A spectral imager provides a 3-D data cube in which the spatial information (2-D) of the image is complemented by spectral information (1-D) about each spatial location. Typically, these systems are operated in a fully-determined (or overdetermined) manner so that the measurements can be computationally inverted into a reliable estimate of the source. We propose a notional system design that is highly underdetermined, yet still computationally invertable. This approach relies on recently-developed concepts in compressive sensing. Because the number of required measurements is greatly reduced from traditional designs, the result is a faster and more economical sensor system.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.