Detectable singularities from dynamic Radon data

Abstract: X-ray tomography has revolutionized diagnostic radiology, and standard methods work very well when the body does not move during the scan. However, in many situations the body does move.  For example, during a scan of the abdomen, the lungs will almost certainly move, even if the patient is told to "hold your breath," and standard reconstruction methods cannot accurately image the body.

In this talk, we will use microlocal analysis to understand what X-ray tomographic data acquisition does to features (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, artifacts could be added 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. 

This is joint work with B.N. Hahn, Institute of Mathematics, University of Würzburg, Germany