A Compressed Sensing Reconstruction Algorithm Based on Hyperbolic Function

The accuracy of the compressed sensing theory reconstruction algorithm is important for signal recovery. Sparsity Adaptive Matching Pursuit (SAMP) has a fixed step size in each iterative process of reconstruction, which has a significant impact on accuracy in actual use, often leading to overestimation and underestimation. In order to solve this problem, combined with the advantages of regular backtracking and variable step size, the article introduces the idea of retrospective in the atom selection stage. Then, the atoms are inspected using backtracking and re-screened. The algorithm uses regularization at the beginning to select atoms with higher energy and reduce the number of atoms in the candidate set at the threshold stage. During reconstruction, because the energy difference of the reconstructed signal decreases rapidly at the initial stage, and then the energy difference decreases slowly. This algorithm takes advantage of the large change rate of the hyperbolic function at the beginning and the slower change rate at the later stage. At first, a large step size is used. When the energy difference reaches a certain threshold, a small step size is used instead. After the actual simulation, the improved algorithm improves the reconstruction accuracy and the effect is better.