Theoretical methods for blur-correction in electron and soft x-ray microscopy

The process of object reconstruction from projections is widely used in many fields. One of the applications is the reconstruction of biological specimens from two-dimensional projections in transmission electron microscopy and transmission x-ray microscopy. Various methods have been developed for correcting the blurring that occurs when the projections are obtained by a real instrument. As the attainable resolution increases, new issues become apparent and need to be taken into account in the imaging model. In this dissertation we concentrate on the point spread function and its impact on the quality and usefulness of the reconstructions from images obtained according to image formation models for the two types of microscopy. Specifically, we consider spatial variance of the point spread function in the direction of the electron or x-ray propagation. The correction methods for this type of blurring in both cases are related, but not identical due to nature of the respective imaging processes. We propose correction methods and demonstrate their efficacy using computer simulations