Comparison of different numerical treatments for x-ray phase tomography of soft tissue from differential phase projections

X-ray imaging of soft tissue is made difficult by their low absorbance. The use of x-ray phase imaging and tomography can significantly enhance the detection of these tissues and several approaches have been proposed to this end. Methods such as analyzer-based imaging or grating interferometry produce differential phase projections that can be used to reconstruct the 3D distribution of the sample refractive index. We report on the quantitative comparison of three different methods to obtain x-ray phase tomography with filtered back-projection from differential phase projections in the presence of noise. The three procedures represent different numerical approaches to solve the same mathematical problem, namely phase retrieval and filtered back-projection. It is found that obtaining individual phase projections and subsequently applying a conventional filtered back-projection algorithm produces the best results for noisy experimental data, when compared with other procedures based on the Hilbert transform. The algorithms are tested on simulated phantom data with added noise and the predictions are confirmed by experimental data acquired using a grating interferometer. The experiment is performed on unstained adult zebrafish, an important model organism for biomedical studies. The method optimization described here allows resolution of weak soft tissue features, such as muscle fibers