Hyperspectral imaging systems can benefit from compressed sensing to reduce data acquisition demands. We present a new reconstruction algorithm to recover the hyperspectral datacube from limited optically compressed measurements, exploiting the inherent spatial and spectral correlations through non-local means regularization. The reconstruction process is solved with the help of split Bregman optimization techniques, including penalty functions defined according to the spatial and spectral properties of the scene and noise sources. For validation purposes, we also implemented a compressive hyperspectral imaging system that relies on a digital micromirror device and a near-infrared spectrometer, where we obtained enhanced and promising reconstruction results when using our proposed technique in contrast with traditional compressive image reconstruction.