摘要
压缩感知(Compressed Sensing:CS)技术是信号处理领域中数据获取和重构的新方法,其在理论上保证了只要源信号在时域或某种变换域中具有稀疏性,可以以远低于Shannon/Nyquist采样定理的采样率对信号进行采样而不至于引起信息丢失,同时,还可以以高概率重构源信号。CS现有算法大都从单重测量信号中恢复稀疏信号源,即为单重测量向量(SMV)模型。而在实际应用中,存在大量的多重测量向量情形,从多重测量向量中恢复未知的具有相同稀疏结构的联合稀疏信号源的模型称为CS的多重测量向量(MMV)模型。本文首先对CS-SMV和CS-MMV模型的基本数学原理进行了详细介绍,讨论了两种情况下稀疏源信号恢复的存在性与唯一性,然后在此基础上重点对近年来出现的各种联合稀疏信号的恢复算法进行了综述,分析了各种算法的性能,较全面的讨论了MMV模型的应用前景。最后对CS-MMV模型的发展趋势进行了总结和展望。
In the basic Compressed sensing（CS）,the unknown sparse signal is recovered from a single measurement vector,this is referred to as a single measurement vector（SMV） model.But in many applications,we should recover the joint sparse source signals from a set of measurement vectors.This is called the multiple measurement vectors（MMV） problem of CS,which addresses the recovery of a set of sparse signal vectors that share common non-zero support.This paper begins with the basic mathematic model of SMV and MMV in detail,followed by the existences and uniqueness conditions of the solution to the SMV and MMV.Then,the algorithms treating MMV model are overviewed and analyzed in detail,which are divided into three classes： convex method,greedy method and Bayesian method.These algorithms mathematics frameworks and performances are especially analyzed.At last,the existing problems that need further research are pointed out and some current challenges and future trends are summed up and predicted.
出处
《信号处理》
CSCD
北大核心
2012年第6期785-792,共8页
Journal of Signal Processing
基金
国家自然科学基金(61001213)
国防基础预研基金(B1420110193)资助课题
关键词
压缩感知
稀疏表示
单重测量向量
多重测量向量
匹配追踪
贪婪算法
Compressed Sensing（CS）
Sparse Representation
Single Measurement Vector（SMV）
Multiple Measurement Vectors（MMV）
Matching Pursuit（MP）
Greedy Algorithm
