Abstract: Aiming at the problem that depth-first multipath matching pursuit algorithm needs known image sparsity and high computational complexity in image reconstruction, a threshold multipath sparsity adaptive image reconstruction algorithm is proposed. In this algorithm, multiple candidate sets are introduced, and thresholds are set to select atoms and adjust the number of candidate sets. Then each iteration selects the path with the smallest residual as a new candidate set to improve the reconstruction speed. In addition, residual difference less than a threshold is used as the stopping condition of the algorithm, so image sparsity is not needed as the input of the algorithm. The experimental results show that the algorithm can achieve good reconstruction effect, while maintaining good time complexity and anti-noise performance.

Key words: compressed sensing （CS）, image reconsturction, threshold multipath, sparsity adaptive