  A blind compressive sensing algorithm is proposed to reconstruct
hyperspectral images from spectrally-compressed measurements.The
wavelength-dependent data are coded and then superposed, mapping the
three-dimensional hyperspectral datacube to a two-dimensional image. The
inversion algorithm learns a dictionary {\em in situ} from the measurements via
global-local shrinkage priors. By using RGB images as side information of the
compressive sensing system, the proposed approach is extended to learn a
coupled dictionary from the joint dataset of the compressed measurements and
the corresponding RGB images, to improve reconstruction quality. A prototype
camera is built using a liquid-crystal-on-silicon modulator. Experimental
reconstructions of hyperspectral datacubes from both simulated and real
compressed measurements demonstrate the efficacy of the proposed inversion
algorithm, the feasibility of the camera and the benefit of side information.
