动态压缩感知理论研究综述

Review of theoretical research on dynamic compressive sensing

动态压缩感知是静态传统压缩感知向动态信号的拓展,广泛应用于医学上的磁感应成像和目标追踪等领域。由于工程中的动态信号在某一转换基下具有随时间缓慢变化的稀疏特性,因而可以运用欠定的测量矩阵对其进行压缩。动态压缩感知理论主要包括动态信号的稀疏表示、动态压缩测量过程和动态信号的重构3个方面的研究内容。全面综述动态压缩感知的基本概念,归纳总结现有动态压缩感知理论中对动态信号的建模方法;对已有的动态信号重构算法进行了归类,并详述了各类算法的计算思路;最后介绍了动态压缩感知的典型应用,并对动态压缩感知信号重构算法的研究前景进行了探讨。

Dynamic compressive sensing is an extension of traditional static compressive sensing to dynamic signals,which has a wide application in MRI,video compressive sensing and target tracking.Since dynamic signals are usually sparse in some transformed matrices and change slowly with time varying,an underdetermined measurement matrix can be used to compress the signals.The research of dynamic compressive sensing mainly focuses on three parts:Sparse representation of dynamic signals,dynamic compressive measurement,and reconstruction of dynamic signals.A comprehensive survey about dynamic compressive sensing is given in this article.At first,the basic concept of dynamic compressed sensing is introduced,which includes several mathematic models of dynamic signals,sparse dictionary learning algorithms and methods of adaptive measurement.Secondly,we classify the reconstruction algorithms into two main parts:Least square based algorithms and Bayesian algorithms,and we also introduce some representative algorithms in detail from each part.Finally,several applications of dynamic compressed sensing are introduced,and we provide a reference for further investigation on reconstruction algorithms.