压缩感知理论投影矩阵优化方法综述

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。

Survey on Optimization Methods for Projection Matrix in Compress Sensing Theory

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 uses 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 compares the structure of those existing optimization methods of projection matrix, the application characteristics 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.