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Previous work on mixed Gaussian and impulse noise (MGIN) reduction has impressive quantitative results. However, the estimation of the statistical properties of the MGIN model that varies within a wide range has not been fully investigated. In this paper, statistical properties of the MGIN model are analyzed in detail with a robust estimation. The paper also proposes a two-stage impulse-then-Gaussian filter for MGIN suppression. which makes use of the estimated statistical properties of MGIN. The proposed filtering scheme applies a impulse proportion adaptive median filter (IPAMF) to impulse noise suppression, and a state-of-the-art discrete cosine transform (DCT) domain filter to Gaussian noise reduction. Numerical results, in terms of the peak signal-to-noise ratio (PSNR), and visual samples demonstrate that the proposed filtering scheme achieves better performance of noise reduction than two existing MGIN filtering schemes.