Analysis of the Orthogonal Matching Pursuit Algorithm with Prior Information

摘要

Compressed sensing uses a small amount of compressed data to represent high dimensional data, where the reconstruction algorithm is one of the main research topics. Among various algorithms, orthogonal matching pursuit (OMP) recovers the original signals in a greedy manner. Recently, the performance bound of OMP algorithm has been widely investigated. In this paper, we study OMP algorithm in the scenario that the decoder has the support probability vector, which can be used as prior information for recovery. We develop the relationship between the restricted isometry property (RIP) constant and prior information. Based on the RIP results, some special cases that are further discussed to provide a deeper understanding of the relationship. The derived results show that the effective prior information is useful for relaxing the performance bound of the RIP isometry .