摘要翻译：
提出了一种新的自适应分层感知算法K-AHS，该算法对稀疏或可压缩信号进行采样，其测量复杂度与压缩感知(CS)相当。与CS相比，K-AHS是自适应的，因为在采样时选择传感矢量，取决于以前的测量结果。在采样之前，用户选择感兴趣信号稀疏的变换域。相应的变换决定了传感向量的集合。K-AHS在稀疏变换域中基于感知树逐步细化初始粗略测量到重要的信号系数，感知树提供了感知向量的自然层次结构。K-AHS直接在稀疏变换域提供重要的信号系数，不需要基于逆优化的重建阶段。因此，K-AHS传感矢量不能满足任何非相干性或受限等距性。通过数学分析证明了K-AHS的采样复杂度，并给出了适用于特定信号模型的最优K项近似采样的一般充分条件。分析结果得到了合成信号和真实世界图像的模拟支持。在标准基准图像上，K-AHS实现了比CS更低的重建误差。
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英文标题：
《Adaptive Hierarchical Sensing for the Efficient Sampling of Sparse and
  Compressible Signals》
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作者：
Henry Sch\"utze, Erhardt Barth, Thomas Martinetz
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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：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：
  We present the novel adaptive hierarchical sensing algorithm K-AHS, which samples sparse or compressible signals with a measurement complexity equal to that of Compressed Sensing (CS). In contrast to CS, K-AHS is adaptive as sensing vectors are selected while sampling, depending on previous measurements. Prior to sampling, the user chooses a transform domain in which the signal of interest is sparse. The corresponding transform determines the collection of sensing vectors. K-AHS gradually refines initial coarse measurements to significant signal coefficients in the sparse transform domain based on a sensing tree which provides a natural hierarchy of sensing vectors. K-AHS directly provides significant signal coefficients in the sparse transform domain and does not require a reconstruction stage based on inverse optimization. Therefore, the K-AHS sensing vectors must not satisfy any incoherence or restricted isometry property. A mathematical analysis proves the sampling complexity of K-AHS as well as a general and sufficient condition for sampling the optimal k-term approximation, which is applied to particular signal models. The analytical findings are supported by simulations with synthetic signals and real world images. On standard benchmark images, K-AHS achieves lower reconstruction errors than CS.
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PDF链接：
https://arxiv.org/pdf/1807.05371