The 2D Adaptive NonLocal Means filter can be tested online here .
Abstract. Partial Differential equations (PDE), waveletsbased methods and neighborhood filters were proposed as locally adaptive machines for noise removal. Recently, Buades, Coll and Morel proposed the NonLocal (NL) means filter for image denoising (see Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Modeling and Simulation. 4 (2005) 490530). This method replaces a noisy pixel by the weighted average of other image pixels with weights reflecting the similarity between local neighborhoods of the pixel being processed and the other pixels. The NLmeans filter was proposed as an intuitive neighborhood filter but theoretical connections to diffusion and nonparametric estimation approaches are also given by the authors. In this paper we propose another bridge, and show that the NLmeans filter also emerges from the Bayesian approach with new arguments. Based on this observation, we show how the performance of this filter can be significantly improved by introducing adaptive local dictionaries and a new statistical distance measure to compare patches. The new Bayesian NLmeans filter is better parametrized and the amount of smoothing is directly determined by the noise variance (estimated from image data) given the patch size. Experimental results are given for real images with artificial Gaussian noise added, and for images with real imagedependent noise.
Adaptive (blockwise) NonLocal means filter Consider a grayscale image defined over a bounded domain , (which is usually a rectangle) and is the noisy observed intensity at pixel . The proposed Adaptive NLmeans filter (ANL) is defined as
Iterative (plugin estimator) Adaptive NonLocal means filter
We are free to substitute the vector
of aggregated estimators (computed from the set of restored blocks
. The corresponding plugin and iterative ANL filter defined as
Experimental results

