We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2-D image fragments (e.g., blocks) into 3-D data arrays which we call "groups." Collaborative filtering is a special procedure developed to deal with these 3-D groups. We realize it using the three successive steps: 3-D transformation of a group, shrinkage of the transform spectrum, and inverse 3-D transformation. The result is a 3-D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.

We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and redundant representations over trained dictionaries. Using the K-SVD algorithm, we obtain a dictionary that describes the image content effectively. Two training options are considered: using the corrupted image itself, or training on a corpus of high-quality image database. Since the K-SVD is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm. This leads to a state-of-the-art denoising performance, equivalent and sometimes surpassing recently published leading alternative denoising methods.

实际图像的稀疏表示是成像应用的非常有效的方法，例如去噪。近年来，随着计算能力的增长，利用一个或多个图像提取的补丁内冗余的数据驱动策略，以增加稀疏性变得更加突出。本文提出了一种新颖的图像去噪算法，利用了由量子多体理论的图像依赖性的基础。基于补丁分析，通过类似于量子力学的术语来形式化局部图像邻域中的相似度测量，可以有效地保留真实图像的局部结构的量子力学中的相互作用。这种自适应基础的多功能性质将其应用范围扩展到图像无关或图像相关的噪声场景，而无需任何调整。我们对当代方法进行严格的比较，以证明所提出的算法的去噪能力，无论图像特征，噪声统计和强度如何。我们说明了超参数的特性及其对去噪性能的各自影响，以及自动化规则，可以在实验设置中选择其值的自动化规则，其实际设置不可用。最后，我们展示了我们对诸如医用超声图像检测应用等实际图像的方法处理实际图像的能力。

该论文通过将基于定向准分析小波包（QWP）与最新的加权核定标准最小化（WNNM）denoising算法相结合，从而提出了图像降级方案。基于QWP的Denoising方法（QWPDN）由降级图像的多尺度QWP变换，使用双变量收缩方法的适应性局部软阈值应用于转换系数，以及从几个分解级别中恢复阈值系数的图像。合并的方法由QWPDN和WNNM算法的几个迭代组成，以每种迭代的方式，从一种算法中的输出将输入提高到另一个算法。提出的方法将QWPDN的功能融合在一起，即使在严重损坏的图像中捕获边缘和精细的纹理模式，并利用了WNNM算法固有的真实图像中的非本地自相似性。多个实验将所提出的方法与包括WNNM在内的六种高级denoing算法进行了比较，证实，在定量度量和视觉感知质量方面，合并的跨增强算法比大多数都优于大多数。

In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method-the K-SVD algorithm-generalizing the K-means clustering process. K-SVD is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence. The K-SVD algorithm is flexible and can work with any pursuit method (e.g., basis pursuit, FOCUSS, or matching pursuit). We analyze this algorithm and demonstrate its results both on synthetic tests and in applications on real image data.

本文的目的是描述一种从贝叶斯推理的观点来描述一种新的非参数降噪技术，其可以自动提高一个和二维数据的信噪比，例如例如，例如，天文图像和光谱。该算法迭代地评估数据的可能的平滑版本，平滑模型，获得与嘈杂测量统计上兼容的底层信号的估计。迭代基于最后一个顺利模型的证据和$ \ Chi ^ 2 $统计数据，并且我们将信号的预期值计算为整个平滑模型的加权平均值。在本文中，我们解释了算法的数学形式主义和数值实现，我们在利用真正的天文观测的电池对峰值信号，结构相似性指数和时间有效载荷来评估其性能。我们完全自适应的贝叶斯算法用于数据分析（Fabada）产生结果，没有任何参数调谐，与标准图像处理算法相当，其参数基于要恢复的真实信号进行了优化，在实际应用中不可能。诸如BM3D的最先进的非参数方法，以高信噪比提供稍微更好的性能，而我们的算法对于极其嘈杂的数据显着更准确（高于20-40 \％$相对错误，在天文领域特别兴趣的情况）。在此范围内，通过我们的重建获得的残差的标准偏差可能变得比原始测量值低的数量级。复制本报告中显示的所有结果所需的源代码，包括该方法的实现，在https://github.com/pablolyanala/fabada公开使用

多曝光融合（MEF）是一种与将不同曝光设置获取的相同场景的不同图像组合成单个图像。所有提议的MEF算法都组合了一组图像，以某种方式从每个曝光的零件中选择。我们提出了一种新的多曝光图像融合链，考虑到噪音。该新方法利用了DCT处理和MEF问题的多像性质。我们提出了一种联合融合和去噪战略，利用时空贴片选择和协作3D阈值化。整体策略允许在不需要恢复每个去噪的曝光图像的情况下抵销和熔断图像集，导致非常有效的过程。

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which demonstrates that randomization offers a powerful tool for performing low-rank matrix approximation. These techniques exploit modern computational architectures more fully than classical methods and open the possibility of dealing with truly massive data sets.This paper presents a modular framework for constructing randomized algorithms that compute partial matrix decompositions. These methods use random sampling to identify a subspace that captures most of the action of a matrix. The input matrix is then compressed-either explicitly or implicitly-to this subspace, and the reduced matrix is manipulated deterministically to obtain the desired low-rank factorization. In many cases, this approach beats its classical competitors in terms of accuracy, speed, and robustness. These claims are supported by extensive numerical experiments and a detailed error analysis.The specific benefits of randomized techniques depend on the computational environment. Consider the model problem of finding the k dominant components of the singular value decomposition of an m × n matrix. (i) For a dense input matrix, randomized algorithms require O(mn log(k)) floating-point operations (flops) in contrast with O(mnk) for classical algorithms. (ii) For a sparse input matrix, the flop count matches classical Krylov subspace methods, but the randomized approach is more robust and can easily be reorganized to exploit multi-processor architectures. (iii) For a matrix that is too large to fit in fast memory, the randomized techniques require only a constant number of passes over the data, as opposed to O(k) passes for classical algorithms. In fact, it is sometimes possible to perform matrix approximation with a single pass over the data.

We introduce a parametric view of non-local two-step denoisers, for which BM3D is a major representative, where quadratic risk minimization is leveraged for unsupervised optimization. Within this paradigm, we propose to extend the underlying mathematical parametric formulation by iteration. This generalization can be expected to further improve the denoising performance, somehow curbed by the impracticality of repeating the second stage for all two-step denoisers. The resulting formulation involves estimating an even larger amount of parameters in a unsupervised manner which is all the more challenging. Focusing on the parameterized form of NL-Ridge, the simplest but also most efficient non-local two-step denoiser, we propose a progressive scheme to approximate the parameters minimizing the risk. In the end, the denoised images are made up of iterative linear combinations of patches. Experiments on artificially noisy images but also on real-world noisy images demonstrate that our method compares favorably with the very best unsupervised denoisers such as WNNM, outperforming the recent deep-learning-based approaches, while being much faster.

A fundamental problem in neural network research, as well as in many other disciplines, is finding a suitable representation of multivariate data, i.e. random vectors. For reasons of computational and conceptual simplicity, the representation is often sought as a linear transformation of the original data. In other words, each component of the representation is a linear combination of the original variables. Well-known linear transformation methods include principal component analysis, factor analysis, and projection pursuit. Independent component analysis (ICA) is a recently developed method in which the goal is to find a linear representation of nongaussian data so that the components are statistically independent, or as independent as possible. Such a representation seems to capture the essential structure of the data in many applications, including feature extraction and signal separation. In this paper, we present the basic theory and applications of ICA, and our recent work on the subject.

基于深度学习的方法保持最先进的导致低级图像处理任务，但由于其黑匣子结构而难以解释。展开的优化网络通过从经典迭代优化方法导出它们的架构而不使用来自标准深度学习工具盒的技巧来构建深神经网络的可解释的替代方案。到目前为止，这种方法在使用可解释结构的同时，在使用其可解释的结构的同时证明了接近最先进的模型的性能，以实现相对的低学习参数计数。在这项工作中，我们提出了一个展开的卷积字典学习网络（CDLNET），并在低和高参数计数方面展示其竞争的去噪和联合去噪和去除脱落（JDD）性能。具体而言，我们表明，当缩放到类似的参数计数时，所提出的模型优于最先进的完全卷积的去噪和JDD模型。此外，我们利用模型的可解释结构提出了网络中阈值的噪声适应性参数化，该阈值能够实现最先进的盲目的表现，以及在训练期间看不见的噪声水平的完美概括。此外，我们表明这种性能延伸到JDD任务和无监督的学习。

Objective methods for assessing perceptual image quality have traditionally attempted to quantify the visibility of errors between a distorted image and a reference image using a variety of known properties of the human visual system. Under the assumption that human visual perception is highly adapted for extracting structural information from a scene, we introduce an alternative framework for quality assessment based on the degradation of structural information. As a specific example of this concept, we develop a Structural Similarity Index and demonstrate its promise through a set of intuitive examples, as well as comparison to both subjective ratings and state-of-the-art objective methods on a database of images compressed with JPEG and JPEG2000. 1

在过去的十年中，图上的信号处理已成为一个非常活跃的研究领域。具体而言，使用从图形上构建的框架（例如图上的小波）在统计或深度学习中的应用数量显着增加。我们特别考虑通过数据驱动的小波紧密框架方法在图表上进行信号的情况。这种自适应方法基于使用Stein的无偏风险估计校准的阈值，该阈值适合于紧密框架表示。我们可以使用Chebyshev-Jackson多项式近似值将其扩展到大图，从而可以快速计算小波系数，而无需计算laplacian特征性组成。但是，紧密框架的过度本质将白噪声转化为相关的噪声。结果，转换噪声的协方差出现在确定的差异项中，因此需要计算和存储框架，从而导致大图的不切实际计算。为了估计这种协方差，我们基于零均值和单位方差随机变量的快速转换制定和分析蒙特卡洛策略。这种新的数据驱动的denoisisy方法可以在差异隐私中发现自然应用。从真实和模拟数据的大小变化图上进行了全面的性能分析。

高光谱成像为各种应用提供了新的视角，包括使用空降或卫星遥感，精密养殖，食品安全，行星勘探或天体物理学的环境监测。遗憾的是，信息的频谱分集以各种劣化来源的牺牲品，并且目前获取的缺乏准确的地面“清洁”高光谱信号使得恢复任务具有挑战性。特别是，与传统的RGB成像问题相比，培训深度神经网络用于恢复难以深入展现的传统RGB成像问题。在本文中，我们提倡基于稀疏编码原理的混合方法，其保留与手工图像前导者编码域知识的经典技术的可解释性，同时允许在没有大量数据的情况下训练模型参数。我们在各种去噪基准上展示了我们的方法是计算上高效并且显着优于现有技术。

无监督的深度学习最近证明了生产高质量样本的希望。尽管它具有促进图像着色任务的巨大潜力，但由于数据歧管和模型能力的高维度，性能受到限制。这项研究提出了一种新的方案，该方案利用小波域中的基于得分的生成模型来解决这些问题。通过利用通过小波变换来利用多尺度和多渠道表示，该模型可以共同有效地从堆叠的粗糙小波系数组件中了解较富裕的先验。该策略还降低了原始歧管的维度，并减轻了维度的诅咒，这对估计和采样有益。此外，设计了小波域中的双重一致性项，即数据一致性和结构一致性，以更好地利用着色任务。具体而言，在训练阶段，一组由小波系数组成的多通道张量被用作训练网络以denoising得分匹配的输入。在推论阶段，样品是通过具有数据和结构一致性的退火Langevin动力学迭代生成的。实验证明了所提出的方法在发电和着色质量方面的显着改善，尤其是在着色鲁棒性和多样性方面。

Tensor robust principal component analysis (TRPCA) is a promising way for low-rank tensor recovery, which minimizes the convex surrogate of tensor rank by shrinking each tensor singular values equally. However, for real-world visual data, large singular values represent more signifiant information than small singular values. In this paper, we propose a nonconvex TRPCA (N-TRPCA) model based on the tensor adjustable logarithmic norm. Unlike TRPCA, our N-TRPCA can adaptively shrink small singular values more and shrink large singular values less. In addition, TRPCA assumes that the whole data tensor is of low rank. This assumption is hardly satisfied in practice for natural visual data, restricting the capability of TRPCA to recover the edges and texture details from noisy images and videos. To this end, we integrate nonlocal self-similarity into N-TRPCA, and further develop a nonconvex and nonlocal TRPCA (NN-TRPCA) model. Specifically, similar nonlocal patches are grouped as a tensor and then each group tensor is recovered by our N-TRPCA. Since the patches in one group are highly correlated, all group tensors have strong low-rank property, leading to an improvement of recovery performance. Experimental results demonstrate that the proposed NN-TRPCA outperforms some existing TRPCA methods in visual data recovery. The demo code is available at https://github.com/qguo2010/NN-TRPCA.

我们介绍了一种确定全局特征解耦的方法，并显示其适用于提高数据分析性能的适用性，并开放了新的场所以进行功能传输。我们提出了一种新的形式主义，该形式主义是基于沿特征梯度遵循轨迹来定义对子曼群的转换的。通过这些转换，我们定义了一个归一化，我们证明，它允许解耦可区分的特征。通过将其应用于采样矩，我们获得了用于正骨的准分析溶液，正尾肌肉是峰度的归一化版本，不仅与平均值和方差相关，而且还与偏度相关。我们将此方法应用于原始数据域和过滤器库的输出中，以基于全局描述符的回归和分类问题，与使用经典（未删除）描述符相比，性能得到一致且显着的改进。

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing, along with a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas. We then summarize recent advances in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning.

胎儿心电图（FECG）首先在20世纪初从母体腹表面记录。在过去的五十年中，最先进的电子技术和信号处理算法已被用于将非侵入性胎儿心电图转化为可靠的胎儿心脏监测技术。在本章中，已经对来自非侵入性母亲腹部录像进行了建模，提取和分析的主要信号处理技术，并详细介绍了来自非侵入性母亲腹部录像的型号的建模，提取和分析。本章的主要主题包括：1）FECG的电生理学从信号处理视点，2）母体体积传导介质的数学模型和从体表的FECG的波形模型，3）信号采集要求，4）基于模型的FECG噪声和干扰取消的技术，包括自适应滤波器和半盲源分离技术，以及5）胎儿运动跟踪和在线FECG提取的最近算法的进步。

本文介绍了使用基于补丁的先前分布的图像恢复的新期望传播（EP）框架。虽然Monte Carlo技术典型地用于从难以处理的后分布中进行采样，但它们可以在诸如图像恢复之类的高维推论问题中遭受可扩展性问题。为了解决这个问题，这里使用EP来使用多元高斯密度的产品近似后分布。此外，对这些密度的协方差矩阵施加结构约束允许更大的可扩展性和分布式计算。虽然该方法自然适于处理添加剂高斯观察噪声，但它也可以扩展到非高斯噪声。用于高斯和泊松噪声的去噪，染色和去卷积问题进行的实验说明了这种柔性近似贝叶斯方法的潜在益处，以实现与采样技术相比降低的计算成本。