A reconstruction formula for soft tissue X-ray phase tomography

In clinical x-ray phase imaging, the significant tissue attenuation cannot be ignored. In x-ray phase tomography, the presence of tissue attenuation requires acquisition of at least two images for the retrieval of tissue phase for a given tomographic view. This paper presents an important observation that the same map of the projected electron densities can determine both the phase and attenuation maps of soft tissues, provided that the dominance of incoherent scattering holds. Based on this observation a new strategy to perform the phase retrieval was developed. A 3-D phase tomography reconstruction formula was derived, which combines the three-dimensional inverse Radon transform with the phase retrievals for soft tissues. This new formula alleviates all the technical difficulties associated with the requirement of acquiring two images per tomographic view for phase-retrievals in x-ray phase tomography.