摘要翻译：
本文利用$L1$-分析方法，讨论了在信号相对于紧框架$D$近似稀疏的情况下信号的恢复问题。我们建立了关于$d$-限制等距性质的几个新的充分条件，以确保关于$d$-近似稀疏的信号的稳定重建。结果表明，如果测量矩阵$\phi$满足条件$\delta_{ts}<t/(4-t)$对于$0<t<4/3$,则可以用$L1$-分析方法稳定地恢复相对于$D$近似稀疏的信号。在$d=i$的情况下，界是尖锐的，参见蔡和张的工作\cite{蔡和张2014}。当$t=1$时，当前界将Lin等人的reuslt的条件$\delta_s<0.307$改进为$\delta_s<1/3$。
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英文标题：
《New sufficient conditions of signal recovery with tight frames via
  $l_1$-analysis》
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作者：
Jianwen Huang, Jianjun Wang, Feng Zhang, Wendong Wang
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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：
  The paper discusses the recovery of signals in the case that signals are nearly sparse with respect to a tight frame $D$ by means of the $l_1$-analysis approach. We establish several new sufficient conditions regarding the $D$-restricted isometry property to ensure stable reconstruction of signals that are approximately sparse with respect to $D$. It is shown that if the measurement matrix $\Phi$ fulfils the condition $\delta_{ts}<t/(4-t)$ for $0<t<4/3$, then signals which are approximately sparse with respect to $D$ can be stably recovered by the $l_1$-analysis method. In the case of $D=I$, the bound is sharp, see Cai and Zhang's work \cite{Cai and Zhang 2014}. When $t=1$, the present bound improves the condition $\delta_s<0.307$ from Lin et al.'s reuslt to $\delta_s<1/3$.
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PDF链接：
https://arxiv.org/pdf/1710.11124