中文摘要：

针对压缩感知中观测矩阵优化问题,在分析观测矩阵列向量间的独立性、观测矩阵与稀疏基间的相关性对重构信号质量影响的基础上,采用QR分解增强观测矩阵列向量的独立性,将QR分解与基于梯度投影的Gram观测矩阵优化算法相结合,提出了改进的基于梯度投影的Gram矩阵优化算法.该算法采用等角紧框架逼近Welch界,减小观测矩阵和稀疏基的相关性;采用梯度投影方法求解观测矩阵;再对观测矩阵进行QR分解,增大观测矩阵列向量之间的独立性.仿真实验表明：与基于梯度投影的Gram矩阵优化算法比较,本算法提高了重构信号的质量.

英文摘要：

To solve the optimization problem of measurement matrix in the compressed sensing,the independence of measurement matrix columns and the coherence between rows of the measurement matrix and columns of sparse basis were analyzed to find out whether they can influence the quality of the reconstruction,so the QRdecomposition was used to enhance the independence of measurement matrix column.By combining the QRdecomposition with the Gram measurement matrix based on gradient projection,an improved algorithm was proposed.The proposed algorithm reduces the correlation between the measurement matrix and sparse matrix by using equiangular tight frame.Secondly,the gradient projection method was used to solve the measurement matrix.Finally,QRdecomposition was used to enhance the independence of measurement matrix column.Simulation results show that the proposed algorithm improves the quality of reconstructed signals compared with the Gram matrix optimization algorithm based on gradient projection.