Shape decomposition technique in electrical impedance tomography (EIT)

Consider a two-dimensional domain containing a medium with unit electrical conductivity and one or more non-conducting cavities. The problem considered here is that of identifying shape and position of the cavities on the sole basis of measurements on the external boundary of the domain. An iterative technique is presented in which a sequence of solutions of the direct problem is generated by a boundary element method on the basis of assumed positions and shapes of the cavities. The key new aspect of the approach is that the cavity boundaries are represented in terms of Fourier coefficients rather than a point-wise discretization. The Fourier coefficients are updated at every step by the Levenberg-Marquardt type algorithm. It is shown that the Fourier decomposition enables the algorithm to image the embedded cavity with unprecedented accuracy and clarity. It also appears possible to extend the method to three dimensions.