Detectable singularities from dynamic Radon data
Provides a theoretical framework for understanding artifact formation in dynamic tomography, relevant for medical or industrial imaging where object motion occurs.
This paper uses microlocal analysis to characterize which singularities of a dynamic object are detectable in X-ray tomographic data, showing that motion can cause some singularities to be undetectable or artificially added, even with full angular coverage.
In this paper, we use microlocal analysis to understand what X-ray tomographic data acquisition does to singularities of an object which changes during the measuring process. Depending on the motion model, we study which singularities are detected by the measured data. In particular, this analysis shows that, due to the dynamic behavior, not all singularities might be detected, even if the radiation source performs a complete turn around the object. Thus, they cannot be expected to be (stably) visible in any reconstruction. On the other hand, singularities could be added (or masked) as well. To understand this precisely, we provide a characterization of visible and added singularities by analyzing the microlocal properties of the forward and reconstruction operators. We illustrate the characterization using numerical examples.