The invention provides improvements in reconstructive imaging of the type in which a volume is reconstructed from a series of measured projection images (or other two-dimensional representations) by utilizing the capabilities of graphics processing units (GPUs). In one aspect, the invention configures a GPU to reconstruct a volume by initializing an estimated density distribution of that volume to arbitrary values in a three-dimensional voxel-based matrix and, then, determining the actual density distribution iteratively by, for each of the measured projections, (a) forward-projecting the estimated volume computationally and comparing the forward-projection with the measured projection, (b) generating a correction term for each pixel in the forward-projection based on that comparison, and (c) back-projecting the correction term for each pixel in the forward-projection onto all voxels of the volume that were mapped into that pixel in the forward-projection.