Research On Greedy Reconstruction Algorithms Of Compressed Sensing

The signal reconstruction of compressed sensing(CS)theory mainly includes greedy algorithms,convex optimization algorithms and combination algorithms.In order to solve the problems of low reconstruction accuracy or long reconstruction time in the reconstruction of one-dimensional and two-dimensional signals,the greedy algorithm is studied and improved.The main work is as follows:(1)Based on the regularization idea of regularization orthogonal matching pursuit(ROMP)algorithm and the backtracking idea of subspace pursuit(SP)algorithm,R-SP algorithm based on regularization and backtracking is proposed.The algorithm includes two stages.In the first stage,the regularization idea is used to select the atoms,and the reliable atoms are selected as the initial input of the second stage to improve the execution efficiency of the algorithm.In the second stage,the backtracking idea is used to re-evaluate the atoms in the support set and eliminate the unreliable atoms,so as to improve the reliability of the reliable atoms in the support set.Two stages of atom selection are used to improve the reliability of the atoms in the support set,so as to improve the reconstruction accuracy and adaptability to sparsity.The combination of regularization and backtracking makes the selection of atoms more accurate and improves the reconstruction accuracy of the algorithm.(2)In order to improve the execution speed of sparsity adaptive matching algorithm(SAMP)algorithm,a pre-estimated sparsity matching pursuit algorithm(EK-SAMP)is proposed.Firstly,the sparsity pre-estimation strategy is used to estimate the sparsity.And the pre-estimated sparsity doesn't exceed the real sparsity of the sparse signal.Then,the pre-estimated sparsity is used as the initial input of the SAMP algorithm.In this way,the iterative process of the SAMP algorithm from zero is avoided,and it is directly based on the pre-estimated sparsity.Thus it can reduce the number of iterations and greatly speed up the efficiency of the algorithm.(3)A variable step size matching pursuit(VSSMP)algorithm is proposed.On the one hand,VSSMP algorithm first estimates the sparsity;on the other hand,the fixed step size is adopted in each iteration in SAMP algorithm,a variable step size is controlled by a threshold value in VSSMP algorithm.If the energy residue of the reconstructed signal is greater than the threshold,the sparsity is far away from the real sparsity,and large step size is used for iteration.If the energy residue is less than the threshold,the sparsity is close to the real sparsity,and small step size should be used for iteration.VSSMP algorithm can improve the reconstruction accuracy and reduce the running time greatly.