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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.
Aiming at the optimization problem of observation matrix in compressed sensing, based on the analysis of the independence of vector of observation matrix vector and the correlation between observation matrix and sparse base on the quality of reconstructed signal, QR decomposition is used to enhance the independence of column vector of observation matrix , A combination of QR decomposition and Gram observation matrix optimization algorithm based on gradient projection is proposed and an improved Gram matrix optimization algorithm based on gradient projection is proposed.The algorithm adopts the isochoric tight frame approach to Welch bound to reduce the correlation between observation matrix and sparse basis The gradient projection method is used to solve the observation matrix, and the observation matrix is QR decomposition to increase the independence of the observation matrix array vector.Experimental results show that compared with Gram matrix optimization algorithm based on gradient projection, The quality of the signal.