Shape reconstruction in 3D electromagnetic induction tomography using a level set technique

We present a novel shape reconstruction technique for 3D low frequency electromagnetic induction tomography which uses a level set representation of the shapes. An efficient adjoint scheme for calculating gradient directions corresponding to the data of each individual probing source is combined with a single-step technique for finding iterative corrections of the latest best guess of the level set function which defines the shapes. We present numerical experiments in 3D which demonstrate that our new technique is able to reconstruct complicated objects buried in the Earth from noisy electromagnetic data in a realistic geophysical setup without a priori knowledge of the topology of the shapes.