New Hardware and Software Design for Electrical Impedance Tomography

Electrical impedance tomography (EIT) is an imaging technique that reconstructs the internal electrical properties of an object from boundary voltage measurements. In this technique a series of electrodes is attached to the surface of an object and alternating current is passed via these electrodes and the resulting voltages are measured. Reconstruction of internal conductivity images requires the solution of an illconditioned nonlinear inverse problem from the noisy boundary voltage measurements. Such unreliable boundary measurements make the solutions unstable. To obtain stable and meaningful solutions regularization is used. This thesis deals with the EIT problem from the perspective of both image reconstruction and hardware design. This thesis consists of two main parts. The first part covers the development of 3D image reconstruction algorithms for single and multi-frequency EIT. The second part relates to the design of novel multi-frequency hardware and performance testing of the hardware using the designed phantom. Three different approaches for image reconstruction of EIT are presented: 1) The dogleg algorithm is introduced as an alternative method to Levenberg-Marquardt for solving the EIT inverse problem. It was found that the dogleg technique requires less computation time to converge to the same result as the Levenberg-Marquardt. 2) We propose a novel approach to build a subspace for regularization using a spectral and spatial multifrequency analysis approach. The approach is based on the construction of a subspace for the expected conductivity distributions using principal component analysis (peA). The advantage of this technique is that priori information for regularization matrix is determined from the statistical nature of the multifrequency data. 3) We present a quadratic constrained least square approach to the EIT problem. The proposed approach is based on the trust region subproblem (TRS), which uses L-curve maximum curvature criteria to fmd a regularization parameter. Our results show that the TRS algorithm has the advantage that it does not require any knowledge of the norm of the noise for its process. 4) The second part of thesis discuses the designing, implementation, and testing a novel 48-channel multifrequency EIT system. The system specifications proved to be comparable with the existing EIT systems with capability of 3-D measurement over selectable frequencies. The proposed algorithms are [mally tested under experimental situation using designed EIT hardware. The conductivity and permittivity images for different targets were reconstructed using four different approaches: dog-leg, principal component analysis (PCA), Gauss-Newton, and difference imaging. In the case of the multi-frequency analysis, the PCA-based approach provided a substantial improvement over the Gauss-Newton technique in terms of systematic error reduction. Our EIT system recovered a conductivity value of 0.08 Sm-l for the 0.07 Sm-l piece of cucumber (14% error).

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