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To reduce image noise, we propose a novel image filter based on grey model via polynomial (GMP). The basic theory and the method of grey prediction model via polynomial are introduced. The new filter makes use of neighborhoods around each noisy pixel to predict its intensity value. Also the singular value decomposition (SVD) is adopted to increase the algorithm stability. The experimental results show that the proposed method, compared with the median filter and GM(1,1) model, improves the effect of the removal of low-density impulse noise, such as salt and pepper noise, and can do better than soma more popular denoising methods. The improved algorithm can effectively eliminate image noise, preserve the image's textures and edges, increase SNR(signal-to-noise ratio) as well as SSIM (structural similarity index), reduce RMSE (root mean square error), and significantly improve the image's visual effect. Therefore it is practicable. [ABSTRACT FROM AUTHOR]