Research On Signal Reconstruction Algorithms Based On Compressed Sensing

In a signal processing model based on traditional sampling theory,if the original analog signal needs to be reconstructed from the discrete signal acquired by sampling without distortion,the sampling frequency of the signal must be more than twice the highest frequency of the original signal.However,with the increasing demand for information and the increasing signal bandwidth,the signal processing framework based on this is facing tremendous pressure in signal sampling,transmission and storage.The Compressed Sensing(CS)theory proposed in recent years provides an effective solution to alleviate these pressures.CS theory realizes parallel sampling of signal sampling and compression,and performs sampling of sparse signals or approximate compressed signals at a lower sampling rate,and is increasingly becoming an important tool for information acquisition,compression,processing,and transmission.Among them,the design of signal reconstruction algorithm is a key step in the success of compressed sensing theory and plays a decisive role.At present,the greedy matching algorithm has received continuous attention from researchers because of its simple structure and small computational complexity.Therefore,this paper mainly studies and improves the greedy matching pursuit algorithm in the signal reconstruction algorithm and its corresponding variant greedy algorithm stochastic gradient matching pursuit algorithm.(1)In order to solve the problem that the compression sampling matching tracking(CoSaMP)algorithm relies heavily on signal sparse information,high pre-selected atomic repetition rate,and excessive number of iterations,the performance of the algorithm reconstruction and practical application are affected.This paper proposes an improved compressed sampling matching pursuit algorithm based on fuzzy threshold strategy,multi-stage and variable step size method.The algorithm continuously adjusts the estimated sparsity by multi-stage and variable step size methods to approximate the true sparsity of the signal and uses it for the expansion of pre-selected atomic sets and the shearing of supporting atomic sets.In addition,the algorithm uses a fuzzy threshold strategy to perform secondary screening of preselected atomic sets to ensure that more relevant atoms are added to the candidate atom set.(2)In order to solve the problem that the stochastic gradient matching pursuit algorithm is inflexible in atomic selection,large in dependence on signal sparsity,and the ability of the atomic influence algorithm which can not fully match the original signal in the preselected atomic concentration group,the computational complexity and computational complexity.In this paper,a new stochastic gradient matching pursuit algorithm,weakly chosen stochastic gradient matching pursuit algorithm,is proposed.In the pre-selection phase,the algorithm rejects the wrong atom and the atom with a small degree of signal matching through the weak selection strategy,and retains the atom that matches the signal more.After these atoms matching the signal are added to the candidate atom set,not only the atom selection is more flexible,but also the accuracy of the algorithm reconstruction and the accuracy of the support set estimation are weakened,and the influence of the sparsity information in the algorithm is weakened.(3)In order to solve the problem that the StoGradMP algorithm requires known signal sparsity,the actual application capability of the algorithm is poor.This paper proposes a stochastic gradient matching pursuit algorithm based on sparsity evaluation strategy.Before the reconstruction algorithm runs,the algorithm uses the sparsity evaluation strategy to initially evaluate the true sparsity of the signal to obtain the estimated sparsity of the signal.This strategy is beneficial to reduce the sparsity adjustment time of the reconstruction algorithm.After that,the sparsity adjustment strategy is used to gradually approximate the true sparsity of the signal and complete the signal reconstruction.Through the improvement of the above method,the performance of the StoGradMP algorithm is improved,and the algorithm is freed from the dependence on signal sparsity,which solves the problem that the actual application ability of the algorithm is poor.