摘要翻译：
本文提出了一种有效的无网格{2-D}线谱估计优化技术--解耦原子范数最小化（D-ANM）。考虑了原子范数最小化(ANM)框架，该框架已成功地应用于一维问题，即使快照数非常有限，也允许对相关源进行超分辨频率估计。目前最先进的二维ANM方法将二维测量值矢量化为一维等效值，这导致了巨大的计算成本，对于实际应用来说可能会变得过于昂贵。通过半定规划(SDP)提出了一种新的二维ANM解耦方法，该方法引入了一个新的矩阵形式的原子集，在不损失最优性的情况下自然地解耦两维联合观测。因此，通过两个解耦的一层Toeplitz矩阵将原来的大规模二维问题等价地重新表述，并通过简单的一维频率估计和配对求解。与传统的矢量化方法相比，所提出的D-ANM技术将计算复杂度降低了几个数量级。它还保留了ANM在精确信号恢复、所需测量数量少和对源相关的鲁棒性方面的优点。对于大规模天线系统如massive MIMO、雷达信号处理和射电天文学来说，复杂性的好处尤其具有吸引力。
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英文标题：
《Efficient Two-Dimensional Line Spectrum Estimation Based on Decoupled
  Atomic Norm Minimization》
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作者：
Zhe Zhang, Yue Wang, Zhi Tian
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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：
  This paper presents an efficient optimization technique for gridless {2-D} line spectrum estimation, named decoupled atomic norm minimization (D-ANM). The framework of atomic norm minimization (ANM) is considered, which has been successfully applied in 1-D problems to allow super-resolution frequency estimation for correlated sources even when the number of snapshots is highly limited. The state-of-the-art 2-D ANM approach vectorizes the 2-D measurements to their 1-D equivalence, which incurs huge computational cost and may become too costly for practical applications. We develop a novel decoupled approach of 2-D ANM via semi-definite programming (SDP), which introduces a new matrix-form atom set to naturally decouple the joint observations in both dimensions without loss of optimality. Accordingly, the original large-scale 2-D problem is equivalently reformulated via two decoupled one-level Toeplitz matrices, which can be solved by simple 1-D frequency estimation with pairing. Compared with the conventional vectorized approach, the proposed D-ANM technique reduces the computational complexity by several orders of magnitude with respect to the problem size. It also retains the benefits of ANM in terms of precise signal recovery, small number of required measurements, and robustness to source correlation. The complexity benefits are particularly attractive for large-scale antenna systems such as massive MIMO, radar signal processing and radio astronomy.
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PDF链接：
https://arxiv.org/pdf/1808.01019