Detectable singularities from dynamic Radon data

TL;DR

This paper uses microlocal analysis to determine which singularities of a moving object are detectable in dynamic X-ray tomography data, revealing limitations and possibilities in reconstructing changing objects.

Contribution

It provides a microlocal characterization of detectable and added singularities in dynamic Radon data, advancing understanding of what features can be reconstructed.

Findings

Not all singularities are detectable due to motion.

Some singularities may be masked or added by the dynamic process.

Numerical examples illustrate the microlocal analysis results.

Abstract

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.