Electrical Impedance Tomography (EIT) is a relatively new medical imaging technique in which electrodes are placed on the surface of the body, current is applied on the electrodes, the resulting voltage is measured on the electrodes, and an image is formed from the reconstructed conductivity distribution. One application is the real-time imaging of heart and lung function. In this case, data is collected on electrodes placed around the circumference of the patient's torso, and the 2-D inverse conductivity problem is solved numerically to form a cross-sectional image of the patient's chest. This research focuses on the further development of the D-bar reconstruction algorithm for 2-D EIT. The algorithm is based on the uniqueness proof by Nachman [Ann. of Math. 143 (1996)] for the 2-D inverse conductivity problem and uses the D-bar method of inverse scattering to solve the full nonlinear inverse problem. An important function arising in this method is the scattering transform. This function, while not physically measurable in experiments, is computed directly from the data, and is a key element of the D-bar equation that must be solved to obtain the conductivity. This paper describes two approaches for computing a regularized approximation to the scattering transform. The approaches are tested on experimental data
collected on a saline-filled tank containing agar heart, lungs, spine and aorta, simulating a cross-section of a human chest.
A 3-D linearization-based reconstruction algorithm for Electrical Impedance Tomography suitable for breast cancer detection using data collected on a rectangular array was introduced by Mueller et al. [IEEE Biomed. Eng., 46(11), 1999]. By considering the scenario as an electrostatic problem, it is possible to model the electrodes with various charges, facilitating the use of the Fast Multipole Method (FMM) for calculating particle interactions and also supporting the use of different electrode models. In this paper the use of FMM is explained and results in form of reconstructed images from experimental data show that this method is an improvement.