Research On Signal Reconstruction Algorithms Based On Compressed Sensing

The traditional signal processing framework is based on the Nyquist sampling theorem,which to sample the signal with the frequency that is not less than twice the frequency of the highest signal frequency to achieve the purpose of undistorted recovery signal.Limited by the cost and physical limit of the sampling equipment,the traditional signal processing framework is increasingly unable to meet the requirements of modern information transmission.Compressed sensing theory broke the limitation of the Nyquist sampling theorm,can recovering the sparse signal and compressible signal without distortion at the sampling rate that far below the sampling rate stipulated by Nyquist sampling theorm.Greedy algorithm,convex optimization algorithm,and non-convex optimization algorithm are proposed for compressed sensing signal reconstruction.In this paper,we make a research and improvement of greedy algorithm which is one kind of the compression sensing reconstruction algorithms.The main work is as follows:(1)In order to solve the problem that the support set is too large and the reconstruction time is too long in the generalized orthogonal matching pursuit algorithm due to it can not eliminate the wrong atom from the support set.In this paper,a backtracking generalized orthogonal matching pursuit algorithm is proposed.When the number of atoms in the support concentration reaches the original signal sparsity in the algorithm,the atoms is reevaluated according to their contribution to the estimated signal.The algorithm only keep a fixed number of highly reliable atoms in the support set and remove the low reliability atoms from the support set to limit the size of the support set,and increase the proportion of the correct atoms in the support set.By limiting the size of the supporting set and improving the reliability of the atoms in the support set,the algorithm can improve the probability of exact reconstruction and reduce the computation cost.(2)In order to improve the atomic selection accuracy of StOMP algorithm,the preselection stagewise orthogonal matching pursuit algorithm is proposed.The algorithm adopts preselection strategy in the atomic selection stage and the idea of preselection strategy is to divide the atomic selection process into two steps.First,the candidate atoms are selected by the threshold selection strategy in the preselection.The atoms who passed the preselection will be selected as candidate atoms to attent the second election which adopts a fixed value selection strategy.When the number of atoms who passed the preselection is less than the number of atoms needed by the second election,all the atoms who passed the preselection are considered to automatically pass the second election.Only the atoms who passed the second election will eventually be selected into the support set to participate in signal reconstruction.The algorithm improves the accuracy of atomic selection by selecting better from better to the candidate atoms.(3)In order to solve the problem that the gOMP algorithm can not complete the signal reconstruction in the case of the sparsity of original signal is unknown,a sparsity adaptive generalized orthogonal matching pursuit algorithm is proposed.The algorithm selects atoms at the atomic selection stage with a fixed value.When the signal residuals drop to a threshold,the sparsity estimation is started.The algorithm divides the sparse estimation process into several stages and determines whether the current estimated sparsity is appropriate by determining whether the signal residuals are monotonically decreasing.If the current estimated sparsity is appropriate,backtracking is performed with the current estimated sparsity.If it is not appropriate,the algorithm will update the current estimate sparsity with a fixed step size and enter the next stage.The sparsity adaptive generalized orthogonal matching pursuit algorithm realize the sparsity adaptive through the "divide and conquer" to iteration process and the "step-by-step approach" to the real sparsity.