Some Improved Reconstruction Algorithms Based On Compressed Sensing

The paper summarizes reconstruction algorithms in details and explores them deeply, especially the paper pays more efforts on the existing convex optimization method and greedy algorithm based on compressed sensing. The paper makes analysis of advantages and disadvantages and possible improved angle of several exsiting algorithms. Then the paper makes two-dimensional image sparse reconstruction experiments to compare the performance of each algorithm. According to the analysis of the disadvantage on the existing algorithms this paper proposes improved algorithm based on regularized orthogonal matching pursuit algorithm, complementary space orthogonal matching pursuit algorithm and iterative hard thresholding algorithm. The paper compares the improved algorithms with the existing algorithms by simulation experiments which approve that the new algorithms improve the reconstruction quality and speed. The details of improved algorithms are as follows:(1)Judging by the low reconstruction accuracy of regularized orthogonal matching pursuit algorithm with low sampling rate, the paper proposes the weighted correlation regularized orthogonal matching pursuit algorithm. Combining with the advantages of backward thought the regularized orthogonal matching pursuit algorithm is proposed. Variable step-size regularization adaptive matching pursuit algorithm improves the regularized adaptive matching pursuit algorithm by changing fixed step-size which may easily lead to excessive estimation of sparsity into variable step-size.(2)The paper puts forward the regularized complementary space orthogonal matching pursuit algorithm and threshold regularization complementary space orthogonal matching pursuit algorithm which overcomes the high computing complexity of the complementary space orthogonal matching pursuit algorithm. The threshold regularization adaptive complementary space orthogonal matching pursuit algorithm is proposed based on threshold regularization complementary space orthogonal matching pursuit algorithm. The regularization complementary space orthogonal matching pursuit algorithm and variable step-size adaptive orthogonal complementary space regularization matching pursuit algorithm improves the regularized orthogonal matching pursuit algorithm in the condition of unknown sparsity.(3)Combining with the advantages of retrospective thought, the paper proposes back iterative hard thresholding algorithm and regularized back iterative hard thresholding algorithm that overcomes the low precision of iterative hard thresholding algorithm. Then the paper proposes sparse adaptive iterative hard thresholding algorithm and regularized adaptive iterative hard thresholding algorithm that need not to know the sparsity. Combining the optimization of variable step-size method which can approach the sparisty exactly on greedy algorithm the paper puts forward variable step-size adaptive iterative hard thresholding algorithm and variable step-size adaptive regularized iterative hard thresholding algorithm.