This paper introduces a hierarchical Bayesian model for the reconstruction of hyperspectral images using compressed sensing measurements. This model exploits known properties of natural images, promoting the recovered image to be sparse on a selected basis and smooth in the image domain. The posterior distribution of this model is too complex to derive closed form expressions for the estimators of its parameters. Therefore, an MCMC method is investigated to sample this posterior distribution. The resulting samples are used to estimate the unknown model parameters and hyperparameters in an unsupervised framework. The results obtained on real data illustrate the improvement in reconstruction quality when compared to some existing techniques.