Level Set Method in EIT Image Reconstructions

Abstract

In present there are a lot of difierent numerical methods, ways and approaches to obtain the stable and efiective image reconstruction process, which can be used for e-cient applications in physical and biological sciences. Electrical Impedance Tomography (EIT) belongs to methods which are very beneflcial, especially in a medical imaging. This method is non-invasive technique and can be used very efiectively for good detection of conductivity tissue changes. Unfortunately the back image reconstruction based on electrical impedance tomography is highly ill-posed inverse problem and it is necessary to flnd such techniques which ofier stable, accurate and not too much time-consuming reconstruction process. This paper proposes new possibilities to improve the stability and the accuracy of today image reconstructions including the level set method. At the present time the image reconstruction problem is a widely investigated problem with many applications in physical and biological sciences. The Electrical Impedance Tomography can be used for reconstruction process. The theoretical background of EIT is given in (1). The currents are applied through the electrodes attached to the surface of the object and the resulting voltages are measured using the same or additional electrodes. An arrangement of EIT system is shown in Fig. 1(left). Finally the internal impedivity distribution is recalculated from the measured voltages and cur- rents. The forward problem is well-posed, but the inverse problem is highly ill-posed. Various numerical techniques with difierent advantages have been developed to solve this problem. The common aim is to reconstruct the impedivity distribution in two or three dimensional models as ac- curately and fast as possible. Usually a set of voltage measurements is acquired from the boundaries of the determined volume, whilst it is subjected to a sequence of low-frequency current patterns, which are preferred to direct current ones to avoid polarization efiects. Since the frequency of the injected current is su-ciently low, usually in the range of 10{100 kHz, EIT can be treated as a quasi-static problem. So we only consider the conductivity ae inside investigated object for simplic- ity. The scalar potential U can be therefore introduced, and so the resulting fleld is conservative and the continuity equation for the volume current density can be expressed by the potential U r ¢ (ae rU) = 0 (1) Equation (1) together with the modifled complete electrode model equations (2) are discretized by the flnite element method (FEM) in the usual way. Using FEM we calculate approximate values of electrode voltages for the approximate element conductivity vector ae(NE), NE is the number of flnite elements. Furthermore, we assume the constant approximation of a conductivity