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We propose a l0 sparsity based approach to remove additive white Gaussian noise from a given image. To achieve this goal, we combine the local prior and global prior together to recover the noise-free values of pixels. The local prior depends on the neighborhood relationships of a search window to help maintain edges and smoothness. The global prior is generated from a hierarchical l0 sparse representation to help eliminate the redundant information and preserve the global consistency. In addition, to make the correlations between pixels more meaningful, we adopt Principle Component Analysis to measure the similarities, which can be both propitious to reduce the computational complexity and improve the accuracies. Experiments on the benchmark image set show that the proposed approach can achieve superior performance to the state-of-the-art approaches both in accuracy and perception in removing the zero-mean additive white Gaussian noise