We have previously introduced a high throughput multiplexing computational spectral imaging device. The device measures scalar projections of pseudo-arbitrary spectral filters at each spatial pixel. This paper discusses simulation and initial experimental progress in performing computational spectral unmixing by taking advantage of the natural sparsity commonly found in the fractional abundances. The simulation results show a lower unmixing error compared to traditional spectral imaging devices. Initial experimental results demonstrate the ability to directly perform spectral unmixing with less error than multiplexing alone.