A Review of Image Denoising Algorithms, with a New One

The search for e-cient image denoising methods still is 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 out- standing performance when the image model corresponds to the algorithm assumptions, but fail in general and create artifacts or remove image flne structures. The main focus of this paper is, flrst, to deflne a general mathematical and experimental methodology to compare and classify classical image denoising algorithms, second, to propose an algorithm (Non Local Means) addressing the preservation of structure in a digital image. The mathematical analysis is based on the analysis of the \method noise", deflned as the difierence 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 de- noising 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 experi- mental: by tables of L2 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.