摘要翻译：
大多数有理系统可以用正交基函数来描述。本文考虑了在一对正交有理函数基下，由有限个线性频域测量值重构有理传递函数的稀疏系数向量。证明了无穷维函数空间中正交有理函数的可压缩表示对的不确定原理。利用这类对的可压缩表示的唯一性是测不准原理的直接结果。并给出了保证在单位圆上用随机抽样的1_1优化以大概率搜索唯一稀疏重构代替1_0优化的测量个数界。
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英文标题：
《Uncertainty Principle and Sparse Reconstruction in Pairs of Orthonormal
  Rational Function Bases》
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作者：
Dan Xiong, Li Chai, Jingxin Zhang
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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：
  Most rational systems can be described in terms of orthonormal basis functions. This paper considers the reconstruction of a sparse coefficient vector for a rational transfer function under a pair of orthonormal rational function bases and from a limited number of linear frequency-domain measurements. We prove the uncertainty principle concerning pairs of compressible representation of orthonormal rational functions in the infinite dimensional function space. The uniqueness of compressible representation using such pairs is provided as a direct consequence of uncertainty principle. The bound of the number of measurements which guarantees the replacement of 1_0 optimization searching for the unique sparse reconstruction by 1_1 optimization using random sampling on the unit circle with high probability is provided as well.
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PDF链接：
https://arxiv.org/pdf/1712.02981