Research On Robust Compressed Sensing Signal Reconstruction Method Based On L₁ Norm

Compressed sensing and sparse sampling are methods used to obtain sparse solutions of underdetermined linear systems,which play an important role in the acquisition and reconstruction of compressible signals.In the process of compressed sensing,it is inevitable to encounter unfavorable signal reconstruction situations such as noise interference and comparator threshold offset.At this time,signal sampling may have abnormal conditions such as data redundancy,data indeterminacy,or data inconsistency.The signal recovery performance will decrease with the appearance of outliers.For this type of compressed sensing method containing some outliers,this paper first reviews the related compressed sensing method,and then carries out the following research work:(1)Through the improvement of the orthogonal matching pursuit method,the study of A Robust Orthogonal Matching Pursuit Based on L1 Norm is completed.In the process of obtaining the sparse signal estimation,the algorithm uses L1 norm estimation to obtain the signal sparse estimation,and realizes the accurate signal reconstruction.The simulation results show that the residual value by using the algorithm can reach 1e-11,which is good for the presence of outliers in the Measurement signal.(2)We proposed a restricted isometry principle based on the L]norm(L1RIP)and an estimation method for the L1RIP constant is proposed.This criterion can be used as a criterion for selecting the measurement matrix in compressed sensing.According to this criterion,a signal sparsity estimation algorithm based on L1RIP is proposed.The sparsity of the signal can be accurately and stably estimated while preserving all of the measurement information even if there are outliers in the Measurement signal.(3)Combined with the principle of reconstruction algorithm based on compressed sensing theory,a MATLAB program is written to realize the algorithm proposed in this paper.In the case of outliers in the Measurement signal,a comparative analysis of the method proposed in this paper and the traditional reconstruction algorithm reveals the robustness of the proposed method.