Phase-wrapping artifacts, statistical image noise and the need for a minimumamount of phase steps per projection limit the practicability of x-ray gratingbased phase-contrast tomography, when using filtered back projectionreconstruction. For conventional x-ray computed tomography, the use ofstatistical iterative reconstruction algorithms has successfully reducedartifacts and statistical issues. In this work, an iterative reconstructionmethod for grating based phase-contrast tomography is presented. The methodavoids the intermediate retrieval of absorption, differential phase and darkfield projections. It directly reconstructs tomographic cross sections fromphase stepping projections by the use of a forward projecting imaging model andan appropriate likelihood function. The likelihood function is then maximizedwith an iterative algorithm. The presented method is tested with tomographicdata obtained through a wave field simulation of grating based phase-contrasttomography. The reconstruction results are in agreement with the expectationsand proof the validity of the concept.
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