Electrical Tomography

Tomography deduces a physical function σ(P) (say a density), at points P inside a living organ, from measurements made on the outside. With suitable interpretation, σ(P) may reveal tumors or other abnormalities. In X-ray tomography, σ(P) is an attenuation coefficient, external measurements supply integrals 1$$\alpha (L) = \int\limits_{L} {\sigma (P)ds}$$ along straight line rays L through the organ, and the integral equation (1) is solved for σ(P) (see [1]). In another kind of tomography, using nuclear magnetic resonance measurements, σ(P) is deduced from integrals over planes instead of lines (see [2]).