Matching pursuit for imaging high-contrast conductivity

We show that imaging an isotropic, high contrast, conductive medium is asymptotically equivalent to the identification of a unique resistor network, given measurements of currents and voltages at the boundary. We show that a matching pursuit approach can be used effectively towards the numerical solution of the high-contrast imaging problem, if the library of functions is constructed carefully and in accordance with the asymptotic theory. We also show how other libraries of functions that at first glance seem reasonable, in fact, do not work well. When the contrast in the conductivity is not so high, we show that wavelets can be used, especially nonorthogonal wavelet libraries. However, the library of functions that is based on the high-contrast asymptotic theory is more robust, even for intermediate contrasts, and especially so in the presence of noise.