder A.: Newton regularizations for impedance tomography: convergence by local injectivity. Inverse Problems, 24(6), 2008.
Google Scholar
Li C., Xu C., Gui C., Fox M. D.: Level set evolution without re-initialization. A new variational formulation, In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2005, volume 1, 430–436.
Google Scholar
Osher S., Sethian J.A.: Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations, Journal of Computational Physics, 1988, 79, 12–49.
Google Scholar
Osher S., Fedkiw R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York 2003.
Google Scholar
Osher S., Santosa F.: Level set methods for optimization problems involving geometry and constraints. Frequencies of a two-density inhomogeneous drum. Journal of Computational Physics, 2001, 171, 272–288.
Google Scholar
Rymarczyk T.: New Methods to Determine Moisture Areas by Electrical Impedance Tomography, International Journal of Applied Electromagnetics and Mechanics 08/2016, 1–9.
Google Scholar
Rymarczyk T., Filipowicz S.F.: The Shape Reconstruction of Unknown Objects for Inverse Problems, Electrical Review, NR 5/2012/3a.
Google Scholar
Rymarczyk T.: Characterization of the shape of unknown objects by inverse numerical methods, Przegląd Elektrotechniczny, R. 88 NR 7b/2012, 138–140, 2012.
Google Scholar
Rymarczyk T, Adamkiewicz P., Duda K., Szumowski J., Sikora J.: New Electrical Tomographic Method to Determine Dampness in Historical Buildings, v.65, 2/2016, Achieve of Electrical Engineering, 2016, 273–283.
Google Scholar
Sethian J.A.: Level Set Methods and Fast Marching Methods. Cambridge University Press, 1999.
Google Scholar
Sokolowski J., Zochowski A.: On the topological derivative in shape optimization, SIAM Journal on Control and Optimization, vol. 37, 1999, 1251–1272.
Google Scholar
Smolik W, Forward Problem Solver for Image Reconstruction by Nonlinear Optimization in Electrical Capacitance Tomography, Flow Measurement and Instrumentation, Vol. 21, Issue 1, March 2010, 70–77.
Google Scholar
Wajman R., Fiderek P., Fidos H., Jaworski T., Nowakowski J., Sankowski D., Banasiak R.: Metrological evaluation of a 3D electrical capacitance tomography measurement system for two-phase flow fraction determination; Meas. Sci. Technol. 2013, Vol. 24 No. 065302.
Google Scholar
Tai C., Chung E., Chan T.: Electrical impedance tomography using level set representation and total variational regularization. Journal of Computational Physics, 2005, vol. 205, no. 1, 357–372.
Google Scholar
Zhao H.-K., Osher S., Fedkiw R.: Fast Surface Reconstruction using the Level Set Method. 1st IEEE Workshop on Variational and Level Set Methods, in conjunction with the 8th International Conference on Computer Vision (ICCV), Vancouver, Canada, 2001, 194–202.
Google Scholar
Authors
Tomasz Rymarczyktomasz.rymarczyk@netrix.com.pl
Netrix S.A., Research and Development Center Poland
Authors
Paweł TchórzewskiNetrix S.A., Research and Development Center Poland
Statistics
Abstract views: 295PDF downloads: 63
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Most read articles by the same author(s)
- Tomasz Rymarczyk, Jan Sikora, SCATTERING BY CIRCULAR VOIDS WITH RIGID BOUNDARY: DIRECT AND INVERSE PROBLEMS FOR OPEN AND CLOSE DOMAINS , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 12 No. 4 (2022)
- Tomasz Rymarczyk, Paweł Tchórzewski, Jan Sikora, DETECTION OF AIR GAPS IN COPPER-MINE CEILING BY ELECTRICAL IMPEDANCE TOMOGRAPHY , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 7 No. 1 (2017)
- Tomasz Rymarczyk, Przemysław Adamkiewicz, MONITORING DAMAGE AND DAMPNESS IN FLOOD EMBANKMENT BY ELECTRICAL IMPEDANCE TOMOGRAPHY , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 7 No. 1 (2017)
- Konrad Kania, Tomasz Rymarczyk, METHODS FOR DETECTION ANALYSIS IN QUALITY CONTROL SYSTEM , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 8 No. 3 (2018)
- Tomasz Rymarczyk, LEVEL SETS AND COMPUTATIONAL INTELLIGENCE ALGORITHMS TO MEDICAL IMAGE ANALYSIS IN E-MEDICUS SYSTEM , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 7 No. 1 (2017)
- Paweł Tchórzewski, SOLUTIONS OF FORWARD PROBLEMS OBTAINED VIA BOUNDARY ELEMENT METHOD FOR NONHOMOGENEOUS DOMAINS IN REGARD TO ELECTRICAL CONDUCTIVITY , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 5 No. 3 (2015)
- Tomasz Rymarczyk, Jan Sikora, IDENTIFICATION OF AN ARBITRARY SHAPE RIGID OBSTACLE ILLUMINATED BY FLAT ACOUSTIC WAVE USING NEAR FIELD DATA , Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska: Vol. 14 No. 4 (2024)