A Review of Image Denoising Algorithms, with a New One

Abstract

The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding performance when the image model corresponds to the algorithm assumptions but fail in general and create artifacts or remove image fine structures. The main focus of this paper is, first, to define a general mathematical and experimental methodology to compare and classify classical image denoising algorithms and, second, to propose a nonlocal means (NL-means) algorithm addressing the preservation of structure in a digital image. The mathematical analysis is based on the analysis of the "method noise," defined as the difference between a digital image and its denoised version. The NL-means algorithm is proven to be asymptotically optimal under a generic statistical image model. The denoising performance of all considered methods are compared in four ways; mathematical: asymptotic order of magnitude of the method noise under regularity assumptions; perceptual-mathematical: the algorithms artifacts and their explanation as a violation of the image model; quantitative experimental: by tables of L 2 distances of the denoised version to the original image. The most powerful evaluation method seems, however, to be the visualization of the method noise on natural images. The more this method noise looks like a real white noise, the better the method.

Non-Local Means Denoising

“…The resemblance is evaluated by comparing a whole window around each pixel, and not just the color. This new filter is called non-local means [1,2] and it writes…”

Accelerating Monte Carlo Renderers by Ray Histogram Fusion

“…Taking the mean as done in the preceding formula is the simplest possible aggregation method as proposed in other denoising algorithms [3,5].…”

“…This is a very classic procedure in patch based image denoising [3,5,20]. Given a noisy patch P x centered at pixel x its denoised version V x is first computed by averaging all the patches being at a Chi-square distance smaller than κ:…”

Parameter-Free Fast Pixelwise Non-Local Means Denoising

“…The Non-Local Means (NLM) image denoising algorithm was introduced in 2005 by Antoni Buades, Bartomeu Coll and Jean-Michel Morel [1] and the success was such that this method has inspired a great number of variants and articles, see [3] for some updated references. Three factors largely explain why the image denoising community has been immersed in the NLM approach: the original algorithm remains simple; it provides great visual quality; it introduces a basic tool to exploit the non-local redundancy of natural images.…”

“…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. The parameters' default values correspond to those in [1], but they turn out to be non optimal for most images. Finally, this code does not implement any algorithmic trick or parallelization of computing, making it a slow running program.…”