• It requires a priori knowledge about the chemistry of the sample before reconstruction • It requires the construction of a robust physical model that models all chemistry accurately in the sinogram data; minor components being overlooked during the inspection of diffraction patterns when preparing the physical model will not be part of the final results • DLSR in its TOPAS version 7 implementation suffers from scalability; even XRD-CT images that are nowadays trivially obtained in experiments (e.g. 256 x 256) cannot be handled due to RAM requirements and the data have to be rebinned losing spatial resolution. • It typically requires laborious data pre-processing to decrease memory requirements (to what is realistically available) and yield stable reconstructions. For example, one needs to create a separate binary mask for each crystalline phase present by analysing the FBP reconstructed XRD-CT volume (which contains parallax artefacts) and/or subtract the background from the sinogram data (in order to make it linear/ use a simple background model) Therefore, our motivation was to develop a method that overcomes all these limitations of the DLSR approach and yield parallax artefact-free XRD-CT images.