Embodiments of methods and apparatus are disclosed for obtaining a radiographic phase-contrast digital computed tomography imaging system and methods for same that can include obtaining a first and second plurality of 2D projection images over a range of scan angles, generating at least two statistically independent reconstructed images of an object from the first plurality of 2D projection images and the second plurality of 2D projection images, determining a material property as a function of volume for each of at least two materials represented in the projection images, using a conditional likelihood determination comprising the material property as a function of volume and the at least two statistically independent reconstructed images to differentiate the at least two materials in a reconstructed image of the object.