Characterization and reduction of artifacts in limited angle x-ray tomography

In this talk we consider the reconstruction problem of limited angle x-ray tomography. Such problems appear naturally in many applications, such as digital breast tomosynthesis, dental tomography or electron microscopy. Many of these modalities still employ the filtered backprojection algorithm (FBP) for practical reconstructions. However, since the FBP algorithm implements an inversion formula for the Radon transform, an essential requirement for its application is the completeness of the tomographic data. Consequently, the application of FBP is not justified in the case of limited angle tomography. As a result, only specific features of the original object can be reconstructed reliably and additional artifacts can be created by the FBP algorithm.

In the course of this talk, we will first present a characterization of the FBP reconstructions at a limited angular range. In particular, we shall give a characterization of visible singularities (i.e. those features that can be reconstructed reliably) at a limited angular range. The main part of this talk is devoted to the characterization of artifacts that may appear in limited angle reconstructions. Our analysis will be presented in the context of microlocal analysis which is a powerful technique that enables us to describe locations and directions of singularities simultaneously. Moreover, we will derive an artifact reduction strategy for the filtered backprojection algorithm and illustrate its performance in some numerical experiments.