Sensing Matrix Optimization for Sparse Signal under Structured Noise Interference

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 similar to 25 dB, and the reconstruction time is reduced by about 40%.