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Due to limited volume, weight and power consumption, micro-satellite has to reduce data transmission and storage capacity by image compression when performs earth observation missions. However, the quality of images may be unsatisfied. This paper consid-ers the problem of recovering sparse signals by exploiting their unknown sparsity patt. To model structured sparsity, the prior correlation of the support is encoded by imposing a trans-formed Gaussian process on the spike and slab probabilities. Then, an efficient approximate message-passing algorithm with structured spike and slab prior is derived for posterior inference, which, combined with a fast direct method, reduces the computational complex-ity significantly. Further, a unified scheme is developed to le the hyperparameters using expectation maximization (EM) and Bethe free energy optimization. Simulation results on both synthetic and real data demonstrate the superiority of the proposed algorithm.