摘要翻译：
带限图信号是定义在图上的平滑变化信号，从部分噪声测量中重建或估计带限图信号是一个特别有趣的问题。然而，选择一个最优的节点子集进行采样是NP困难的。如果我们允许在一个节点上进行多个测量，我们将这个问题公式化为一个线性回归模型的实验设计。通过将其松弛为一个凸优化问题，在给定总样本容量预算的情况下，得到了每个节点的样本比例。然后，我们使用一个概率量化来得到每个待采样节点的数目。此外，通过摄动分析，我们分析了样本大小对目标函数是否定义良好的影响。最后，我们通过各种数值实验证明了所提方法的性能。
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英文标题：
《Design of Sampling Set for Bandlimited Graph Signal Estimation》
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作者：
Xuan Xie, Hui Feng, Junlian Jia, Bo Hu
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最新提交年份：
2017
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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：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：
  It is of particular interest to reconstruct or estimate bandlimited graph signals, which are smoothly varying signals defined over graphs, from partial noisy measurements. However, choosing an optimal subset of nodes to sample is NP-hard. We formularize the problem as the experimental design of a linear regression model if we allow multiple measurements on a single node. By relaxing it to a convex optimization problem, we get the proportion of sample for each node given the budget of total sample size. Then, we use a probabilistic quantization to get the number of each node to be sampled. Moreover, we analyze how the sample size influences whether our object function is well-defined by perturbation analysis. Finally, we demonstrate the performance of the proposed approach through various numerical experiments.
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PDF链接：
https://arxiv.org/pdf/1711.07345