Some embodiments of the invention provide a method of determining a material characteristic of material in a sample by iterative tomographic reconstruction. The method conducts one or more X-ray tomography scans of a sample, and then determines one or more estimated material characteristics, such as atomic number and density, for multiple volume elements in the sample using a tomographic reconstruction algorithm. These estimated material characteristics are then modified by reference to stored known material characteristic data. Preferably, determining the composition of the sample volume during reconstruction includes segmenting the sample into regions of common composition, the segmenting being performed during iterative reconstruction instead of being based on the voxel characteristics determined upon the completion of iterative reconstruction. Preferred versions will perform one or more additional iterations of the tomographic reconstruction algorithm, where each iteration updates the one or more estimated material characteristics for the volume elements.