In the article, we propose a robust impulse denoising method based on noise accumulation and harmonic analysis techniques (NAHAT filter). Noise accumulation technique is used to improve the ability to detect noisy pixels, and a harmonic function is used to gain the accuracy of restoring gray values of the detected noisy pixels. The proposed method can remove impulse noise very effectively even under high-density impulse noise levels. Moreover, the proposed method can preserve image structures such as the edges and textures well. Based on experimental results, the proposed method obtains good performance under various noise levels as well as outperforms other similar state-of-the-art impulse denoising methods.