Fractal coding has been widely used as an image compression technique in many image processing problems in the past few decades. On the other hand side, most of the natural images have the characteristic of nonlocal self-similarity that motivates low-rank representations of them. We would employ both the fractal image coding and the nonlocal self-similarity priors to achieve image compression in image denoising problems. Specifically, we propose a new image denoising model consisting of three terms: a patch-based nonlocal low-rank prior, a data-fidelity term describing the closeness of the underlying image to the given noisy image, and a quadratic term measuring the closeness of the underlying image to a fractal image. Numerical results demonstrate the superior performance of the proposed model in terms of peak-signal-to-noise ratio, structural similarity index and mean absolute error.

中文翻译：

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一种分形图像编码的非局部低秩正则化方法

在过去的几十年中，分形编码作为一种图像压缩技术被广泛应用于许多图像处理问题。另一方面，大多数自然图像具有非局部自相似性的特征，这激发了它们的低秩表示。我们将同时使用分形图像编码和非局部自相似先验来实现图像去噪问题中的图像压缩。具体来说，我们提出了一个新的图像去噪模型，它由三个项组成：一个基于补丁的非局部低秩先验，一个描述底层图像与给定噪声图像的接近度的数据保真项，以及一个测量图像接近度的二次项。将基础图像转换为分形图像。数值结果证明了所提出的模型在峰值信噪比方面的优越性能，