Some configurations of method for reconstructing a volumetric image of an object include obtaining a tomosynthesis projection dataset of an object. The method also includes utilizing the tomosynthesis projection dataset and additional information about the object to minimize a selected energy function or functions to satisfy a selected set of constraints. Alternatively, constraints are applied to a reconstructed volumetric image in order to obtain an updated volumetric image. A 3D volume representative of the imaged object is thereby obtained in which each voxel is reconstructed and a correspondence indicated to a single one of the component material classes.