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.

我们提出了一种统一的非局部方法的观点，用于单图像去噪，其中 BM3D 是最流行的代表，根据它们的相似性将噪声补丁收集在一起以进行协同处理。我们的一般估计框架基于二次风险的最小化，在两个步骤中近似，并适应光子和电子噪声。在第一步中依靠无偏风险估计（URE），在第二步中依靠从深度学习理论中借鉴的 “内部适应” 概念，我们展示了我们的方法能够重新解释和融合先前的最先进的非局部方法。在这个框架内，我们提出了一种名为 NL-Ridge 的新型去噪算法，它利用了补丁的线性组合。虽然在概念上更简单，但我们展示了 NL-Ridge 可以胜过成熟的最先进的单图像去噪算法。

图像去噪的非局部参数方法统一框架

A unified framework of non-local parametric methods for image denoising

Non-local methods exploiting the self-similarity of natural signals have been
well studied, for example in image analysis and restoration. Existing
approaches, however, rely on k-nearest neighbors (KNN) matching in a fixed
feature space. The main hurdle in optimizing this feature space w.r.t.
application performance is the non-differentiability of the KNN selection rule.
To overcome this, we propose a continuous deterministic relaxation of KNN
selection that maintains differentiability w.r.t. pairwise distances, but
retains the original KNN as the limit of a temperature parameter approaching
zero. To exploit our relaxation, we propose the neural nearest neighbors block
(N3 block), a novel non-local processing layer that leverages the principle of
self-similarity and can be used as building block in modern neural network
architectures. We show its effectiveness for the set reasoning task of
correspondence classification as well as for image restoration, including image
denoising and single image super-resolution, where we outperform strong
convolutional neural network (CNN) baselines and recent non-local models that
rely on KNN selection in hand-chosen features spaces.

研究了利用自然信号的自相似性进行非局部方法，提出了一种对 KNN 选择规则进行连续确定性松弛的方法，即通过温度参数逐渐接近零将原始 KNN 保持为极限，利用提出的神经最近邻块 (N3 块) 用于现代神经网络建筑中，并展示了其在图像恢复等任务中的有效性。