摘要翻译：
本文研究了压缩感知(CS)中测量矩阵的确定性构造问题。首先，利用列替换的概念，给出了包含全一码字的大最小距离线性码的构造定理。然后，应用线性码上的一个已有定理，构造了确定性感知矩阵。为了评价这个过程，给出了两个构造传感矩阵的例子。第一个示例包含大小为${{p}^{2}}\乘以{{p}^{3}}$和一致性${1}/{p}\；$的矩阵，第二个示例包含大小为$p\left(p-1\right)\乘以{{p}^{3}}$和一致性${1}/{\left(p-1\right)}\；$的矩阵，其中$p$为素数。基于Welch界，两个算例都渐近达到最优结果。此外，通过提出一个新的定理，利用列替换将任意传感矩阵的大小调整为更大尺寸的传感矩阵，并计算了其相干性。然后，通过一个算例，将所提方法的性能与已知方法进行了比较。仿真结果表明，无论是在已创建的传感矩阵中还是在已调整的传感矩阵中，列替换方法都具有令人满意的性能。
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英文标题：
《A General Approach for Construction of Deterministic Compressive Sensing
  Matrices》
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作者：
MohamadMahdi Mohades, Mohamad Hossein Kahaei
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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：
  In this paper, deterministic construction of measurement matrices in Compressive Sensing (CS) is considered. First, by employing the column replacement concept, a theorem for construction of large minimum distance linear codes containing all-one codewords is proposed. Then, by applying an existing theorem over these linear codes, deterministic sensing matrices are constructed. To evaluate this procedure, two examples of constructed sensing matrices are presented. The first example contains a matrix of size ${{p}^{2}}\times {{p}^{3}}$ and coherence ${1}/{p}\;$, and the second one comprises a matrix with the size $p\left( p-1 \right)\times {{p}^{3}}$ and coherence ${1}/{\left( p-1 \right)}\;$, where $p$ is a prime integer. Based on the Welch bound, both examples asymptotically achieve optimal results. Moreover, by presenting a new theorem, the column replacement is used for resizing any sensing matrix to a greater-size sensing matrix whose coherence is calculated. Then, using an example, the outperformance of the proposed method is compared to a well-known method. Simulation results show the satisfying performance of the column replacement method either in created or resized sensing matrices.
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PDF链接：
https://arxiv.org/pdf/1802.01358