In this paper, we propose a novel algorithm for image reconstruction from compressive measurements of wavelet coefficients. By incorporating independent Laplace priors on separate wavelet sub-bands, the inhomogeneity of wavelet coefficient distributions and therefore the structural sparsity within images are modeled effectively. We model the problem by adopting a Bayesian formulation, and develop a fast greedy reconstruction algorithm. Experimental results demonstrate that the reconstruction performance of the proposed algorithm is competitive with state-of-the-art methods while outperforming them in terms of running times.