Nearly Sharp Restricted Isometry Condition of Rank Aware Order Recursive Matching Pursuit

摘要

In this paper, we analyze the performance guarantee of the rank aware order recursive matching pursuit (RA-ORMP) algorithm in recovering a group of jointly sparse vectors. Specifically, we show that RA-ORMP accurately reconstructs any group of l linearly independent jointly K-sparse vectors, provided that a sampling matrix satisfies the restricted isometry property (RIP) of order K + 1 withegin{equation*}{delta _{K + 1}} < rac{{sqrt l }}{{sqrt {K + rac{l}{4}} + sqrt {rac{l}{4}} }}.end{equation*}Furthermore, we show the near-optimality of the proposed guarantee by providing a group of l jointly K-sparse vectors that cannot be recovered by RA-ORMP underegin{equation*}{delta _{K + 1}} geq sqrt {rac{l}{K}} .end{equation*}