Comparing D-Bar and Common Regularization-Based Methods for Electrical Impedance Tomography

Objective: To compare D-bar difference reconstruction with regularized linear reconstruction in electrical impedance tomography. Approach: A standard regularized linear approach using a Laplacian penalty and the GREIT method for comparison to the D-bar difference images. Simulated data was generated using a circular phantom with small objects, as well as a \u27Pac-Man\u27 shaped conductivity target. An L-curve method was used for parameter selection in both D-bar and the regularized methods. Main results: We found that the D-bar method had a more position independent point spread function, was less sensitive to errors in electrode position and behaved differently with respect to additive noise than the regularized methods. Significance: The results allow a novel pathway between traditional and D-bar algorithm comparison

High-order regularized regression in Electrical Impedance Tomography

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral transform, that maps changes in the electrical properties of a domain to their respective variations in boundary data. Using perturbation theory the transform is approximated to yield a high-order misfit unction which is then used to derive a regularized inverse problem. In particular, we consider the nonlinear problem to second-order accuracy, hence our approximation method improves upon the local linearization of the forward mapping. The inverse problem is approached using Newton's iterative algorithm and results from simulated experiments are presented. With a moderate increase in computational complexity, the method yields superior results compared to those of regularized linear regression and can be implemented to address the nonlinear inverse problem

Frequency-Division Multiplexing for Electrical Impedance Tomography in Biomedical Applications

Electrical impedance tomography (EIT) produces an image of the electrical impedance distribution of tissues in the body, using electrodes that are placed on the periphery of the imaged area. These electrodes inject currents and measure voltages and from these data, the impedance can be computed. Traditional EIT systems usually inject current patterns in a serial manner which means that the impedance is computed from data collected at slightly different times. It is usually also a time-consuming process. In this paper, we propose a method for collecting data concurrently from all of the current patterns in biomedical applications of EIT. This is achieved by injecting current through all of the current injecting electrodes simultaneously, and measuring all of the resulting voltages at once. The signals from various current injecting electrodes are separated by injecting different frequencies through each electrode. This is called frequency-division multiplexing (FDM). At the voltage measurement electrodes, the voltage related to each current injecting electrode is isolated by using Fourier decomposition. In biomedical applications, using different frequencies has important implications due to dispersions as the tissue's electrical properties change with frequency. Another significant issue arises when we are recording data in a dynamic environment where the properties change very fast. This method allows simultaneous measurements of all the current patterns, which may be important in applications where the tissue changes occur in the same time scale as the measurement. We discuss the FDM EIT method from the biomedical point of view and show results obtained with a simple experimental system