Compared to conventional attenuation imaging, Talbot-Lau X-ray grating interferometry applied within a polychromatic setup suffers from additional artifacts. Among those are beam hardening and dispersion effects due to the complex coupling of different physical effects involved in the image formation process. In computed tomography these effects lead to image degradation, such as cupping and streak artifacts, hampering diagnostic use.
In this paper, we seek to reduce these artifacts in an iterative reconstruction framework. To this purpose, we define a model of the polychromatic forward projection that includes prior knowledge about the physical setup. Using this model we derive a maximum likelihood algorithm for simultaneous reconstruction of the attenuation, phase and scatter images.
In our experiments on a synthetic ground-truth phantom, we compare filtered backprojection reconstruction with the proposed approach. The proposed method considerably reduces strong beam hardening artifacts in the phase images, and almost completely removes these artifacts in the absorption and scatter images.