改进的压缩感知测量矩阵优化方法

压缩感知理论中，测量矩阵优化是一类通过减小测量矩阵与稀疏字典的互相关性来改善测量矩阵性能的方法。本文提出一种能够同时降低整体相关系数和最大值相关系数的测量矩阵优化算法，该算法分为两步:一是通过平均化Gram矩阵特征值来降低测量矩阵的整体相关系数；二是利用阈值函数收缩Gram矩阵非对角线上较大值。两个步骤交替执行，直到解出符合优化要求的测量矩阵。该算法在保证整体相关系数降到最低的同时，又使最大值相关系数显著降低。实验结果表明，与现有算法进行对比，本文方法在降低相关系数和重构成功率上都有一定优势。 

Improved optimization algorithm for measurement matrix in compressed sensing

In compressed sensing theory, the measurement matrix optimization is a kind of approach of improving performance by decreasing the mutual coherence between the measurement matrix and sparse dictionary. This paper presents a measurement matrix optimization algorithm, which can decrease the global coherent coefficient and the maximum coherent coefficient at the same time. This algorithm is divided into two steps. First, average the eigenvalues of the Gram matrix to decrease the global coherent coefficient. Second, use threshold function to shrink the off-diagonal elements of the Gram matrix. Two steps are alternately performed until the measurement matrix which meets the requirement of the optimal solution is worked out. This algorithm ensures that the global coherent coefficient is reduced to the minimum while the maximum coherent coefficient is significant reduced. Experimental results show that this proposed algorithm is better than the existing algorithms in deceasing coherent coefficient and the success rate of reconstruction.