A Fast Non-Local Image Denoising Algorithm A. Dauwe, B. Goossens, H.Q. Luong and W. Philips IPI-TELIN-IBBT, Ghent University, Sint-Pietersnieuwstraat 41, 9000 Ghent, Belgium ABSTRACT In this paper we propose several improvements to the original non-local means algorithm introduced by Buades et al. which obtains state-of-the-art denoising results. The strength of this algorithm is to exploit the repetitive character of the image in order to denoise the image unlike conventional denoising algorithms, which typically operate in a local neighbourhood. Due to the enormous amount of weight computations, the original algorithm has a high computational cost. An improvement of image quality towards the original algorithm is to ignore the contributions from dissimilar windows. Even though their weights are very small at first sight, the new estimated pixel value can be severely biased due to the many small contributions. This bad influence of dissimilar windows can be eliminated by setting their corresponding weights to zero. Using the preclassification based on the first three statistical moments, only contributions from similar neighborhoods are computed. To decide whether a window is similar or dissimilar, we will derive thresholds for images corrupted with additive white Gaussian noise. Our accelerated approach is further optimized by taking advantage of the symmetry in the weights, which roughly halves the computation time, and by using a lookup table to speed up the weight computations. Compared to the original algorithm, our proposed method produces images with increased psnr and better visual performance in less computation time. Our proposed method even outperforms state-of-the-art wavelet denoising techniques in both visual quality and psnr values for images containing a lot of repetitive structures such as textures: the denoised images are much sharper and contain less artifacts. The proposed optimizations can also be applied in other image processing tasks which employ the concept of repetitive structures such as intra-frame super-resolution or detection of digital image forgery. Keywords: Non-local image denoising, repetitive structures 1. INTRODUCTION Digital images are often corrupted by noise. The origin of noise is usually found in the acquisition or transmission process. In this paper, we focus on the classic image denoising problem: the objective is to design an algorithm that can remove additive zero-mean white stationary Gaussian noise, while preserving the original image details and fine structures. Numerous and diverse denoising methods have already been proposed in the past decades, just to name a few algorithms: total variation, 1 bilateral filter or kernel regression 2, 3 and wavelet-based techniques. 4–7 All of these methods estimate the denoised pixel value based on the information provided in a surrounding local limited window. Unlike these local denoising methods, non-local methods estimate the noisy pixel is replaced based on the information of the whole image. The motivation to develop non-local methods is to exploit similar patterns and structures in an image. This relatively new class of denoising methods originates from the non-local means. 8, 9 Other denoising methods based on this concept are developed in 3d transform-domain filtering 10 and in a training- based framework. 11 Unlike fractal-based methods, we exploit the similarity of small patches in the same scale, i.e. spatially. Besides repetitivity in texture, we can also find this recurrent property in other parts of the image, such as repetition in different but similar objects, along edges and in uniform areas, etc. The non-local method is Further author information: (Send correspondence to H.Q. Luong) H.Q. Luong: E-mail: hiep.luong@telin.ugent.be, Telephone: +32 (0) 9 264 79 66 B. Goossens: E-mail: bart.goossens@telin.ugent.be Image Processing: Algorithms and Systems VI, edited by Jaakko T. Astola, Karen O. Egiazarian, Edward R. Dougherty, Proc. of SPIE-IS&T Electronic Imaging, SPIE Vol. 6812, 681210, © 2008 SPIE-IS&T · 0277-786X/08/$18 SPIE-IS&T Vol. 6812 681210-1 2008 SPIE Digital Library -- Subscriber Archive Copy