The inverse conductivity problem via the calculus of functions of bounded variation

In this work, a novel approach for the solution of the inverse conductivity problem from one and multiple boundary measurements has been developed on the basis of the implication of the framework of functions. The space of the functions of bounded variation is recommended here as the most appropriate functional space hosting the conductivity profile under reconstruction. For the numerical investigation of the inversion of the inclusion problem, we propose and implement a suitable minimization scheme of an enriched—constructed herein—functional, by exploiting the inner structure of space. Finally, we validate and illustrate our theoretical results with numerical experiments.