Department of Mathematics

We present a new joint reconstruction method for thesimultaneous reconstruction of attenuation coefficient and electron density from X-ray transmission and Compton-scattered backscattered data. After introducing some ideas from microlocal analysis, we use them to describe what features are visible in both limited data sets.  We show that the Compton and X-ray CT data set are complementary–this ensures that most features (wavefront directions) of the object are visible from the combined data. However, both limited-data reconstruction methods introduce streak artifacts in standard reconstruction methods.

In addition, we introduce a new joint reconstruction scheme for low effective atomic number imaging.  Motivated by our microlocal results, we develop a Lambda tomography penalty term in the regularization procedure in the algorithm to integrate the two data sets together. We evaluate our reconstruction method on the “parallel line segment” acquisition geometry of [Webber, J. and Miller, E., Inverse Problems 36(2020), 025007] which is motivated by a specific architecture for airport security screening.  Finally, we show the effectiveness of our method in combating the noise and image artifacts on simulated phantoms.