Generalized non-local means for iterative denoising

Non-local means (NL-means) filter removes independent and identically distributed (i.i.d.) image noises using self-similarity. In this paper, we derive a generalized NL-means (GNL-means), which is specifically used to deal with non-i.i.d. noises in the NL-means filtered images. Inspired by BM3D and LPG-PCA, which perform denoising iteratively, our idea is also to iteratively apply NL-means. However, NL-means can't be applied directly due to the correlated noises in the image filtered by NL-means. We modify the original NL-means to incorporate noise dependence into the weight function, and show how the new weight can be calculated and give a reasonable estimator. We evaluate GNL-means on several benchmark images, and compare it to NL-means and other state-of-the-art non-local methods including BM3D and LPG-PCA. Our experimental results demonstrate that, while it is not surprising that BM3D essentially achieves the best denoising effect, GNL-means always performs better than NL-means, and better than LPG-PCA on average.