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### 基于奇异值分解的压缩感知观测矩阵优化算法

1. 国防科技大学 电子对抗学院, 合肥 230037
• 收稿日期:2017-07-31 修回日期:2017-09-12 出版日期:2018-02-10 发布日期:2018-02-10
• 通讯作者: 李周
• 作者简介:李周(1993-),男,河北邱县人,硕士研究生,主要研究方向:压缩感知、计算机软件;崔琛(1962-),男,河北易县人,教授,硕士,主要研究方向:无线传感网络、软件工程、可视计算。

### Observation matrix optimization algorithm in compressive sensing based on singular value decomposition

1. Institute of Electronic Engineering, National University of Defense Technology, Hefei Anhui 230037, China
• Received:2017-07-31 Revised:2017-09-12 Online:2018-02-10 Published:2018-02-10

Abstract: In order to solve the problem of large correlation coefficients when obtaining the observation matrix from the optimized Gram matrix in Compressive Sensing (CS), based on the optimized Gram matrix obtained in the existing algorithm, the value of the row vector in the observation matrix when the objective function takes the extreme value was obtained based on the extreme value of the equivalent transformation of the objective function, the analytic formula of the row vector when the objective function takes the extreme value was elected from the values mentioned above by Singular Value Decomposition (SVD) of the error matrix, then a new observation matrix optimization algorithm was put forward by using the idea of optimizing the target matrix row by row in the K-SVD algorithm, the observation matrix was optimized iteratively row by row, and the difference between the correlations of the observation matrix generated by adjacent two iterations was taken as a measure of whether or not the iteration is completed. Simulation results show that the relevance between the observation matrix and the sparse base in the improved algorithm is better than that in the original algorithm, thus reducing the reconstruction error.