Abstract: For the past few years, Compressed Sensing（CS） has been developed very fast. In many applications of CS, the data measurement can be achieved by filtering and sub-sampling. In this paper, a new matrix with Legendre Sequence is constructed, which is based on Convolutional Compressed Sensing. After sub-sampling, a new deterministic measurement matrix is gotten. For signals that are sparse, the proposed matrix can guarantee a stable recovery. The results show that, the proposed matrix can offer comparable performance with a random Gaussian matrix in K-sparse signal reconstruction.

Key words: deterministic matrix, convolutional compressed sensing, coherence, Legendre sequence

摘要： 近年来，压缩感知理论飞速发展。很多压缩感知的应用中，信号的测量可以通过卷积滤波和之后的二次采样完成。在此基础上，实现了一种由勒让德（Legendre）序列构造的矩阵。该矩阵在经过二次采样之后，得到一种新的确定性测量矩阵。对于一个K-稀疏的信号，通过该测量矩阵可以对信号进行稳定的恢复重建。据仿真结果显示，在对K-稀疏信号进行恢复的过程中，该测量矩阵的恢复效果与高斯随机测量矩阵的应用效果相当。

关键词: 确定性测量矩阵, 卷积压缩感知, 相关性, 勒让德序列