Sparse Signal and Image Reconstruction Algorithm for Adaptive Dual Thresholds Matching Pursuit Based on Variable-step Backtracking Strategy

The traditional greedy algorithm requires the signal sparsity as a known condition, and in most application scenarios, the signal sparsity is unknown, resulting in poor signal reconstruction accuracy. In order to solve such problems, this paper proposes an adaptive dual threshold matching pursuit algorithm based on a variable-step backtracking strategy (SBATMP). Firstly, the suboptimal set of atoms is selected through two adaptive thresholds. Then, through the variable-step backtracking strategy, the atoms are selected twice to obtain the optimal atomic set. The algorithm can improve the complete reconstruction rate of the signal under the condition of unknown sparsity, and the variable-step backtracking strategy can effectively reduce the complexity of the algorithm. Through the reconstruction simulation experiment, the one-dimensional signal reconstruction accuracy can reach 100%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\%$$\end{document} under the condition that the ratio of the sparsity to the measured value is less than 0.25. The reconstruction speed can be improved by 0.021-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-$$\end{document}0.186 s. For the two-dimensional image signal, the PSNR of the reconstructed image by the SBATMP algorithm is increased by 1.193–5.781dB, and the SSIM is increased by 0.0116-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-$$\end{document}0.0645 under the compression ratio of 0.7.