In this paper, we study the problem of automatic identification of pigments applied to paintings using hyperspectral reflectance data. Here, we cast the problem of pigment identification in a novel way by decomposing the spectrum into pure pigments. The pure pigment exemplars, chosen and prepared in our laboratory based on historic sources and archaeological examples, closely resemble the materials used to make ancient paintings. To validate our algorithm, we created a set of mock-up paintings in our laboratory consisting of a broad palette of mixtures of pure pigments. Our results clearly demonstrate more accurate estimation of pigment composition than purely distance-based methods such as spectral angle mapping (SAM) and spectral correlation mapping (SCM). In addition, we studied hyperspectral imagery acquired of a Roman-Egyptian portrait, excavated from the site of Tebtunis in the Fayum region of Egypt, and dated to about the 2nd century CE. Using ground truth information obtained using Raman spectroscopy, we show qualitatively that our method accurately detects pigment composition for the specific pigments hematite and indigo.