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在这个简短的论述中,我们提供一些基于这一新理论的关键性数学见解,并解释了一些压缩采样和其他领域,如统计学、信息论、编码理论以及理论性的计算机科学之间的交互。-In this short survey, we provide some of the key mathematical insights underlying this new theory, and explain some of the interactions between compressive sampling and other fields such as statistics, information theory, coding theory, and theoretical computer science.
Date : 2025-12-30 Size : 110kb User : tianjingyu

经典的香农采样定理认为,为了不失真地恢复模拟信号,采样频率应该不小于奈奎斯特频率(即模拟信号 频谱中的最高频率)的两倍.但是其中除了利用到信号是有限带宽的假设外,没利用任何的其它先验信息.采集到 的数据存在很大程度的冗余.Donoho等人提出的压缩感知方法(Compressed Sensing或Compressive Sampling, CS)充分运用了大部分信号在预知的一组基上可以稀疏表示这一先验信息,利用随机投影实现了在远低于奈奎斯 特频率的采样频率下对压缩数据的直接采集.该方法不仅为降低采样频率提供了一种新思路,也为其它科学领域 的研究提供了新的契机.该文综述性地阐述了压缩感知方法的基本原理,给出了其中的一些约束问题和估计方法, 并介绍压缩感知理论的相关问题———矩阵填充,最后讨论了其未来可能的应用前景. -According to the conventional Shannon s sampling theorem,in order to represent the analog signal,the sampling rate should not be less than twice the Nyquist sampling rate.Howev- er,this theorem only makes use of the bandwidth information.As a result,the collected data contain many redundant information.The recently proposed sampling method,compressed sens- ing or compressive sampling(CS),can collect compressed data at the sampling rate much lower than that needed in Shannon s sampling theorem by exploring the compressibility of the signal. This paper presents a review on the basic theory of CS.Some of the restrictions and recovery methods in CS are also discussed.Finally,some potential applications based on CS are presented.
Date : 2025-12-30 Size : 287kb User : 德隆

compressive sensing using OMP
Date : 2025-12-30 Size : 406kb User : haba star

详细介绍压缩采样技术的原理和帮助学习压缩采样新技术-Details compressive sampling techniques and principles to help learn new techniques compressed samples
Date : 2025-12-30 Size : 255kb User : 陈钦
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