INVERSE BIOMEDICAL IMAGING USING SEPARATELY ADAPTED MESHES FOR PARAMETERS AND FORWARD MODEL VARIABLES

Many important existing and upcoming biomedical imaging modalities lead to nonlinear relationships between state variables from which measurements result and the tissue properties one would like to reconstruct, and typically involve partial differential equations. For such cases, exact reconstruction formulas are rarely known and their solution requires numerical techniques such as the finite element method that approximates all involved variables on a mesh. Traditionally, the same mesh is used for all involved variables. In this contribution, we argue that this is inappropriate and meshes should be chosen independently of each other for the various variables involved. We support this claim through a numerical experiment