A Regularization Process for Electrical Impedance Equation Employing Pseudoanalytic Function Theory

Cesar Marco Antonio Robles Gonzalez,Ariana Guadalupe Bucio Ramirez,Volodymyr Ponomaryov,Marco Pedro Ramirez Tachiquin

doi:10.1155/2014/964081

Cesar Marco Antonio Robles Gonzalez, Ariana Guadalupe Bucio Ramirez + Show 2 more

Open Access

https://doi.org/10.1155/2014/964081

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Abstract

The electrical impedance equation is considered an ill-posed problem where the solution to the forward problem is more easy to achieve than the inverse problem. This work tries to improve convergence in the forward problem method, where the Pseudoanalytic Function Theory by means of the Taylor series in formal powers is used, incorporating a regularization method to make a solution more stable and to obtain better convergence. In addition, we include a comparison between the designed algorithms that perform proposed method with and without a regularization process and the autoadjustment parameter for this regularization process.

Highlights

The electrical impedance tomography (EIT) problem, which is set by employing the electrical impedance equation, was mathematically posed by Calderon [1] in 1980 proving that the solution of this problem exists as being unique and steady
The examples investigated are designed to compare the results when a regularization method is used in the process versus the actual method, which does not employ a regularization procedure. As it is exposed in the works [9, 10], the possibility to employ geometrical distributions functions and mathematical expression in the algorithm, which use the Taylor series in formal powers, let us analyse the electrical impedance equation (1), emphasizing the possibility to approximate the forward problem to this equation
The regularization method employed in the approximation for the forward Dirichlet boundary value problem for (1) gives a stability to the process permitting better convergence by smoothing the conductivity functions employed within the domain

Summary

Introduction

The electrical impedance tomography (EIT) problem, which is set by employing the electrical impedance equation, was mathematically posed by Calderon [1] in 1980 proving that the solution of this problem exists as being unique and steady. Some methods should be employed to correct these perturbations present advantages and disadvantages, such as a regularization method that permits to suppress the noise in the measurements. Due to this problem and the continuous advances in the field, the EIT is not considered a practical medical imaging procedure

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