Legendre序列测量矩阵的构造研究

Measurement Matrix Construction Based on Legendre Sequences

测量矩阵是压缩感知理论的重要研究内容,对信号的测量和重构都有重大影响。理论上,随机性测量矩阵可以保证精确重构,但不能保证每一次都可以精确重构,且硬件实现复杂。从工程应用的角度来看,确定性测量矩阵更具有实际意义。文章利用legendre序列构造一种确定性的测量矩阵,根据legendre序列的自相关特性证明了该测量矩阵满足重构要求,并在此基础上加入了分块操作,进一步降低了实现的复杂性。仿真实验表明:该测量矩阵的重构性能高于同条件下的高斯测量矩阵,且避免了随机性测量矩阵的不确定性,具有一定实用价值。

The measurement matrix is an important research content of the compressive sensing theo- ry, which has a great influence on signal measurement and reconstruction. In theory, the random measurement matrix can guarantee the uniqueness of the reconstruction. Though, it can not guaran- tee accurate reconstruction each time and the hardware implementation is also complex. From the point of view of engineering application, the deterministic measurement matrix is of practical signifi- cance. In this paper, a deterministic measurement matrix is constructed by using legendre se- quences. According to the self correlation of legendre sequences, the measurement matrix is proved to meet reconstruction requirement, and the operation of the sub block is added on this basis. The simulation results show that the reconstruction performance of the measurement matrix is higher than that of the Gauss measurement matrix under the same condition, and it avoids the uncertainty of the random measurement matrix, and has some practical value.