Fast reconstruction of resistance images

Resistance imaging involves the reconstruction of the distribution of electrical resistivity within a conducting object from measurements of the voltages or voltage gradients developed on the boundary of the object while current is flowing within the object. In general, the relationship between the distribution of resistivity in the object and the voltage profile on the object boundary is non-linear and attempts to reconstruct the distribution of resistivity from these profiles usually appear to involve time consuming iterative solutions. If it is assumed that the required resistivity distribution is close to a known reference distribution then it can be shown that there is an approximately linear relationship between the perturbation of the boundary voltage gradient measurements from those of the reference distribution and the logarithm of the resistivity perturbation from the reference distribution. The reconstruction problem then becomes solvable by linear methods. In particular it has proved possible to construct a single-pass back-projection method which can produce images of resistivity from a 16 electrode data collection system. Although the present implementation of this algorithm also assumes that the data is produced from a two-dimensional distribution of resistivity within a circular boundary and that the reference distribution is always uniform it seems capable of reconstructing useful images using data from three dimensional objects, including human subjects.