Detecting materials of interest in containers using X-ray measurements is a critical problem in aviation security. Conventional X-ray systems obtain single- or dual-energy measurements, which are subsequently processed using computed tomography (CT) to obtain estimates of attenuation properties of different regions. Recently, novel detectors enable the measurement of the X-ray transmission intensities on multiple energy bands, leading to the use of spectral CT to construct additional properties of regions to assist in material identification. In this paper, we discuss the problem of material classification using spectral CT. We introduce a new basis representation which can accurately represent energy-dependent X-ray transmission characteristics in a few dimensions, and propose a class of reconstruction techniques for obtaining features of different regions. We illustrate the advantages of our approach over alternative approaches using different basis representations as well as CT reconstructions in each energy band using simulated spectral CT experiments. Our results illustrate that there are significant advantages to using our basis representation in both detection and material classification performance, particularly in the presence of complex materials or mixtures involving atoms with high atomic number.