Non-Local Means Denoising

Abstract

We present in this paper a new denoising method called non-local means. The method is based on a simple principle: replacing the color of a pixel with an average of the colors of similar pixels. But the most similar pixels to a given pixel have no reason to be close at all. It is therefore licit to scan a vast portion of the image in search of all the pixels that really resemble the pixel one wants to denoise. The paper presents two implementations of the method and displays some results. Source CodeThe source code (ANSI C), its documentation, and the online demo are accessible at the IPOL web page of this article 1 . Some of the files use algorithms possibly linked to patent [3]. These files are made available for the exclusive aim of serving as scientific tool to verify the soundness and completeness of the algorithm description. Compilation, execution and redistribution of these files may violate exclusive patents rights in certain countries. The situation being different for every country and changing over time, it is your responsibility to determine which patent rights restrictions apply to you before you compile, use, modify, or redistribute these files. The rest of files are distributed under GPL license. A C/C++ implementation is provided. Please see the readme file or the online documentation for details.

Parameter-Free Fast Pixelwise Non-Local Means Denoising

“…We write here the denominator of the fraction in the exponential as h 2 , thus following the notation in [3,1,4], whereas one reads 2h 2 in most subsequent articles about NLM. The estimation of the oracle |u(x) − u(y)| is performed using the Gaussian Euclidean norm V (x) − V (y) 2,a , where a is the standard deviation of the Gaussian and where V (x) is the patch of size d × d centered at x in image v:…”

“…Finally, this code does not implement any algorithmic trick or parallelization of computing, making it a slow running program. While the IPOL article [4] describes both the pixelwise NLM (NLM-P) ([1] Section 5.1) and the blockwise NLM (NLM-B) ([1] Section 5.5.2), the published demo and code implement the blockwise version only 2 . The present article aims to propose a fast and parameter-free implementation of the pixelwise NLM as described in [1] (pages 510-512).…”

“…The choice to consider (5) rather than (7) is related to the concern to implement the original NLM algorithm. Note that in [4] and unlike [1,3], the authors do subtract 2σ 2 to the square of the norm. In the discrete setting, the Gaussian Euclidean norm writes (10) and d s = (d − 1)/2 being the patch side half-length, d being an odd number.…”

“…Despite the number of NLM codes that can be found in the Internet, it seems that there are only two implementations that fulfill these conditions: the nlmeans module included in MegaWave2 [11] and written by Lionel Moisan and the IPOL article [4] from Buades, Coll and Morel. The first code implements the pixelwise NLM algorithm given in [1] (Section 5.1) for gray-level images only and using the Euclidean norm instead of the uniform one to define neighbor patches.…”

An ICI Based Algorithm for Fast Denoising of Video Signals

“…In order to obtain the best possible estimate from noisy data, a robust, efficient and reliable denoising method is required. Various denoising methods have been proposed in the last few decades, a review of which can be found in [2], where their features are elaborated and compared.…”