基于改进目标Gram矩阵的鲁棒测量矩阵优化  

Optimization of Robust Measurement Matrix Based on Improved Target Gram Matrix

作　　者：王艺霖 李荣鹏 宋学力[1] WANG Yi-lin;LI Rong-peng;SONG Xue-li(School of Science,Chang'an University,Xi'anShaanxi 710064,China)

机构地区：[1]长安大学理学院,陕西西安710064

出　　处：《计算机仿真》2024年第7期429-435,共7页Computer Simulation

基　　金：长安大学高校基本科研业务费专项资金资助项目(310812163504)。

摘　　要：测量矩阵优化是压缩感知的重要内容,其中目标Gram矩阵的设计和测量矩阵的更新是测量矩阵优化过程中的两个重要步骤。然而在目前的优化模型中,两个步骤效果无法同时达到最优,如何使两个重要步骤的效果同时达到最优成为亟待解决的问题。针对上述问题,提出了一种基于改进目标Gram矩阵的鲁棒测量矩阵优化方法。首先,证明了所采用目标Gram矩阵的优越性,即整体降低测量矩阵与稀疏基的三种相关性;其次,证明了所采用测量矩阵更新方法的优越性,即降低稀疏误差影响,提高测量矩阵的鲁棒性;最后,将最优目标Gram矩阵应用于最优测量矩阵更新方法,提高了信号重构精度。实验结果表明,提出的测量矩阵优化方法有效提高了二维信号重构质量。The optimization of the measurement matrix is an important part of compressed sensing.The design of the target Gram matrix and the update of the measurement matrix are two important steps in the optimization of the measurement matrix.However,in the current optimization models,the effects of the two steps cannot be optimal at the same time,and how to optimize the effects of the two important steps at the same time has become an urgent problem to be solved.Aiming at this problem,a robust measurement matrix optimization method based on improved target Gram matrix is proposed.Firstly,the superio rity of the adopted target Gram matrix is proved,that is,overall reduction of three mutual coherences between measurement matrix and sparse basis;Secondly,the sup eriority of the adopted measurement matrix update method is proved,that is,reduction of the sparse error and impr ovement of robustness of the measurement matrix;Finally,the optimal target Gram matrix is applied to the optimal measurement matrix update method,which improves the signal reconstruc tion accuracy.The experimental results show that,the measurement matrix optimization method proposed in this paper effectively improves the reconstruction quality of two-dimensional signals.

关 键 词：压缩感知测量矩阵 相关性 稀疏误差 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]