摘要翻译：
本文提出了一种图信号处理算法，用于揭示高维、图光滑、严重损坏的数据集的内在低秩分量和底层图。在我们的问题表述中，我们假设低阶分量上的扰动是稀疏的，信号在图上是光滑的。我们提出了一种利用图估计低秩分量的算法，并用较好的估计低秩分量对图进行精化。我们提出将低秩估计和图精化联合进行，这样低秩估计可以从精化的图中受益，图精化可以利用改进的低秩估计。我们建议用交替优化来解决这个问题。此外，我们进行了数学分析，以理解和量化不精确图对低秩估计的影响，证明了我们的方案与图精化作为估计低秩分量的一个集成步骤。我们对所提出的算法进行了大量的实验，并与目前最先进的低秩估计和图学习技术进行了比较。我们的实验使用合成数据和真实的大脑成像(MEG)数据，这些数据是在受试者被呈现不同类别的视觉刺激时记录的。我们观察到，我们提出的算法在估计低阶分量方面具有竞争力，在降维表示中充分捕获了任务相关的内在信息，从而在分类任务中获得了更好的性能。此外，我们注意到，我们的估计图表明，作为神经科学的发现，视觉活动兼容的大脑活跃区域。
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英文标题：
《Joint Estimation of Low-Rank Components and Connectivity Graph in
  High-Dimensional Graph Signals: Application to Brain Imaging》
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作者：
Rui Liu, Hossein Nejati, Ngai-Man Cheung
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最新提交年份：
2018
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分类信息：

一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Image and Video Processing        图像和视频处理
分类描述：Theory, algorithms, and architectures for the formation, capture, processing, communication, analysis, and display of images, video, and multidimensional signals in a wide variety of applications. Topics of interest include: mathematical, statistical, and perceptual image and video modeling and representation; linear and nonlinear filtering, de-blurring, enhancement, restoration, and reconstruction from degraded, low-resolution or tomographic data; lossless and lossy compression and coding; segmentation, alignment, and recognition; image rendering, visualization, and printing; computational imaging, including ultrasound, tomographic and magnetic resonance imaging; and image and video analysis, synthesis, storage, search and retrieval.
用于图像、视频和多维信号的形成、捕获、处理、通信、分析和显示的理论、算法和体系结构。感兴趣的主题包括：数学，统计，和感知图像和视频建模和表示；线性和非线性滤波、去模糊、增强、恢复和重建退化、低分辨率或层析数据；无损和有损压缩编码；分割、对齐和识别；图像渲染、可视化和打印；计算成像，包括超声、断层和磁共振成像；以及图像和视频的分析、合成、存储、搜索和检索。
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一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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英文摘要：
  This paper presents a graph signal processing algorithm to uncover the intrinsic low-rank components and the underlying graph of a high-dimensional, graph-smooth and grossly-corrupted dataset. In our problem formulation, we assume that the perturbation on the low-rank components is sparse and the signal is smooth on the graph. We propose an algorithm to estimate the low-rank components with the help of the graph and refine the graph with better estimated low-rank components. We propose to perform the low-rank estimation and graph refinement jointly so that low-rank estimation can benefit from the refined graph, and graph refinement can leverage the improved low-rank estimation. We propose to address the problem with an alternating optimization. Moreover, we perform a mathematical analysis to understand and quantify the impact of the inexact graph on the low-rank estimation, justifying our scheme with graph refinement as an integrated step in estimating low-rank components. We perform extensive experiments on the proposed algorithm and compare with state-of-the-art low-rank estimation and graph learning techniques. Our experiments use synthetic data and real brain imaging (MEG) data that is recorded when subjects are presented with different categories of visual stimuli. We observe that our proposed algorithm is competitive in estimating the low-rank components, adequately capturing the intrinsic task-related information in the reduced dimensional representation, and leading to better performance in a classification task. Furthermore, we notice that our estimated graph indicates compatible brain active regions for visual activity as neuroscientific findings.
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PDF链接：
https://arxiv.org/pdf/1801.02303