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First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper proposes a method to recover signals from compressive measurements. The method consists of jointly estimating the signal and a Gaussian Mixture Model (GMM) capable of representing it succinctly. The main contribution of the paper is the idea of imposing a sparse structure on the GMM adapted to the case when the signal of interest corresponds to image patches. This is further exploited by a more structured prior that promotes an appropriate group-sparsity pattern (essentially interactions between adjoining pixels are not penalized by the sparsity-inducing penalty).