Following the pioneering works of Rudin, Osher and Fatemi on total variation (TV) and of Buades, Coll and Morel on non-local means (NL-means), the last decade has seen a large number of denoising methods mixing these two approaches, starting with the nonlocal total variation (NLTV) model. The present article proposes an analysis of the NLTV model for image denoising as well as a number of improvements, the most important of which being to apply the denoising both in the space domain and in the Fourier domain, in order to exploit the complementarity of the representation of image data. A local version obtained by a regionwise implementation followed by an aggregation process, called Local Spatial-Frequency NLTV (L-SFNLTV) model, is finally proposed as a new reference algorithm for image denoising among the family of approaches mixing TV and NL operators. The experiments show the great performance of L-SFNLTV in terms of image quality and of computational speed, comparing with other recently proposed NLTV-related methods.

中文翻译：

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空频域非局部总变异图像去噪

继Rudin，Osher和Fatemi在总变数（TV）以及Buades，Coll和Morel在非局部均值（NL-means）方面的开创性工作之后，近十年来，出现了许多将这两种方法结合在一起的去噪方法，从非本地总变异（NLTV）模型开始。本文提出了一种用于图像去噪的NLTV模型的分析方法，并提出了许多改进措施，其中最重要的是在空间域和傅里叶域中均采用去噪，以利用图像的去噪性。图像数据的表示。通过区域实施和聚合过程获得的本地版本，称为本地空间频率NLTV（L-SFNLTV）模型，最终提出了一种在电视和NL运算符混合的方法系列中作为图像去噪的新参考算法。实验表明，与其他最近提出的NLTV相关方法相比，L-SFNLTV在图像质量和计算速度方面均具有出色的性能。