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In this paper, a new method to remove salt and pepper noise from an image through sparse representation is proposed. The proposed method consists of two stages. In the first stage, the positions of noise pixels are detected by thresholding the absolute difference between the noisy image and its sparse representation. In the next stage, the pixels that are detected as noisy pixels are removed and then filled using image inpainting through sparse representation. The experimental results show that the proposed filter is suitable for removing impulse noise from an image.