高斯随机观测矩阵的改进

在压缩感知理论中，要想精确地重构信号，观测矩阵必须满约束等距性条件，大部分随机矩阵都具备此条件，并可作为观测矩阵，如高斯随机矩阵、傅里叶矩阵和贝努利随机矩阵等。其中高斯随机矩阵是研究较多的观测矩阵。然而，该类矩阵重构信号时的效果并不十分理想，恢复后的信号相对误差较大。主要针对高斯随机矩阵的上述问题，对其进行改进。改进的观测矩阵保留了高斯随机矩阵的随机独立性，很好的满足约束等距性条件。先通过对时域稀疏信号的压缩感知重构，来验证改进后的观测矩阵的性能，然后将其扩展到变换域信号的压缩感知重构。实验结果表明，改进后的观测矩阵比原高斯随机矩阵具有更好的性能。

Improvement of Gauss random measurement matrix

In the compressed sensing theory, to accurately reconstruct signal, the measurement matrix must restrict condition of restricted isometry property (RIP), most of the random matrix satisfy this condition, and can be used as the measurement matrix, such as Gauss, Fourier and Bernoulli random matrix. Among them, Gauss random matrix is an common measurement matrix. However, the effect of this kind of matrix reconstructed signal is not very satisfactory. In this paper, we mainly deal with the above problems of Gauss random matrix. The improved measurement matrix preserves the random independence of Gauss random matrix, and satisfies the condition of RIP. the performance of the improved measurement matrix is verified by the reconstruction of compressed sensing in time domain, and then it is extended to the transform domain compressed sensing reconstruction. The experimental results show that the improved measurement matrix has better performance than the original Gauss random matrix.