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

Filtering multi-dimensional images such as color images, color videos,
multispectral images and magnetic resonance images is challenging in terms of
both effectiveness and efficiency. Leveraging the nonlocal self-similarity
(NLSS) characteristic of images and sparse representation in the transform
domain, the block-matching and 3D filtering (BM3D) based methods show powerful
denoising performance. Recently, numerous new approaches with different
regularization terms, transforms and advanced deep neural network (DNN)
architectures are proposed to improve denoising quality. In this paper, we
extensively compare over 60 methods on both synthetic and real-world datasets.
We also introduce a new color image and video dataset for benchmarking, and our
evaluations are performed from four different perspectives including
quantitative metrics, visual effects, human ratings and computational cost.
Comprehensive experiments demonstrate: (i) the effectiveness and efficiency of
the BM3D family for various denoising tasks, (ii) a simple matrix-based
algorithm could produce similar results compared with its tensor counterparts,
and (iii) several DNN models trained with synthetic Gaussian noise show
state-of-the-art performance on real-world color image and video datasets.
Despite the progress in recent years, we discuss shortcomings and possible
extensions of existing techniques. Datasets and codes for evaluation are made
publicly available at this https URL

本研究比较了超过 60 种图像去噪方法，其中 BM3D 方法在各种去噪任务中展现出了有效性和高效性，同时发现多种 DNN 模型能够在对抗真实数据的去噪任务中展现出最优的性能。该研究还引入了一个新的彩色图像和视频数据集用于基准测试。

多维图像去噪方法的全面比较

A Comprehensive Comparison of Multi-Dimensional Image Denoising Methods

We propose an image representation scheme combining the local and nonlocal
characterization of patches in an image. Our representation scheme can be shown
to be equivalent to a tight frame constructed from convolving local bases (e.g.
wavelet frames, discrete cosine transforms, etc.) with nonlocal bases (e.g.
spectral basis induced by nonlinear dimension reduction on patches), and we
call the resulting frame elements {\it convolution framelets}. Insight gained
from analyzing the proposed representation leads to a novel interpretation of a
recent high-performance patch-based image inpainting algorithm using Point
Integral Method (PIM) and Low Dimension Manifold Model (LDMM) [Osher, Shi and
Zhu, 2016]. In particular, we show that LDMM is a weighted
$\ell_2$-regularization on the coefficients obtained by decomposing images into
linear combinations of convolution framelets; based on this understanding, we
extend the original LDMM to a reweighted version that yields further improved
inpainting results. In addition, we establish the energy concentration property
of convolution framelet coefficients for the setting where the local basis is
constructed from a given nonlocal basis via a linear reconstruction framework;
a generalization of this framework to unions of local embeddings can provide a
natural setting for interpreting BM3D, one of the state-of-the-art image
denoising algorithms.

该研究论文提出了一种图像表示方案，其中等价于使用局部和非局部 patches 刻画构建紧密的帧图像，并称其为卷积 framelets。分析该表示方案得出了高性能的 patch-based image inpainting 算法的新解释，并提出了对其的改进。此外，还建立了卷积 framelet 系数的能量集中性质，为一些成像处理算法提供了自然的框架。