TOPOLOGICAL ALGORITHMS TO SOLVE INVERSE PROBLEM IN ELECTRICAL TOMOGRAPHY

Tomasz Rymarczyk

doi:10.5604/01.3001.0010.4583

Open full text

pdf

Published: Mar 3, 2017

DOI: https://doi.org/10.5604/01.3001.0010.4583

Issue Vol. 7 No. 1 (2017)

Articles

STUDY OF DEGRADATION AND GRANULAR FLOW PROCESSES USING X-RAY IMAGING
Laurent Babout , Krzysztof Grudzień, Marcin Janaszewski, Łukasz Jopek

5-10
TWO-PHASE FLOW REGIME THREE-DIMENSONAL VISUALIZATION USING ELECTRICAL CAPACITANCE TOMOGRAPHY – ALGORITHMS AND SOFTWARE
Robert Banasiak, Radosław Wajman, Tomasz Jaworski, Paweł Fiderek, Dominik Sankowski

11-16
INTELLIGENT SYSTEM FOR THE TWO-PHASE FLOWS DIAGNOSIS AND CONTROL ON THE BASIS OF RAW 3D ECT DATA
Paweł Fiderek, Tomasz Jaworski, Robert Banasiak, Jacek Nowakowski, Jacek Kucharski, Radosław Wajman

17-23
METHODS FOR MONITORING GRAVITATIONAL FLOW IN SILOS USING TOMOGRAPHY IMAGE PROCESSING
Krzysztof Grudzień, Dominik Sankowski

24-29
FLOW VELOCITY MEASUREMENT METHODS USING ELECTRICAL CAPACITANCE TOMOGRAPHY
Volodymyr Mosorov, Krzysztof Grudzień, Dominik Sankowski

30-36
ACCELERATION OF IMAGE RECONSTRUCTION PROCESS IN THE ELECTRICAL CAPACITANCE TOMOGRAPHY 3D IN HETEROGENEOUS, MULTI-GPU SYSTEM
Michał Majchrowicz, Paweł Kapusta, Lidia Jackowska-Strumiłło, Dominik Sankowski

37-41
APPLICATION OF FRACTIONAL CALCULUS FOR MODELLING OF TWO-PHASE GAS/LIQUID FLOW SYSTEM
Jacek Nowakowski, Piotr Ostalczyk, Dominik Sankowski

42-45
MULTI PHASE FLOW MEASUREMENTS WITH THE APPLICATION OF ECT/ERT DECART MULTIMODALITY TOMOGRAPH
Jacek Nowakowski, Robert Banasiak, Radosław Wajman, Dominik Sankowski

46-49
PARAMETRIC METHODS FOR ECT INVERSE PROBLEM SOLUTION IN SOLID FLOW MONITORING
Andrzej Romanowski, Krzysztof Grudzień, Hela Garbaa, Lidia Jackowska-Strumiłło

50-54
TOPOLOGICAL ALGORITHMS TO SOLVE INVERSE PROBLEM IN ELECTRICAL TOMOGRAPHY
Tomasz Rymarczyk

55-58
MONITORING DAMAGE AND DAMPNESS IN FLOOD EMBANKMENT BY ELECTRICAL IMPEDANCE TOMOGRAPHY
Tomasz Rymarczyk, Przemysław Adamkiewicz

59-62
LEVEL SETS AND COMPUTATIONAL INTELLIGENCE ALGORITHMS TO MEDICAL IMAGE ANALYSIS IN E-MEDICUS SYSTEM
Tomasz Rymarczyk

63-67
NONDESTRUCTIVE METHOD TO DETERMINE MOISTURE AREA IN HISTORICAL BUILDING
Tomasz Rymarczyk, Przemysław Adamkiewicz

68-71
HYBRID TECHNIQUES TO SOLVE OPTIMIZATION PROBLEMS IN EIT
Tomasz Rymarczyk, Paweł Tchórzewski

72-75
USING ELECTRICAL IMPEDANCE TOMOGRAPHY IN LINEAR ARRAYS OF MEASUREMENT
Tomasz Rymarczyk

76-79
COUPLING BOUNDARY ELEMENT METHOD WITH LEVEL SET METHOD TO SOLVE INVERSE PROBLEM
Tomasz Rymarczyk, Paweł Tchórzewski, Jan Sikora

80-83
DETECTION OF AIR GAPS IN COPPER-MINE CEILING BY ELECTRICAL IMPEDANCE TOMOGRAPHY
Tomasz Rymarczyk, Paweł Tchórzewski, Jan Sikora

84-87
MEASURING DATA ACQUISITION HARDWARE FOR ELECTRICAL IMPEDANCE TOMOGRAPHY
Tomasz Rymarczyk, Karol Duda, Paweł Rymarczyk, Daniel Olchowy, Jan Sikora

88-91
CONCEPT OF DETECTION SYSTEM TO LOCALIZE INSIDE CLOSED AREA BY RADIO TOMOGRAPHIC IMAGING
Tomasz Rymarczyk, Przemysław Adamkiewicz, Jakub Szumowski, Konrad Niderla, Łukasz Gołąbek, Jan Sikora

92-95
IDEA OF PARAMETRIC AND SEMANTIC OPEN PLATFORM SMART DEVICES SENSOR
Tomasz Rymarczyk, Grzegorz Kłosowski, Przemysław Adamkiewicz, Karol Duda, Jakub Szumowski, Paweł Tchórzewski

96-100
IDEA OF ELECTRICAL TOMOGRAPHY SYSTEM FOR MONITORING LUNG VENTILATION
Tomasz Rymarczyk, Przemysław Adamkiewicz, Paweł Tchórzewski

101-104
METHODS OF SMALL CAPACITANCE MEASUREMENT IN ELECTRICAL CAPACITANCE TOMOGRAPHY
Waldemar Smolik, Jacek Kryszyn, Tomasz Olszewski, Roman Szabatin

105-110
DEVELOPMENT OF ELECTRICAL CAPACITANCE TOMOGRAPH DESIGN IN THE NUCLEAR AND MEDICAL ELECTRONICS DIVISION
Jacek Kryszyn, Waldemar Smolik, Tomasz Olszewski, Roman Szabatin

111-114
LINEAR OVER RANGES ITERATIVE ALGORITHMS FOR IMAGE RECONSTRUCTION IN ELECTRICAL CAPACITANCE TOMOGRAPHY
Waldemar Smolik, Jacek Kryszyn

115-120
NEEDLE DETECTOR OF X-RAY AND GAMMA RADIATION
Grzegorz Domański, Roman Szabatin, Piotr Brzeski, Bogumił Konarzewski

121-124
DEVELOPMENT OF MAGNETIC NANOPARTICLES TOMOGRAPHY IN NUCLEAR AND MEDICAL ELECTRONICS DIVISION
Przemysław Wróblewski, Waldemar Smolik

125-129
GAIN PREDICTION THEORY OF SINGLE FOIL GAS ELECTRON MULTIPLIER DETECTOR
Grzegorz Domański, Roman Szabatin, Jerzy Kalenik, Adam Jaworski, Przemysław Wróblewski, Waldemar Smolik, Robert Kurjata, Bogusław Konarzewski, Michał Dziewiecki, Janusz Marzec, Krzysztof Zaremba, Marcin Ziembicki, Andrzej Rychter, Jacek Kryszyn, Piotr Brzeski, Jan Szmidt

130-132
INCREASING THE SIGNAL TO NOISE RATIO IN LOW-FIELD MR SCANNER AT DEPARTMENT OF NUCLEAR AND MEDICAL ELECTRONICS
Michał Wieteska, Wojciech Obrębski, Ewa Piątkowska-Janko, Błażej Sawionek, Piotr Bogorodzki

133-136
TOOLBOX FOR 3D MODELLING AND IMAGE RECONSTRUCTION IN ELECTRICAL CAPACITANCE TOMOGRAPHY
Jacek Kryszyn, Waldemar Smolik

137-145
2D MODELLING OF A SENSOR FOR ELECTRICAL CAPACITANCE TOMOGRAPHY IN ECTSIM TOOLBOX
Jacek Kryszyn, Waldemar Smolik

146-149
COIL DESIGN WITH LITZE WIRE FOR MAGNETIC PARTICLE SPECTROMETRY
Przemysław Wróblewski, Waldemar Smolik

150-153
BOUNDARY ELEMENT METHOD MODYFICATIONS FOR USE IN SOME IMPEDANCE AND OPTICAL TOMOGRAPHY APPLICATIONS
Maciej Pańczyk, Jan Sikora

154-160
REVIEW OF METHODS OF MEASURING BASED ON OPTICAL TOMOGRAPHY APPLICABLE TO DETERMINING FLOW PARAMETERS OF GAS-LIQUID
Mariusz Rząsa, Ewelina Podgórni

161-164

DOI

https://doi.org/10.5604/01.3001.0010.4583

Authors

Tomasz Rymarczyk

tomasz.rymarczyk@netrix.com.pl

Netrix S.A., Research and Development Center, Poland

Abstract

In this paper, there were investigated topological algorithms to solve the inverse problem in electrical tomography. The level set method, material derivative, shape derivative and topological derivative are based on shape and topology optimization approach to electrical impedance tomography problems with piecewise constant conductivities. The cost of the numerical algorithm is enough good, because the shape is captured on a fixed grid. The proposed solution is initialized by using topological sensitivity analysis. Shape derivative and material derivative (or topological derivative) have been incorporated with level set methods to investigate shape optimization problems.

Keywords:

topological methods, inverse problem, finite element method, electrical impedance tomography

References

Allaire G., Gournay F. De, Jouve F., Toader A. M.: Structural optimization using topological and shape sensitivity via a level set method, Control and Cybernetics, vol. 34, 2005, 59–80.

Chan T. and Vese L.: Active contours without edges, IEEE Transactions on Image Processing, vol. 10, 2001, 266–277.

Hintermüller M., Laurain A., Novotny A.A.: Second-order topological expansion for electrical impedance tomography, Advances in Computational Mathematics, 36(2), 2012, 235–265.

Ito K., Kunish K., Li Z.: The Level-Set Function Approach to an Inverse Interface Problem. Inverse Problems, Vol. 17, No. 5, 2001, 1225–1242.

Kapusta P., Majchrowicz M., Sankowski D., Jackowska-Strumiłło L., Banasiak R.: Distributed multi-node, multi-GPU, heterogeneous system for 3D image reconstruction in Electrical Capacitance Tomography – network performance and application analysis. Przegląd Elektrotechniczny, Vol. 89, No. 2b, 2013, 339–342.

Osher S., Sethian J.A.: Fronts Propagating with Curvature Dependent Speed: Algorithms Based on Hamilton-Jacobi Formulations, Journal of Computational Physics, 79, 1988, 12–49.

Osher S., Fedkiw R.: Level Set Methods and Dynamic Implicit Surfaces. Springer, New York 2003

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, 171, 2001, 272–288.

Rymarczyk T.: Using electrical impedance tomography to monitoring flood banks, International Journal of Applied Electromagnetics and Mechanics 45, 2014, 489–494.

Rymarczyk T.: Characterization of the shape of unknown objects by inverse numerical methods, Przegląd Elektrotechniczny, R. 88, nr 7b/2012, 138–140.

Rymarczyk T., Sikora J.: Different Approaches to Level Set Method and Its Applications, chapter in Algorithms, Networking and Sensing for Data Processing Mobile Computing and Applications, edited by A. Romanowski, D. Sankowski and J. Sikora, Lodz University of Technology Monograph, Lodz 2016.

Rymarczyk T, Adamkiewicz P., Duda K., Szumowski J., Sikora J.: New Electrical Tomographic Method to Determine Dampness in Historical Buildings, Achieve of Electrical Engineering, v.65, 2/2016, 273–283.

Smolik W.: Forward Problem Solver for Image Reconstruction by Nonlinear Optimization in Electrical Capacitance Tomography, Flow Measurement and Instrumentation, Vol. 21, Issue 1, 2010, 70–77.

Sokolowski J., Zochowski A.: On the topological derivative in shape optimization, SIAM Journal on Control and Optimization, vol. 37, 1999, 1251–1272.

Szulc K.: Topological derivative-theory and applications. Informatyka, Automatyka, Pomiary w Gospodarce i Ochronie Środowiska, 1, 2015, 7–13 [DOI: 10.5604/20830157.1148040].

Tai C., Chung E., Chan T.: Electrical impedance tomography using level set representation and total variational regularization. Journal of Computational Physics, vol. 205, no. 1, 2005, 357–372.

Wajman R., Banasiak R.: Tunnel-based method of sensitivity matrix calculation for 3D-ECT imaging, Sensor Review, Vol. 34 Iss: 3, 273–283, 2014.

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.

Rymarczyk, T. (2017). TOPOLOGICAL ALGORITHMS TO SOLVE INVERSE PROBLEM IN ELECTRICAL TOMOGRAPHY. Informatyka, Automatyka, Pomiary W Gospodarce I Ochronie Środowiska, 7(1), 55–58. https://doi.org/10.5604/01.3001.0010.4583

TOPOLOGICAL ALGORITHMS TO SOLVE INVERSE PROBLEM IN ELECTRICAL TOMOGRAPHY

Issue Vol. 7 No. 1 (2017)

Archives

DOI

Authors

Abstract

Keywords:

References

License

Article Sidebar

Issue Vol. 7 No. 1 (2017)

Archives

Main Article Content

DOI

Authors

Abstract

Keywords:

References

Article Details

License