We will discuss the use of level sets for object detection and specification in two important inverse problems arising in geophysical and medical imaging. The geophysical application which we address is 'Low Frequency electromagnetic Induction Tomography' (in 3D), which is governed by the 3D system of Maxwell's equations. The medical application which we address is 'Diffuse Optical Tomography' (in 2D) which is governed by a linear Boltzmann or radiative transfer equation. We will present and discuss various numerical examples of
reconstructions with level sets for both applications.
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