A method and apparatus uses multi-material decomposition of three or more material components to generate material-component images from spectral images reconstructed from spectral computed tomography data. In three-component material decomposition e.g., the Mendonça method is used for multi-material decomposition when the attenuation values satisfy an assumed volume fraction condition (i.e., for a given voxel, the attenuation values are within a triangle having vertices given by unit volume fractions of three respective material components). However, when the volume fraction condition fails (e.g., the attenuation values are outside the triangle), either a shortest-Hausdorff-distance method or a closest-edge method is used for multi-material decomposition. For example, the attenuation values of the voxel are projected onto a lower-dimensional space (e.g., the space of a closest edge) and decomposed into a pair/single material component(s) of the lower-dimensional space.