On image denoising methods
On image denoising methods
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发表时间：
2004
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通讯作者：
A. Buades;B. Coll;J. Morel
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作者：
A. Buades;B. Coll;J. Morel
在泛函分析和统计学的交叉点上，寻找有效的图像去噪方法仍然是一个有效的挑战。尽管最近提出的方法的复杂性，大多数算法尚未达到理想的适用性水平。当图像模型与算法假设相对应时，所有算法都表现出出色的性能，但通常会失败并产生伪影或去除图像精细结构。本文的主要重点是，第一，定义一个通用的数学和实验方法来比较和分类经典的图像去噪算法，第二，提出一种算法（非局部均值）解决的数字图像中的结构保存。数学分析是基于“方法噪声”的分析，定义为数字图像和其去噪版本之间的差异。在一个通用的统计图像模型下，NL-均值算法也被证明是渐近最优的。所有考虑的方法的去噪性能进行了比较，在四种方式;数学：渐近的大小顺序的方法噪声的规律性假设下;感知数学：算法的文物和他们的解释，作为一个违反图像模型;定量实验：表的L距离的去噪版本的原始图像。然而，最强大的评估方法似乎是自然图像上的方法噪声的可视化。该方法噪声越像真实的白色噪声，该方法越好。
The search for efficient 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 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, 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”, defined as the difference between a digital image and its denoised version. The NL-means algorithm is also 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 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.