Holger Kohr: Electron tomography of biological samples

Electron tomography (ET) aims at the reconstruction of the three-dimensional distribution of the refractive index from a series of two-dimensional projections taken at varying orientations. These projections are acquired with the help of a transmission electron microscope (TEM) by the irradiation of a specimen with an electron beam. A close investigation of the underlying physical principles together with several substantial simplifications finally lead to a linear model including an X-ray transform and a convolution.

One way to solve this ill-posed problem is the method of approximate inverse. This general framework for the solution of inverse problems is adapted to the particular situation and results in a very fast non-iterative algorithm by the exploitation of operator invariances. Furthermore, it enables the direct recovery of features of an approximate solution without the need to compute that solution itself.