一种基于拟牛顿法的CS投影矩阵优化算法

发布时间：2019-06-24 09:44

【摘要】：压缩感知(Compressed Sensing,CS)理论中,投影矩阵优化是一类通过提高观测数据信息量而改善性能的方法.由于投影矩阵与稀疏字典内积构造的Gram矩阵必定奇异,基于广义逆矩阵求解方法存在计算精度的问题.本文提出了一种利用拟牛顿法的CS投影矩阵优化算法.该算法分为两步:一是利用阈值函数约束Gram矩阵非对角线元素,使投影矩阵与稀疏字典的互相关系数逼近Welch界;二是采用秩2校正得到Hessian阵逆近似去修正梯度搜索方向.两个步骤交替执行,直到解出符合优化要求的投影矩阵.该算法始终保持下降性,具有超线性收敛速度,避免了矩阵函数二阶导数复杂的计算,计算量较小.实验结果表明,当信号稀疏度或观测数据相同时,本文算法的重构结果优于其他算法.
[Abstract]:In compressed perception (Compressed Sensing,CS) theory, projection matrix optimization is a kind of method to improve the performance by increasing the amount of observation data. Because the Gram matrix constructed by projection matrix and sparse dictionary inner product is bound to be singular, the solution method based on generalized inverse matrix has the problem of computational accuracy. In this paper, a CS projection matrix optimization algorithm based on quasi-Newton method is proposed. The algorithm is divided into two steps: one is to use the threshold function to constrain the non-diagonal elements of the Gram matrix, so that the correlation between the projection matrix and the sparse dictionary approximates the Welch bound; the other is to obtain the inverse Hessian matrix approximation to correct the gradient search direction by rank 2 correction. The two steps are performed alternately until the projection matrix that meets the optimization requirements is solved. The algorithm always maintains the descending property and has the superlinear convergence speed, which avoids the complex calculation of the second derivative of the matrix function and has a small amount of computation. The experimental results show that when the signal sparsity or observation data are the same, the reconstruction results of this algorithm are better than those of other algorithms.
【作者单位】：北京航空航天大学自动化科学与电气工程学院;
【基金】：国家自然科学基金(No.60543006) 教育部博士点基金(No.201003259)
【分类号】：TN911.7

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