一种压缩感知词典快速构造方法

摘要

This paper presents a measurement and sensing dictionary construction algorithm in compressive sensing based on the alternating projection method.Gram-like matrix of measurement and sensing dictionaries is projected on the set of ideal Gram matrix,then the obtained matrix is projected on the set of Gram-like matrix.This procedure is repeated until the termination condition is met and a pair of measurement and sensing dictionaries will be obtained.The off diagonal entries of the Gram-like matrix reach or approach the Welch bound.The algorithm in this paper involves a novel method to project a matrix on the set of Gram-like matrix,which can reduce the computation amount.This algorithm improves the performance of greedy algorithm such as OMP.%提出一种基于交互投影方法的量测词典和感知词典构造算法.将量测词典和感知词典的类Gram矩阵向理想Gram矩阵集合投影并得到投影矩阵,再将此矩阵向类Gram矩阵集合投影,此过程如此继续直至满足终止条件,可得到一对弱相关量测和感知词典,其类Gram矩阵非主对角线元素接近或者达到Welch界.该算法采用一种新的向类Gram矩阵投影方法,可以极大地降低计算量,此算法得到的词典可有效提高OMP算法性能.