动态压缩感知综述

A Survey on Dynamic Compressed Sensing

动态压缩感(Dynamic compressed sensing,DCS)知由视频信号处理问题引出,是压缩感知(Compressed sensing,CS)理论研究领域中新兴起的一个研究分支,旨在处理信号支撑集随时间发生变化的时变稀疏信号,较为成功的应用范例是动态核磁共振成像.本文首先介绍动态系统模型,给出时变稀疏信号支撑集缓慢变化的定义、时变稀疏信号的稀疏表示和感知测量的方法;其次,建立一个统一的时变稀疏信号重构模型,基于该模型对现有算法进行分类,简要综述时变稀疏信号的重构算法,并且对比分析算法的性能;最后,讨论动态压缩感知的应用,并对其研究前景进行展望.

In video signal processing, dynamic compressed sensing（DCS） is a novel branch of compressed sensing（CS）theory for recovery of compressible, possibly with a slowly varying sparsity pattern, signal from a time sequence of noisy observations. Dynamic compressed sensing has been employed in dynamic magnetic resonance image reconstruction successfully. The system model for dynamic compressed sensing is first introduced, including definitions of slowly varying supports, sparse representations and stable measurement of the time-varying sparse signal. Then, a unified framework is formulated for reconstruction of the time-varying sparse signal. Based on the framework, classification is conducted for the existing algorithms whose main ideas, reconstruction procedures and performance are also commented briefly. Finally,the applications and future directions of dynamic compressed sensing are pointed out.