摘要翻译：
宽带频谱的有效估计对于认知无线电等应用具有重要意义。近年来，基于压缩感知的亚奈奎斯特采样方案被提出，以大大降低采样率。然而，量子化的重要问题还没有得到充分的解决，特别是对于高分辨率谱和参数估计。在本文中，我们的目标是从其噪声复值随机线性测量的重量化中恢复频谱稀疏信号及其相应的参数，如频率和振幅，例如仅象限信息。我们首先刻画了高斯噪声下的Cramer-Rao界，它突出了在固定比特预算下，不同信噪比下样本复杂度和比特深度之间的权衡。其次，我们提出了一种新的基于原子范数软阈值的信号恢复算法，该算法等效于适当设计的替代信号相对于激发谱稀疏性的原子范数的近端映射。该算法既适用于单测量向量的情况，也适用于多测量向量的情况。结果表明，在高斯测量模型下，当量化测量次数超过K log n阶时，谱信号就能以较高的概率精确重建。K为谱稀疏程度，$n$为信号维数。最后，通过数值仿真验证了所提出的方法。
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英文标题：
《Quantized Spectral Compressed Sensing: Cramer-Rao Bounds and Recovery
  Algorithms》
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作者：
Haoyu Fu and Yuejie Chi
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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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一级分类：Computer Science        计算机科学
二级分类：Information Theory        信息论
分类描述：Covers theoretical and experimental aspects of information theory and coding. Includes material in ACM Subject Class E.4 and intersects with H.1.1.
涵盖信息论和编码的理论和实验方面。包括ACM学科类E.4中的材料，并与H.1.1有交集。
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一级分类：Mathematics        数学
二级分类：Information Theory        信息论
分类描述：math.IT is an alias for cs.IT. Covers theoretical and experimental aspects of information theory and coding.
它是cs.it的别名。涵盖信息论和编码的理论和实验方面。
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英文摘要：
  Efficient estimation of wideband spectrum is of great importance for applications such as cognitive radio. Recently, sub-Nyquist sampling schemes based on compressed sensing have been proposed to greatly reduce the sampling rate. However, the important issue of quantization has not been fully addressed, particularly for high-resolution spectrum and parameter estimation. In this paper, we aim to recover spectrally-sparse signals and the corresponding parameters, such as frequency and amplitudes, from heavy quantizations of their noisy complex-valued random linear measurements, e.g. only the quadrant information. We first characterize the Cramer-Rao bound under Gaussian noise, which highlights the trade-off between sample complexity and bit depth under different signal-to-noise ratios for a fixed budget of bits. Next, we propose a new algorithm based on atomic norm soft thresholding for signal recovery, which is equivalent to proximal mapping of properly designed surrogate signals with respect to the atomic norm that motivates spectral sparsity. The proposed algorithm can be applied to both the single measurement vector case, as well as the multiple measurement vector case. It is shown that under the Gaussian measurement model, the spectral signals can be reconstructed accurately with high probability, as soon as the number of quantized measurements exceeds the order of K log n, where K is the level of spectral sparsity and $n$ is the signal dimension. Finally, numerical simulations are provided to validate the proposed approaches.
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PDF链接：
https://arxiv.org/pdf/1710.03654