中文摘要：

为了优化高斯矩阵,对部分哈达玛矩阵与高斯矩阵的统计学参数作了对比分析,确定了导致部分哈达玛矩阵信号重构能力好的主要因素,并提出了高斯矩阵优化算法。验证了优化算法对不同规模高斯矩阵的通用性和有效性,确定了优化矩阵对各种稀疏信号重构算法的适用性。最后对优化矩阵的性能作了初步的理论和实验分析,优化矩阵的信号重构能力可达到、甚至超过哈达玛矩阵。研究成果为测量矩阵的分析、设计和优化提供了新的思路和方法。

英文摘要：

This paper compared and analyzed statistical parameters of partial Hadamard matrices and Gauss matrices in order to optimize Gauss matrices. It determined the main influencing factors that led to partial Hadamard matrices’ excellent behavior. Moreover,this paper proposed the optimization algorithm of Gauss matrices. It verified the validation and generality of optimization algorithm by Gauss matrices of different size,and determined optimal matrices’ applicability to different sparse signal reconstruction algorithms. At last,it conducted preliminary theory experiment analysis of optimal matrices’ performance. Optimal matrices were as much as partial Hadamard matrices more in the signal recovery ability. The research results provide a new idea and method for the analysis,design and optimization of measurement matrices.