采样方法研究综述

Survey of Sampling Methods

Nyquist-Shannon采样定理从提出至今已经过了近70年的发展历程,为模拟世界到数字世界的转变作出了巨大贡献。在这70年的进程中,围绕如何在不丢失信号中有用信息的前提下,降低采样速率和减少采集数据量的主题、新的采样理论和采样方法也不断涌现。本文在总结和回顾现有采样技术原理和框架的基础上,结合个人见解对单通道随机采样、压缩传感采样、有限新息率采样及X-采样等稀疏采样方法的特点、适用场合、最新进展和公开问题及难点进行了评价,并对稀疏采样发展前景予以展望,并为采样技术改进和拓展等应用领域提供参考。

Nyquist-Shannon sampling theorem was presented about 70 years ago, which contributed a lot to the transform from analog mode to digital one. In the process of 70 years development, focusing on how to reduce the sampling rate and amount of data without information loss, many novel sampling theo- ries are proposed and developed, including random sampling, compressive sensing based sampling, finite rate of innovation sampling and Xampling. Based on the overview of the present sparse sampling theories and frameworks, the features and application fields are summarized, the latest developments are intro- duced, several open problems are reviewed and the existing difficulties of these new sampling methods with personal opinions are discussed. Finally, the prospect of sparse sampling technology is drafted to provide a refer for improving the sampling technology and expanding the application fields.