TOPOLOGICAL ALGORITHMS TO SOLVE INVERSE PROBLEM IN ELECTRICAL TOMOGRAPHY

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.
  Google Scholar

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

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

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.
  Google Scholar

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.
  Google Scholar

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.
  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, 171, 2001, 272–288.
  Google Scholar

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

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

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.
  Google Scholar

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.
  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, 2010, 70–77.
  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

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

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.
  Google Scholar

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