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Minimization of Objective Function in Electrical Impedance Tomography by Topological Derivative DOI:10.15199/48.2019.06.25

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Electrical impedance tomography (EIT) is a non-invasive problem of image reconstruction in which the distribution of conductivity in an object domain can be reconstructed using external voltage measurements. EIT is an imaging technique with existing and potential uses in engineering and medical problems. In this method, electric currents are injected into a conductive object through electrodes placed on its surface, and the resulting electrical potential on the electrodes is determined. In the opposite case, the objective function is minimized in an iterative procedure, using the measured and modeled data, the internal conductivity profile is calculated. Electric tomography can be used in industrial, medical and geophysical applications. Recently, there has been a dramatic increase in the field of chest imaging, with an emphasis on lung ventilation and heart rhythm monitoring. The finite element method was applied to domain modeling, and topological algorithms were used to solve the inverse problem [21]. The problem of topology optimization applied in the EIT is to find the conductivity distribution of the object, which minimizes the difference between electrical potentials obtained from measurements of electrodes at the boundary of the object and numerically simulated electrical potentials [3,4,8,14-16]. Topological Derivative The optimization problem is usually defined as the minimization of a given activity [2,6,9-11,13,22]. Shape derivatives and topological derivatives have been included in the level determination methods to investigate problems related to shape optimization [17, 18]. The basic method of shape optimization is a topological derivative evaluated for a given functional shape defined in the geometric field and dependent on the classical solution of the elliptical problem of the limit of value. The topological derivative is defined as the first term of asymptotic expansi[...]

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