Eric Todd Quinto: Microlocal Analysis in Compton Tomography: Joint Compton/X-ray-CT Reconstruction

Abstract:

We present a new tomographic reconstruction method motivated by a problem in luggage testing. We take both X-ray CT and Compton tomography data of an object. Each of these data sets is limited, and neither images the complete object. We show that, by putting both data sets together, we can image essentially all details of the object. 

We will provide a gentle introduction to the deep mathematics, microlocal analysis, which precisely describes singularities. We use this to describe what features are visible from each limited data set. We show that the Compton and X-ray CT data sets are complementary—they each see different features, and when put together, most features of the object are visible from the combined data. However, both X-ray and Compton data can introduce streak artifacts in standard reconstruction methods.

For this reason, we develop a new joint reconstruction algorithm. We introduce a novel penalty term in the regularization procedure of the algorithm to integrate the two data sets together. We provide reconstructions (pictures of the objects obtained from the data) from simulated data to show the effectiveness of our method in combating noise and image artifacts.

Joint work with James Webber and Eric Miller