An improved electrical impedance tomography system.

摘要

Electrical impedance tomography (EIT) is an imaging technique for which a fast and accurate reconstruction procedure remains challenging. Recent studies suggested different methods for robust images reconstruction but few were found to be applicable in the medical field. In this study, fast as well as noise-robust reconstruction algorithms were developed. A simple EIT acquisition system was built. The EIT acquisition system is a 36-electrode system where current is injected and voltages are measured.; The reconstruction procedure adapted in this work was based on solving the full nonlinear least square problem. The nonlinear least square problem was solved using Gauss-Newton methods with modifications added due to the ill-conditioned reconstruction procedure. During this study, two new techniques based on the Levenberg-Marquardt regularization were used to reconstruct images: The trust region reflective Newton method and the secant Levenberg-Marquardt method. The first method was found to be globally convergent but slow and time consuming due to the evaluation of the Jacobian matrix at each step. To avoid the evaluation of the Jacobian in each iteration, the method of Levenberg-Marquardt with Broyden update of the Jacobian (secant Levenberg-Marquardt method) was used. This approach was found to be faster but locally convergent.; The EIT reconstruction procedure is an ill-conditioned procedure with many possible sources of noise and errors, which tend to make it even more complicated. Furthermore, the Levenberg-Marquardt method introduces perturbations to the solution. In this work, the singular value decomposition was used to analyze the properties of the EIT inverse problem. The reconstruction of images was based on two procedures: truncated singular value decomposition (TSVD), which is analogous to an ideal filter in signal processing, and Tikhonov regularization, which is analogous to a smooth filter. Truncated singular value decomposition reconstruction was found to have good convergence properties and the ability to introduce less noise, or errors, in the conductivity image than other methods. Tikhonov regularization with two techniques for finding the regularization parameter, L-curve criterion and discrepancy principle, was used in this work. Although both techniques were able to produce good images, Tikhonov regularization with discrepancy principle was found to be more stable. TSVD and Tikhonov regularization were found to converge in a few steps with super-linear (quadratic) convergence. The null hypothesis of no difference in the noise level between the reconstructed image using the Levenberg-Marquardt method and the singular value decomposition method was rejected.; The last part of this work demonstrates the development of a three-dimensional EIT imaging system. The hardware was the same as in the two-dimensional acquisition, with a slight modification in the electrode arrangement and the acquisition software. Images were reconstructed using the trust region reflective Newton method.; The image quality in 2D and 3D can be further improved if more information about the errors and noise are available. For example, information about the error in the finite element modeling can be used in the image reconstruction, and the method of the total least squares can be used to solve the least square problem.