基于有限域上向量空间的压缩感知矩阵的构造

New construction of deterministic compressed sensing matrices based on vector space over finite fields

基于有限域上的向量空间,构造新的压缩感知矩阵,计算其相关参数,将其与DeVore构造的基于有限域上多项式的压缩感知矩阵进行对比,证明当满足一定条件时,基于有限域上向量空间构造的压缩感知矩阵的信号恢复性能优于DeVore所构造的矩阵。数值仿真说明,构造的矩阵在恢复信号能力方面优于高斯随机矩阵和DeVore构造的矩阵。

A compressed sensing matrix based on vector spaces over finite fields is constructed, and the coherence of the matrix is computed. A comparison is made with the matrix constructed by DeVore based on polynomials over finite fields. The character of compressing and recovering signals is better than that of the matrix constructed by DeVore when the matrix is satisfied some conditions. The favorable performance of the matrix is demonstrated by numerical simulations.