不同条件下非相干帧的构造算法 设计约束

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摘要翻译：
单位范数有限帧是正交基的推广，在信号处理中有许多应用。一个框架的一个重要性质是它的相干性，这是一个度量框架的任意两个向量彼此接近的度量。低相干帧在压缩感知应用中很有用。当用作度量矩阵时，它们成功地恢复了线性反问题的高度稀疏解。本文描述了各种低相干帧类型的设计算法：实数、复数、单数（常数）复数、稀疏实数复数、非负实数复数和谐波（从傅里叶矩阵中选择行）。所提出的方法是基于解决一系列的凸优化问题，这些问题更新帧的每个向量。该更新降低了与其他帧向量的一致性，同时也对其条目施加了其他约束。数值实验表明，与Welch界以及其他竞争算法相比，该方法在压缩感知应用中的有效性。
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英文标题：
《Algorithms for the Construction of Incoherent Frames Under Various
  Design Constraints》
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作者：
Cristian Rusu, Nuria Gonzalez-Prelcic, Robert W. Heath Jr
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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：
  Unit norm finite frames are generalizations of orthonormal bases with many applications in signal processing. An important property of a frame is its coherence, a measure of how close any two vectors of the frame are to each other. Low coherence frames are useful in compressed sensing applications. When used as measurement matrices, they successfully recover highly sparse solutions to linear inverse problems. This paper describes algorithms for the design of various low coherence frame types: real, complex, unital (constant magnitude) complex, sparse real and complex, nonnegative real and complex, and harmonic (selection of rows from Fourier matrices). The proposed methods are based on solving a sequence of convex optimization problems that update each vector of the frame. This update reduces the coherence with the other frame vectors, while other constraints on its entries are also imposed. Numerical experiments show the effectiveness of the methods compared to the Welch bound, as well as other competing algorithms, in compressed sensing applications.
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PDF链接：
https://arxiv.org/pdf/1801.09678

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关键词：Applications Optimization Experimental Successfully Construction frame 感知 正交 实数 each