Research Of Sensing Matrix Optimization Based On Bayesian

Compressed sensing theory breaks through the limitation of traditional sampling theorem on signal sampling rate,and can realize sparse reconstruction under under-sampling conditions.However,due to the noise interference in the signal,the system noise and error will be introduced in the process of sparse representation and compression measurement,which leads to the unsatisfactory effect of sparse reconstruction.The optimization of perception matrix can improve the efficiency of obtaining important information in compression measurement,effectively reduce the interference of noise to compression process and improve the reconstruction effect.Sparse Bayesian theory can utilize the prior information of signals and realize the sparse reconstruction of signals through hyper-parameter estimation.Therefore,it is of great significance to combine the prior information of signal with the optimization of perception matrix to improve the performance of sparse reconstruction and anti-noise.This dissertation studies the optimization of perception matrix based on sparse Bayesian theory under the condition of structural interference noise.Firstly,the theory of compressed sensing and the design and characteristics of measurement matrix are described.Different types of sparse reconstruction algorithms are introduced,and the principles of sparse reconstruction algorithms related to this dissertation are analyzed in detail.Then,aiming at the problem of sparse signal processing with structural noise interference,this dissertation presents an optimization method of perception matrix based on sparse Bayesian theory: using the sparse signal model with additive interference,energy constraints are applied to the perception matrix to minimize the trace of the posterior covariance matrix of the signal,and the optimal design of the perception matrix is realized from the signal sparsity and reconstruction.The universality of the algorithm and the deviation of prior information are simulated and analyzed.The simulation results show that the signal reconstruction error can be reduced by about 27 dB under different sparseness conditions by using the optimized perception matrix,and that the signal reconstruction error can be reduced by about 15 dB by using different types of sparse reconstruction algorithms.For the sparse Bayesian reconstruction algorithm with excellent performance,the signal reconstruction time can be reduced by about 40%.Under the condition of high signal-to-noise ratio,deviation has a great influence on the effect of signal reconstruction,and there will be large jump-type reconstruction error;interference prior information deviation will reduce the effect of reconstruction,but it still has better reconstruction performance than random perception matrix;noise prior information deviation has no obvious influence on the effect of reconstruction.Finally,the optimal perception matrix is applied to inverse synthetic aperture radar imaging,and the sparse representation model of radar echo signal is established.The simulation results show that the optimization of perception matrix can effectively reduce the shadow of noise to radar sparse imaging under the condition of structural noise jamming.Sound,improve the imaging effect.