Shape reconstruction in 3D low-frequency electromagnetic induction tomography using level sets and adjoint fields

Most of the techniques which are used for the electromagnetic imaging of the subsurface have in common that they mathematically define nonlinear inverse problems which are moreover severely ill-posed. This makes it extremely difficult to derive reconstruction algorithms which have the potential of being applied successfully not only to synthetically created data, but also to real data which are usually noisy. Moreover, in many situations the objects of interest have a high contrast to the background parameter distribution. Due to the resulting strong nonlinearity of the inverse problem, the application of straightforward linearization techniques, as for example Born-type methods, is therefore often not justified.