Several biomedical imaging methods rely on the interaction between tissue and the near field of electromagnetic sources. Examples are diffuse photon density wave imaging, magnetic induction tomography (MIT) and, more recently, the reconstruction of electrical tissue properties with magnetic resonance imaging (EPMRI). All these methods have in common that the image reconstruction procedure is based on a usually undetermined, ill-posed inverse scattering problem which aims at the mapping of certain physical properties of the scatterer, e.g. electrical conductivity, dielectric permittivity, absorption or scattering coefficients.
This project shall focus onto the improvement of both the existing measurement hardware as well as well as image reconstruction techniques for MIT, EPMRI and for inverse near--infrared spectroscopy (NIRS) imaging of brain activity. The latter is a special application of diffuse photon density wave imaging. The inverse techniques shall be based on special regularization techniques including templating with physical and statistical prior models, shape optimization of sub-regions with partly known parameter distribution and total bounded variation. Hardware improvement includes the optimization of sensor locations and applied excitation patterns as well as their implementation in a real prototype. For the solution of the underlying partial differential equations and their adjoints efficient numerical solvers are mandatory. For MIT we will use a coupled fast finite and boundary element approach to approximate the Maxwell system while in NIRS imaging the diffusion approximation of the Boltzmann equation will be tackled with a fast finite element method. As the consideration of anisotropic parameters is still poorly explored in both imaging modalities, the potential of an anisotropic approach should also be investigated.