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Hybrid topological derivative and gradient-based methods for electrical impedance tomography. (English) Zbl 1253.35215
Summary: We present a technique to reconstruct the electromagnetic properties of a medium or a set of objects buried inside it from boundary measurements when applying electric currents through a set of electrodes. The electromagnetic parameters may be recovered by means of a gradient method without a priori information on the background. The shape, location and size of objects, when present, are determined by a topological derivative-based iterative procedure. The combination of both strategies allows improved reconstructions of the objects and their properties, assuming a known background.
MSC:
35R30Inverse problems for PDE
35Q61Maxwell equations
78A46Inverse scattering problems