压缩感知理论投影矩阵优化方法综述  

Survey on Optimization Methods for Projection Matrix in Compress Sensing Theory

作　　者：郑红[1] 李振[1] 

机构地区：[1]北京航空航天大学自动化科学与电气工程学院,北京100191

出　　处：《数据采集与处理》2014年第1期43-53,共11页Journal of Data Acquisition and Processing

基　　金：国家自然科学基金(60543006)资助项目;教育部博士点基金(201003259)资助项目;重点实验室基金(9140C150105100C1502)资助项目

摘　　要：通过优化投影矩阵的结构可提高压缩感知(Compressed sensing,CS)的重构性能及信号适应的稀疏度范围。该类方法利用迭代更新Gram矩阵使CS投影矩阵逼近最优结构,不同于以往的投影矩阵设计问题,它是一类新的改进CS性能方法。本文阐述了该问题的产生起源、理论基础、目标函数、理想模型以及与编码理论的交叉。在此基础上,分析、总结和比较现有投影矩阵优化方法的构造原理、应用特点以及存在的问题,最后讨论了其未来可能的发展方向。实验结果验证了分析结论的正确性。Some studies have shown that optimizing the projection matrix can improve the reconstruction of compressed sensing and the sparsity range of signal adaption. This method u- ses iterative updated Gram matrix to maximum the optimization of compressed sensing（CS） projection matrix. It is a new method for enhancing the CS performance, which is different from previous design problems of projection matrix. Here,it analyzes, summarizes and com- pares the structure of those existing optimization methods of projection matrix, the application char- acteristics as well as existing problems, and concludes with the discussion of its possible direction of future development. The experimental results are used to verify the analysis of the conclusions.

关 键 词：压缩感知 投影矩阵 GRAM矩阵 互相关系数 

分 类 号：TN911.7[电子电信—通信与信息系统]