A Real-Time Algorithm for the Location Search of Discontinuous Conductivities with One Measurement

We consider an inverse problem for finding the anomaly of discontinuous electrical conductivity by one current-voltage observation. We develop a real-time algorithm for determining the location of the anomaly. This new idea is based on the observation of the pattern of a simple weighted combination of the input current and the output voltage. Combined with an estimation of size, this algorithm gives a good initial guess for Newton-type schemes. We give a rigorous proof for the location search algorithm. Both the mathematical analysis and its numerical implementation indicate our location search algorithm is very fast, stable, and efficient.