基于SVD与最小化互相干系数的测量矩阵优化方法  

Optimization of the measurement matrix based on SVD and Mutual Coherence Minimization

作　　者：张瑞 孟晨 王成 王强 Zhang Rui;Meng Chen;Wang Cheng;Wang Qiang(Shijiazhuang Campus,Army Engineering University,Shijiazhuang Hebei,050003)

机构地区：[1]陆军工程大学石家庄校区,河北石家庄050003

出　　处：《电子测试》2021年第20期37-39,32,共4页Electronic Test

基　　金：国家自然科学基金(61501493)资助项目。

摘　　要：在压缩感知过程中,测量矩阵的设计与选择将直接影响到信号压缩感知的效果。为了提高信号的重构精度与压缩感知性能,提出了一种新的测量矩阵优化算法。首先,对基础测量矩阵进行奇异值分解,然后优化其非零奇异值得到新的测量矩阵,同时借鉴最小化互相干系数的思想对测量矩阵与稀疏变换矩阵的Gram矩阵进一步进行优化,得到最终优化的测量矩阵。仿真结果表明,与传统的测量矩阵和传统的优化方法相比,提出的新算法有效地提高了优化后的测量矩阵的重构精度与压缩感知性能。In the process of compressive sensing,the design and selection of the measurement matrix will directly affect the effect of signal compressive sensing.In order to improve the reconstruction accuracy and compressive sensing performance of the signal,a new measurement matrix optimization algorithm is proposed.Firstly,the singular value decomposition of the base measurement matrix is carried out,and then its non-zero singular values are optimized to the new measurement matrix,while the Gram matrix of the measurement matrix and the sparse transformation matrix are further optimized by borrowing the idea of minimizing the mutual coherence coefficients to obtain the final optimized measurement matrix.The simulation results show that the proposed new algorithm effectively improves the reconstruction accuracy and compression-aware performance of the optimized measurement matrix compared with the conventional measurement matrix and the conventional optimization method.

关 键 词：压缩感知 测量矩阵优化 奇异值分解 GRAM矩阵 

分 类 号：TN911.7[电子电信—通信与信息系统]