# Acceleration of image reconstruction in 3D Electrical Capacitance Tomography in heterogeneous, multi-GPU system using sparse matrix computations and Finite Element Method

## Paweł Kapusta, Michał Majchrowicz, Dominik Sankowski, Lidia Jackowska-Strumiłło

DOI: http://dx.doi.org/10.15439/2016F344

Citation: Proceedings of the 2016 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 8, pages 679–683 (2016)

Abstract. 3D Electrical Capacitance Tomography provides a lot of challenging computational issues that have been reported in the past by many researchers. Image reconstruction using deterministic methods requires execution of many basic operations of linear algebra, such as matrix transposition, multiplication, addition and subtraction. Due to significant sizes of matrices used in ECT for image reconstruction and the fact that only small number of elements in these matrices are non-zero means, that often some kind of sparse format is used. However both parallel and distributed algorithms are not optimized for sparse formats. Moreover best image reconstruction quality is achieved by using algorithms of which significant part is FEM and which are hard to parallelize or distribute. In order to solve these issues a new set of algorithms had to be developed, which are specifically optimized for the purpose of image reconstruction in ECT.

### References

- Banasiak, R., Wajman, R., Fidos, H., Jaworski, T., Fiderek, P., Kapusta, P., Majchrowicz, M., Sankowski, D., “Fusion of three-dimensional electrical capacitance tomography and fuzzy logic inference for phases fraction and flow structures identification in horizontal and vertical gas-liquid flow pipelines.,” 7th World Congress on Industrial Process Tomography, Kraków, 2013, pp. 818–827.
- Garbaa, H., Jackowska-Strumiłło, L, Grudzień, K., Romanowski, A., “Neural network approach to ECT inverse problem solving for estimation of gravitational solids flow,” In Proc. of the 2014 Federated Conf. on Computer Science and Inf. Systems, AAIA’14, Vol. 2, Warsaw, Poland, 2014, pp 19-26
- Kapusta, P., Majchrowicz, M, “Accelerating Image reconstruction algorithms in Electrical Capacitance Tomography using Multi-GPU system,” Advanced Numerical Modelling, International Interdisciplinary PhD Workshop, Warsaw, Electrotechnical Institute, 2011, pp. 47–49.
- 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,” Przeglad ̨ Elektrotechniczny, 89 (2 B), 2013, pp. 339-342.
- Majchrowicz, M., Kapusta, P., Banasiak, R. , “Applying parallel and distributed computing for image reconstruction in 3D Electrical Capacitance Tomography,” Zeszyty Naukowe AGH - Automatyka, Vol 14, Issue 3/2, 2010, Kraków, Wydawnictwa AGH, pp. 711–722.
- Majchrowicz, M., Kapusta, P., W as, ̨ Ł., Wiak, S, “Application of General-Purpose Computing on Graphics Processing Units for Acceleration of Basic Linear Algebra Operations and Principal Components Analysis Method,” Man-Machine Interactions 3, Advances in Intelligent Systems and Computing Volume 242, Springer International Publishing, 2014, pp. 519–527.
- Majchrowicz, M., Kapusta, P., Jackowska-Strumiłło, L., Sankowski, D., “Analysis of Application of Distributed Multi-Node, Multi-GPU Heterogeneous System for Acceleration of Image Reconstruction in Electrical Capacitance Tomography,” Image Processing & Communications, vol. 20, Issue 3, 2015, pp. 5–14.
- Sankowski, D., Grudzień, K., Chaniecki, Z., Banasiak, R., Wajman, R., Romanowski, A., “Process tomograhy development at Technical University of Lodz,” Electrical Capacitance Tomography Theoretical Basis and Applications, edited by Dominik Sankowski and Jan Sikora, Warszawa, 2010, pp. 70-95.
- Yang, W.Q., Peng, L. “Review of image reconstruction algorithms for electrical capacitance tomography, Part 1: Principles.,” International Symposium on Process Tomography in Poland, Wrocław, 2002a, pp. 123–132.
- Yang, W.Q., Peng, L., “Review of image reconstruction algorithms for electrical capacitance tomography, Part 2: Evaluation.,” International Symposium on Process Tomography in Poland, Wrocław, 2009, pp. 133–140.
- Yang, W., Peng, L, “Image reconstruction algorithms for electrical capacitance tomography,” Measurement Science and Technology, 14(1), Bristol, 2003, IOP Publishing, pp. R1–R13.