稀疏信号结构性噪声干扰下的感知矩阵优化

Sensing Matrix Optimization for Sparse Signal under Structured Noise Interference

针对具有结构性噪声干扰的稀疏信号处理问题,该文提出一种基于贝叶斯理论的感知矩阵优化设计方法。结合具有加性干扰的稀疏信号模型,通过对感知矩阵进行能量约束,最小化信号的后验协方差矩阵的迹,实现感知矩阵的优化设计。仿真不同信号稀疏度和重构算法时,感知矩阵优化对信号重构误差和重构时间的影响;分析信号先验信息存在偏差时,感知矩阵优化对重构效果的影响。仿真结果表明,优化后的感知矩阵能够更好地获取稀疏信号中的重要信息,信号重构精度的均方误差减小约15～25 dB,重构时间减少约40%。

To solve sparse signal processing problem with structural noise interference,a method of sensing matrix optimization design based on sparse Bayesian theory is proposed.Combining the sparse signal model with additive interference,the design of the sensing matrix is realized by minimizing the trace of the posterior covariance matrix and the energy constraint of sensing matrix.The effects of sensing matrix optimization on the reconstruction error and reconstruction time are simulated using difference sparse signal and reconstruction algorithms,and the effects of the sensing matrix optimization on the reconstruction effect are analyzed when there is a bias in the prior information.The simulation results show that the optimized sensing matrix can obtain the important information in the sparse signal,the mean square error of the signal reconstruction accuracy is reduced by about 15~25 dB,and the reconstruction time is reduced by about 40%.