Apparatus and methods for Compton scattering radiography employing a variable energy X-ray source and a detector capable of detecting the temporal intensity profile of scattered X-ray pulses disposed on one side of an object to be imaged. Based on analysis of the measurement of the instantaneous intensity of the detected photons and the beam position relative to the object, an image is generated. Each voxel can be reconstructed to yield a measure of variation in the density of the material of the object.