In this work, we propose an image denoising approach, specifically for “salt-and-pepper noise,” based on the optimized sparse approximation for restoring images contaminated by high-density impulse noise. The proposed method first uses the inverse-distance weighting-based prediction to estimate noise-recovered pixels. It then utilizes DCT-based sparse approximation to further refine the denoised results with the ant colony optimization. Experiments on an image benchmark dataset demonstrate that the proposed method yields better results compared to the state-of-the-art image noise removal methods.