Project B3: Elastic energy regularization for inverse obstacle problems

A frequent task in nondestructive testing and medical imaging is the estimation of the shape and location of an unknown object, e.g. a material defect, an inclusion, or a tumor. Often the unknown domain is assumed to be star-shaped with respect to a known point, and derivatives of the radial component of a parametrization are use as regularization term. However, assuming the domain to be star-shaped is a severe limitation, and the regularization term is not invariant under changes of coordinates. In this project we study the bending energy as regularization term, which avoids both problems and leads to a new interesting class of regularization methods.