Parallel hybrid algorithm for solution in electrical impedance equation

Volodymyr Ponomaryov; Marco Robles-Gonzalez; Ariana Bucio-Ramirez; Marco Ramirez-Tachiquin; Eduardo Ramos-Diaz

doi:10.1117/12.2075315

27 February 2015 Parallel hybrid algorithm for solution in electrical impedance equation

Volodymyr Ponomaryov, Marco Robles-Gonzalez, Ariana Bucio-Ramirez, Marco Ramirez-Tachiquin, Eduardo Ramos-Diaz

Proceedings Volume 9400, Real-Time Image and Video Processing 2015; 94000I (2015) https://doi.org/10.1117/12.2075315
Event: SPIE/IS&T Electronic Imaging, 2015, San Francisco, California, United States

Abstract

This work is dedicated to the analysis of the forward and the inverse problem to obtain a better approximation to the Electrical Impedance Tomography equation. In this case, we employ for the forward problem the numerical method based on the Taylor series in formal power and for the inverse problem the Finite Element Method. For the analysis of the forward problem, we proposed a novel algorithm, which employs a regularization technique for the stability, additionally the parallel computing is used to obtain the solution faster; this modification permits to obtain an efficient solution of the forward problem. Then, the found solution is used in the inverse problem for the approximation employing the Finite Element Method. The algorithms employed in this work are developed in structural programming paradigm in C++, including parallel processing; the time run analysis is performed only in the forward problem because the Finite Element Method due to their high recursive does not accept parallelism. Some examples are performed for this analysis, in which several conductivity functions are employed for two different cases: for the analytical cases: the exponential and sinusoidal functions are used, and for the geometrical cases the circle at center and five disk structure are revised as conductivity functions. The Lebesgue measure is used as metric for error estimation in the forward problem, meanwhile, in the inverse problem PSNR, SSIM, MSE criteria are applied, to determine the convergence of both methods.

Citation Download Citation

Volodymyr Ponomaryov, Marco Robles-Gonzalez, Ariana Bucio-Ramirez, Marco Ramirez-Tachiquin, and Eduardo Ramos-Diaz "Parallel hybrid algorithm for solution in electrical impedance equation", Proc. SPIE 9400, Real-Time Image and Video Processing 2015, 94000I (27 February 2015); https://doi.org/10.1117/12.2075315

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KEYWORDS

Finite element methods

Inverse problems

Error analysis

Tomography

Algorithm development

Parallel computing

Visualization

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