结构化压缩感知研究进展

Research Advances on Structured Compressive Sensing

压缩感知(Compressive sensing,CS)是一种全新的信息采集与处理的理论框架.借助信号内在的稀疏性或可压缩性,可从小规模的线性、非自适应的测量中通过非线性优化的方法重构信号.结构化压缩感知是在传统压缩感知基础上形成的新的理论框架,旨在将与数据采集硬件及复杂信号模型相匹配的先验信息引入传统压缩感知,从而实现对更广泛类型的信号准确有效的重建.本文围绕压缩感知的三个基本问题,从结构化测量方法、结构化稀疏表示和结构化信号重构三个方面对结构化压缩感知的基本模型和关键技术进行详细的阐述,综述了结构化压缩感知的最新的研究成果,指出结构化压缩感知进一步研究的方向.

Compressive sensing （CS） is a newly developed theoretical framework for information acquisition and pro- cessing. Using the non-linear optimization methods, the signals can be recovered from fewer linear and non-adaptive measurements by taking advantage of the sparsity or compressibility inherent in real world signals. Structured com- pressive sensing is a new framework which can treat more general signal classes to achieve the accurate and effective reconstruction in practice by introducing the prior information matching with data acquisition hardware and compli- cated signal models to traditional compressive sensing. In this paper, the basic models and key techniques of structured compressive sensing are introduced in terms of the structured measurements, the structured dictionary representation and the structured signal reconstruction, which correspond to three basic aspects of compressive sensing, and the recent developments of structured compressive sensing are reviewed in detail. Finally, the current and future challenges of the structured compressive sensing are discussed.