基于梯度下降法与QR分解的观测矩阵优化  

Optimization of Measurement Matrix Based on Gradient Descent Method and QR Decomposition

作　　者：兰明然 王友国[1] 郑丹青[1] 翟其清[2] 

机构地区：[1]南京邮电大学理学院,江苏南京210046 [2]南京邮电大学通信与信息工程学院,江苏南京210003

出　　处：《计算机技术与发展》2017年第1期190-194,共5页Computer Technology and Development

基　　金：国家自然科学基金资助项目(61179027)

摘　　要：观测矩阵的设计是压缩感知(CS)理论的核心问题。基于压缩感知理论,可通过降低观测矩阵同稀疏变换基间的相关性和增大观测矩阵独立性的方式来优化观测矩阵。基于此提出一种新的优化方法。用梯度下降法处理Gram矩阵,降低其非对角线元素;对得到的观测矩阵进行QR分解。对所得到的观测矩阵进行仿真实验,以此来检验该算法的有效性。仿真实验结果表明,该方法在提高峰值信噪比和重构稳定性方面较为理想,尤其当压缩比取0.30左右时,相对比未经优化的观测矩阵,峰值信噪比有相当显著的提高,约提升67%。The design of the measurement matrix is the core of the theory of Compressive Sensing （ CS ）. Based on the CS, the perform- ance of the measurement matrix is improved by the way which is that the correlation between the measurement matrix and sparse trans- formed matrix is reduced and that the column independence of the measured matrix is increased. Depending on this, a method to improve the performance of the observation matrix is proposed. The Gram matrix is processed by the gradient descent method to reduce non-diag- onal elements and the matrix obtained from the last step is dealt by the QR decomposition. The simulation experiment is carded out on the measurement matrix to test the validity of the algorithm. The result shows that the measurement matrix dealt by this method has better per- formance in Peak Signal-Noise Ratio （PSNR） and stability of reconstruction especially when the compression ratio is 0.30,and the PSNR of this matrix is 67% higher than the matrix without any treatments.

关 键 词：压缩感知 观测矩阵 梯度下降法 QR分解 

分 类 号：TP301[自动化与计算机技术—计算机系统结构]