关键词: 压缩采样, 测量矩阵, 等角紧框架, 梯度下降, 稀疏性

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