  Nowadays, modern electron microscopes deliver images at atomic scale. The
precise atomic structure encodes information about material properties. Thus,
an important ingredient in the image analysis is to locate the centers of the
atoms shown in micrographs as precisely as possible. Here, we consider scanning
transmission electron microscopy (STEM), which acquires data in a rastering
pattern, pixel by pixel. Due to this rastering combined with the magnification
to atomic scale, movements of the specimen even at the nanometer scale lead to
random image distortions that make precise atom localization difficult. Given a
series of STEM images, we derive a Bayesian method that jointly estimates the
distortion in each image and reconstructs the underlying atomic grid of the
material by fitting the atom bumps with suitable bump functions. The resulting
highly non-convex minimization problems are solved numerically with a trust
region approach. Well-posedness of the reconstruction method and the model
behavior for faster and faster rastering are investigated using variational
techniques. The performance of the method is finally evaluated on both
synthetic and real experimental data.
