Quantitative analysis of metal artifacts in X-ray tomography

In an X-ray CT scan with metallic objects, it is known that direct application of the filtered back-projection formula leads to streaking artifacts in the reconstruction. These are characterized mathematically in terms of wave front sets in [Park, Choi, and Seo, Comm. Pure Appl. Math., 2017]. In this work, we give a quantitative microlocal analysis of such artifacts. We consider metal regions with strictly convex smooth boundaries and show that the streaking artifacts are conormal distributions to straight lines tangential to at least two boundary curves. For metal regions with piecewise smooth boundaries, we analyze the streaking artifacts especially due to the corner points. Finally, we study the reduction of the artifacts using appropriate filters.