Elektrik Empedans Tomografide Eliptik Yapılardaki İletkenlik Dağılımları Geriçatım Probleminin Yapay Sinir Ağları ile İncelenmesi

Abstract

Electric Impedance Tomography is the method that shows the conductivity distribution in any geometry. In this study, the image of the conductivity distribution in circle and ellipse geometries is tried to be obtained. Forward problem and inverse problem solutions of EIT are discussed.

The forward problem of EIT is linear and stable. The Finite Element Method is used for solving forward problem of circle and ellipse geometries. The analytical solution and FEM results of geometries were compared and it was shown that FEM can be applied in different geometries.

The inverse problem of EIT is a nonlinear and ill-posed problem where the accuracy of the solution is discussed. Due to this structure, the problem has been evaluated and solved in both linear and nonlinear manner. The inverse problem solution is also known as the image reconstruction. Optimization techniques in general and artificial neural network models can be used for such inverse problem solving. Specifically, for circle and ellipse geometries, their conductivity values were studied by using virtual voltage values obtained through specially designed electrode patterns which are supposed to be placed around the geometry. Using FEM used for the forward solution, a database can be generated with inhomogeneous distributions specified in different locations and conductivities. Artificial neural network has been trained by using tension values obtained from the surface and distributions under different conductivity scenarios. Training input for those cases are measured voltage values observed from the boundary. At the end of the learning stage, the trained neural network was tested and error values were tabulated. Within the framework of artificial neural network structures, mainly Radial Based Neural Networks and Multilayer Perceptron were selected and compared with the patterns obtained by selected optimization methods.

In order to provide comparative results, neural network structures were trained by using generated 69 different patterns to get reconstruction images of the circle geometry with a resolution of 256 pixels. Among reconstructed images obtained using this database, the radial basis function neural network is found more successful than the others when all reconstruction algorithms attempt to provide the images for the structures whose conductivity is larger than the base distribution. In the results obtained with the same database, Gauss-Newton algorithm is more successful for structures whose conductivity is smaller than the value of base distribution. In another experiment, 85 different circle geometries were used to train selected neural networks for the reconstruction images of the circle geometry with a resolution of 576 pixels in order to increase the resolution. The circle geometries, in this case, consist of a single structure with different conductivities. According to the analysis among reconstructed images, the radial basis neural network structure, like the circle geometry with a resolution of 256 pixels, has also been found to be more successful than other reconstruction models with the minimum error rate up to 7,46.10-4. The Gauss-Newton algorithm is, on the other hand, more successful for low conductivity structures. Besides, although neural network structures have been trained for a single inhomogeneity in the pattern, especially the radial basis neural network structure has reached the error rate of 6,78.10-4 in the test stage for the geometries with unseen different structures, specifically two different conductivities at the same time. The neural network structure was trained using 41 differently defined patterns with two different larger conductivities, the error rate of the reconstruction image was 1,049.10-3 for patterns tested with radial basis network structure.

The reconstruction images of the ellipse geometry with a resolution of 246 pixels have been used in providing 69 different patterns of the neural networks training set. It is observed that the multi-layered neural network structure trained by the Levenberg-Marquardt learning algorithm under the generated database has been more successful than other methods by reducing the error rate to 6,49.10-4 for structures whose conductivity is greater than the base distribution. For the geometries with smaller conductivities, the radial basis neural network structure was found better with the error rate of 1,12.10-4. The resolution of the elliptic geometries was increased to 589 and 91 patterns were used for the neural network training phase. With this database, the error rate is reached to 9,21.10-4 when the radial based neural network structure was used for the reconstruction whose conductivity has been smaller than the base homogeneity. While 91 patterns used for training have a single inhomogeneity with different conductivities, the radial basis neural network structure was rated as more successful with the error rate of 3,89.10-4 for new test data set including two separately positioned inhomogeneities. There were not any reconstruction images obtained by the Gauss-Newton algorithm since those data were used to test the neural systems estimation capability for unseen and unknown distributions. In the next step, neural network structures were trained by using 43 patterns for the reconstruction of two inhomogeneities with different conductivities within the elliptic frame with a high resolution of 589 pixels. The radial basis neural network structure was observed as more successful with the error rate of 1,42.10-3 obtained using this database. According to those results, the reconstruction images obtained with the artificial neural network structures are more successful than optimization methods selected in this thesis. They have given remarkable results by using the sufficient number of neurons used in the training session. The radial basis neural network structure achieved faster learning and lower reconstruction error than those obtained by the multi-layer perceptron structure.

Using this conductivity distribution information, the region and size of abnormal tissues and structures such as tumor detection and blood clot can be determined, especially in the medical field.

Keywords: Electrical Impedance Tomography, forward problem, inverse problem, reconstruction techniques, Gauss-Newton algorithm, artificial neural networks.