Iterative image reconstruction for electrical impedance tomography using adaptive techniques

Abstract

This thesis will focus on the development of EIT reconstruction methods that strike a balance between reconstruction accuracy and cost efficiency in solving forward and inverse problems. Previous work has focused more on the accuracy of the algorithms rather than the efficiency of the algorithms. In the forward problem, an overly refined forward model is always used to obtained the predicted voltages to ensure the accuracy of the forward solution. However, the accuracy should only achieve the measurement precision of the hardware equipment and any refinement effort to improve beyond this limited precision will be a waste of computation power. In the inverse problem, direct reconstruction methods, e.g. NOSER and D-bar, are considered to be efficient but less accurate. Iterative methods, e.g. Gauss-Newton, are cost expensive and limited their use in only small-scale problems. Another issue with the inverse problem is that fixed uniform meshes are always used for reconstruction, which may generate a large number of elements that are not necessarily needed and lead to waste in computational power. To improve efficiency without reducing the accuracy of the solutions in both the forward and inverse problems, the thesis will first study the effects of the FEM mesh on the accuracy of forward solution and suggest a relatively accurate and efficient model size for the three-dimensional cylinder geometry. Secondly, an efficient reconstruction algorithm will be proposed to adaptively improve the accuracy of the reconstructed images using optimal current patterns. It will be shown that accurate and stable solutions will be obtained with much lower memory cost and storage. The algorithm is further improved by combining it with adaptive meshing to adaptively determine the reconstruction mesh at each iteration. The combination could optimize the reconstruction process with efficient meshing and optimal current patterns. Thirdly, a method in estimating the relationship between the ventilation and the perfusion during the breathing cycle is proposed and evaluated using human subject data.