Recently, my first first-author manuscript related to my thesis work on x-ray phase contrast was published. The paper summarizes artifacts experienced while using a tabletop x-ray phase contrast micro-CT system. While the focus of the paper is limited to grating-based x-ray phase contrast systems, the empirical methods used to solve the beam hardening problem are quite generalizable. I first learned about these interpolation-based empirical corrections from researching previous x-ray corrections that are referenced in the paper, but along the way I enjoyed digging more into the math of solving least squares problems and how they are implemented. The following tutorials document some of my explorations and provide background to the paper.
Manuscript Citation and Links
- Nelson, B.J., Leng, S., Shanblatt, E.R., McCollough, C.H. and Koenig, T. (2021), Empirical beam hardening and ring artifact correction for x‐ray grating interferometry (EBHC‐GI). Med Phys. https://doi.org/10.1002/mp.14672
- solving interpolation problems with Vandermonde Matrices
- performing matrix inversion via LU decomposition
using interpolation to fix image artifacts in CT
- this tutorial is built upon the previous two but is most related to the paper