Maximum-likelihood estimation is an important method of inference.
Recently, maximum-likelihood techniques have been successfully
applied to absorption tomography of weakly as well as strongly
absorbing materials. In this presentation we generalize this
method to the phase contrast tomography, which combines the phase
estimation and tomography. Unlike the standard phase fitting
followed by the filtered back-projection, the developed procedure
gives reasonable results also when applied to very noisy data or
data consisting of only a few measured projections. The proposed
method could therefore considerably shorten measuring times in
applications involving low intensity beams, such as phase
tomography with low intense X-ray beams or neutrons.