Spectral imaging, a combination of spectroscopy and imaging, is a powerful tool for providing in situ material classification across a spatial scene. Typically spectral imaging analyses are interested in classification, though conventionally the classification is performed only after reconstruction of the spectral datacube, which can have upwards of 10⁹ signal elements. In this dissertation, I present a computational spectral imaging system, the Adaptive Feature-Specific Spectral Imaging Classifier (AFSSI-C), which yields direct classification across the spatial scene without reconstruction of the source datacube. With a dual disperser architecture and a programmable spatial light modulator which induces spectral filtering, the AFSSI-C measures specific projections of the spectral datacube which in turn feed an adaptive Bayesian classification and feature design framework. I present my work related to the design, construction, and testing of this instrument, which ultimately demonstrated significantly improved classification accuracy compared to legacy spectral imaging systems by first showing agreement with simulation, and then comparing to expected performance of traditional systems. As a result of its open aperture and adaptive filters, the AFSSI-C achieves 250 X better accuracy than pushbroom, whiskbroom, and tunable filter systems for a four-class problem at 0 dB TSNR (task signal-to-noise ratio) - a point where measurement noise is equal to the minimum separation between the library spectra. The AFSSI-C also achieves 100 X better accuracy than random projections at 0 dB TSNR.