Research On Signal Reconstruction Algorithm Based On Compressed Sensing

Compressed sensing reconstruction algorithms are mainly divided into two categories: greedy algorithms and convex optimization algorithms.In this paper,we mainly study the greedy algorithm used in the reconstruction algorithm of the compressed sensing signal by the following methods:(1)In view of the fact that the regularized orthogonal matching pursuit algorithm needs to use the sparsity K of the signal as the a priori condition,a weakly selective regularized orthogonal matching pursuit algorithm is proposed.The algorithm can first determine the correlation between different iterative residuals and the atoms in the measurement matrix without knowing the signal sparsity,and then adaptively determine the atomic number and atomic candidate of the original signal according to the weak selection criterion of the atom.The set,and then use the regularization principle to select the optimal atomic group for signal reconstruction from the candidate set,and finally realize signal reconstruction.The simulation results show that the improved algorithm can achieve lower mean square error and bit error rate for signal reconstruction.In addition,the improved algorithm does not use signal sparsity as a priori condition and is more practical.(2)This section proposes a new strategy: the atomic pre-selection strategy,which can continuously optimize the segmentation orthogonal matching pursuit algorithm in the atom selection process.The main idea of this strategy is to divide the atomic selection process into two steps: the first step is atomic preselection and the second step is atomic check.Firstly,the candidate atom is selected in the first round by the threshold strategy.The atomic check refers to the selection of the candidate atoms after the primary selection,that is,the candidate atoms after the selection,using the fixed value selection strategy.Will be finally selected into the support set.In this chapter,three different algorithms,the pre-selected piecewise orthogonal matching pursuit algorithm,the piecewise orthogonal matching pursuit algorithm and the generalized orthogonal matching pursuit algorithm are simulated.The simulation of these three different algorithms further illustrates the other algorithms.The effect has obvious disadvantages compared to the pre-selected segmentation orthogonal matching pursuit algorithm.(3)A new compressed sensing greedy matching tracking reconstruction algorithm,called sparsity and step adaptive regularization matching pursuit(SSARMP)algorithm,is proposed.Compared with other traditional matching pursuit algorithms,SSARMP has obvious advantages,that is,it can recover the sparse signal and is compared with the sparse adaptive matching pursuit(SAMP)algorithm under the condition that the signal sparsity is not known before.The algorithm can obtain the compression ratio estimate by first estimating the compression ratio of the signal,and then set the estimated value as the final value of the first stage.When selecting the atoms of the candidate set and changing the final set of atoms,the regularization idea and the variable step size are added.Reliable numerical sparsity estimation can reduce the number of iterations of the algorithm.Regularization and variable step size can significantly improve the accuracy of signal reconstruction.Therefore,SSARMP can ultimately achieve better complexity and better signal reconstruction accuracy.The simulation results show that SSARMP requires fewer iterations than the improved sparsity adaptive matching pursuit algorithm,and the performance is better than all the above algorithms,especially for Gaussian sparse signals.