Analysis and accurate reconstruction of incomplete data in X-ray differential phase-contrast computed tomography

X-ray differential phase-contrast computed tomography (DPC-CT) is a powerful physical and biochemical analysis tool. In practical applications, there are often challenges for DPC-CT due to insufficient data caused by few-view, bad or missing detector channels, or limited scanning angular range. They occur quite frequently because of experimental constraints from imaging hardware, scanning geometry, and the exposure dose delivered to living specimens. In this work, we analyze the influence of incomplete data on DPC-CT image reconstruction. Then, a reconstruction method is developed and investigated for incomplete data DPC-CT. It is based on an algebraic iteration reconstruction technique, which minimizes the image total variation and permits accurate tomographic imaging with less data. This work comprises a numerical study of the method and its experimental verification using a dataset measured at the W2 beamline of the storage ring DORIS III equipped with a Talbot-Lau interferometer. The numerical and experimental results demonstrate that the presented method can handle incomplete data. It will be of interest for a wide range of DPC-CT applications in medicine, biology, and nondestructive testing.