Factor analysis and target transformation techniques have been applied to Miniature Thermal Emission Spectrometer (Mini-TES) spectra to isolate the end-member surface and atmospheric component spectral shapes at Meridiani Planum. The surface spectral shapes recovered from the Mini-TES data set include coarse, gray hematite, surface dust, basaltic sand, and the silica/sulfate-rich outcrop. In addition, two atmospheric spectral shapes are identified, indicating the variable nature of the atmosphere over the course of the MER rover missions. Linear deconvolution of the basaltic spectral shape indicates that it is high in plagioclase and pyroxene, including pigeonite, with smaller amounts of glass/phyllosilicate and olivine. Linear deconvolution of the outcrop spectral shape indicates that it is composed primarily of amorphous silica/glass/phyllosilicates and Mg-, Ca-, and Fe-bearing sulfates, with smaller amounts of plagioclase.