基于超素数的托普利兹观测矩阵构造方法

观测矩阵在信号压缩感知中十分重要,直接决定信号的重构质量。为保证信号的重构精度,要求观测矩阵具有很强的随机性,但随机矩阵硬件实现非常困难;确定性观测矩阵易于实现,但其重构精度不足。针对观测矩阵对随机性与确定性的双重要求,提出利用超素数产生超长周期的伪随机序列,解决确定性观测矩阵对随机性的要求;结合托普利兹观测矩阵的确定性结构特征,得到一种改进的托普利兹观测矩阵。实验仿真表明:改进的托普利兹观测矩阵与高斯随机观测矩阵和常用托普利兹观测矩阵相比,其信号重构精度得到了很好的改善,且易于硬件实现。

A constructing method of the toeplitz measurement matrix based on super prime numbers

Measurement matrix is of great importance in compressed sensing(CS), and it determines a signal reconstructing performance. The random measurement matrix can reconstruct the original signal with high accuracy, but it is hard to put into practice. Although the deterministic measurement matrix is easy to implement, the reconstruction accuracy is low. In order to solve this problem, some super prime numbers are introduced to generate the pseudo sequences with long periods to meet the randomness requirements. Toeplitz measurement matrices are presented to meet the hardware implementation requirement. Simulation results show that the presented method has higher performance compared with the Gauss random measurement matrix and the Toeplitz measurement matrix, and it is easy to perform.