一种近似奇异值分解的观测矩阵优化方法  

AN OPTIMISATION METHOD OF MEASUREMENT MATRIX BASED ON APPROXIMATE SINGULAR VALUE DECOMPOSITION

作　　者：牛亚坤[1] 玉振明[2] 李陶深[1] 

机构地区：[1]广西大学计算机与电子信息学院,广西南宁530004 [2]梧州学院,广西梧州543002

出　　处：《计算机应用与软件》2016年第1期195-197,262,共4页Computer Applications and Software

基　　金：广西自然科学基金项目(2013GXNSFAA019323)

摘　　要：压缩感知观测矩阵的优化通常采用迭代或最优化的思想,其主要缺点是运算复杂度高。针对这种情况,提出一种基于奇异值分解的观测矩阵优化方法。首先对随机矩阵进行奇异值分解,其次减小随机矩阵的奇异值到适定的范围,进而得到条件数相对小的观测矩阵。理论分析和实验结果表明,该方法得到的观测矩阵与稀疏基的互干性较小,能够精确重构信号。与现有的其他优化方法相比,该方法具有实现简单,计算复杂度低和重构精度高的特点。To optimising compressed sensing measurement matrix usually adopts the idea of iteration .or optimisation, but its main drawback is the high computing complexity. In view of this, we put forward a singular value decomposition-based measurement matrix optimisation method. First it carries out singular value decomposition on the random matrix, and then decreases its singular value to a proper range, so that gets the measurement matrix with relatively smaller condition numbers. Theoretical analysis and experimental results all reveal that the measurement matrix derived from the proposed method has smaller mutual coherence with the sparsity transformed matrix, and can accurately reconstruct the signal. Compared with other existing optimisation methods, this method has the advantages in terms of simple implementation, low computing complexity and high reconstructed precision.

关 键 词：压缩感知 观测矩阵 奇异值分解 互干性 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]