A shape decomposition technique in electrical impedance tomography

Consider a two-dimensional domain containing a medium with unit electrical conductivity and one or more non-conducting objects. The problem considered here is that of identifying shape and position of the objects 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 probl em is generated by a boundary element method on the basis of assumed positi ons and shapes of the objects. The key new aspect of the approach is that t he boundary of each object is represented in terms of Fourier coefficients rather than a point-wise discretization. These Fourier coefficients generat e the fundamental "shapes" mentioned in the title in terms of which the obj ect shape is decomposed. The iterative procedure consists in the successive updating of the Fourier coefficients at every step by means of the Levenbe rg-Marquardt algorithm. It is shown that the Fourier decomposition-which, e ssentially, amounts to a form of image compression-enables the algorithm to image the embedded objects with unprecedented accuracy and clarity. In a s eparate paper, the method has also been extended to three dimensions with e qually good results, (C) 1999 Academic Press.