A robust reconstruction algorithm for sparse signals is proposed to focus on the problem that sparse signal reconstruction has unstable performance. Firstly

the signal is reconstructed by using the half thresholding algorithm. Then

initial value and initial parameters are changed to perform new iterations

and a new termination condition is applied

so that it is possible for the algorithm to escape from the local minima with large error

and the success rate of the signal reconstruction is improved. Experimental results of signal recovery and image reconstruction on Gaussian signals

sign signals and natural image signals show that the proposed algorithm increases the success rate of recovering signals

and its performance is better than that of the half thresholding algorithm and other competitive ones. Comparisons with the half thresholding algorithm show that the success rate of signal recovery of the proposed algorithm has an increase of 30%-40% in average with better robustness.