Abstract: In compressive sampling, measurement matrices should have very small coherence with the sparsity basis. Random measurement matrices have been used since they present small coherence with almost any sparsity basis. This paper proposes a gradient-based alternating minimization approach which is a variant of Grassmannian frame designing. The purpose is to optimize an initially random measurement matrix to a matrix which presents a smaller coherence than the initial one. The simulation results prove that measurement matrix generated by the proposed method has better performance.

Key words: compressed sensing, measurement matrix, Equiangular Tight Frame（ETF）, gradient descent, sparsity

摘要： 在压缩采样中，测量矩阵应该和表达字典有尽可能小的相干性，随机测量矩阵一直被使用是因为其和任何表达字典都有较小的相干性。提出一种基于梯度迭代最小化方法，作为格拉斯曼框架设计的一种变体，通过优化一个初始的随机测量矩阵来得到相干性更小的测量矩阵。仿真结果表明所设计的测量矩阵具有更好的性能。

关键词: 压缩采样, 测量矩阵, 等角紧框架, 梯度下降, 稀疏性