An improved non-local denoising algorithm

Recently, the NLMeans filter has been proposed by Buades et al. for the suppression of white Gaussian noise. This filter exploits the repetitive character of structures in an image, unlike conventional denoising algorithms, which typically operate in a local neighbourhood. Even though the method is quite intuitive and potentially very powerful, the PSNR and visual results are somewhat inferior to other recent state-of-the-art non-local algorithms, like KSVD and BM-3D. In this paper, we show that the NLMeans algorithm is basically the first iteration of the Jacobi optimization algorithm for robustly estimating the noise-free image. Based on this insight, we present additional improvements to the NLMeans algorithm and also an extension to noise reduction of coloured (correlated) noise. For white noise, PSNR results show that the proposed method is very competitive with the BM-3D method, while the visual quality of our method is better due to the lower presence of artifacts. For correlated noise on the other hand, we obtain a significant improvement in denoising performance compared to recent wavelet-based techniques.