基于OMMP算法的多测量向量问题的重构  

Reconstruction of MMV problem based on OMMP algorithm

作　　者：冯晓艳 王金平 FENG Xiaoyan;WANG Jinping(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《宁波大学学报（理工版）》2024年第1期43-50,共8页Journal of Ningbo University：Natural Science and Engineering Edition

基　　金：国家自然科学基金(62071262)。

摘　　要：正交多匹配追踪算法(OMMP算法)是正交匹配追踪算法(OMP算法)的一种拓展,近年来受到很多相关研究人员的关注.不同于OMP算法,OMMP算法在每次迭代中识别多个指标.本文分析了在限制等距性(RIP)和多向量信噪比(MSNR)条件下,用于解决多测量向量问题的OMMP算法的鲁棒性.此外,在给出的限制等距常数(RIC)的条件下,用归纳假设的方法证明了当V=0以及整数N满足1≤N≤(m-1)/K时,OMMP算法可以准确恢复K-行稀疏矩阵X.As an extension of OMP,orthogonal multi-matching pursuit(OMMP)has received much attention in recent years.Unlike the OMP,OMMP algorithm identifies N≥1indexes per iteration.In this paper,the robustness of the OMMP for multiple measurement vector(MMV)problem under the restricted isometry property(RIP)and multi-signal-to-noise ratio(MSNR),which will be mentioned in introduction,is presented.Furthermore,the induction hypothesis is used to show that the OMMP algorithm can exactly recover K-row sparse matrix in K iterations under the RIP condition presented when=V=0 and integer N with 1≤N≤(m-1)/K.

关 键 词：压缩感知 正交多匹配追踪 限制等距性 多测量向量 

分 类 号：O177.92[理学—数学] O29[理学—基础数学]