We propose a unified view of non-local methods for single-image denoising, for which BM3D is the most popular representative, that operate by gathering noisy patches together according to their similarities in order to process them collaboratively. Our general estimation framework is based on the minimization of the quadratic risk, which is approximated in two steps, and adapts to photon and electronic noises. Relying on unbiased risk estimation (URE) for the first step and on ``internal adaptation'', a concept borrowed from deep learning theory, for the second, we show that our approach enables to reinterpret and reconcile previous state-of-the-art non-local methods. Within this framework, we propose a novel denoiser called NL-Ridge that exploits linear combinations of patches. While conceptually simpler, we show that NL-Ridge can outperform well-established state-of-the-art single-image denoisers.

翻译：我们提出了一种用于单幅图像去噪的非局部方法的统一视角，其中BM3D是最具代表性的方法，该方法通过根据相似性收集含噪图像块并进行联合处理来实现去噪。我们的通用估计框架基于二次风险的最小化，该风险通过两步近似，并适用于光子噪声和电子噪声。第一步依赖于无偏风险估计（URE），第二步则借用深度学习理论中的“内部适应”概念，我们证明了该方法能够重新解释并调和先前最先进的非局部方法。在此框架内，我们提出了一种名为NL-Ridge的新型去噪器，它利用图像块的线性组合。尽管概念上更简单，但我们展示了NL-Ridge能够超越已建立的先进单幅图像去噪器。