一种鲁棒的稀疏信号重构算法
A Robust Reconstruction Algorithm for Sparse Signals

针对稀疏信号重构性能不稳定的问题,结合半阈值迭代算法,提出了一种鲁棒的稀疏信号重构算法。该算法首先对随机信号采用半阈值迭代算法进行重构,以获得初步的重构信号,然后改变迭代初值和参数初值进行新的迭代计算,同时增加一个新的循环终止条件,在保证算法稳定性与收敛速度的同时,使迭代结果跳出相对误差较大的局部极小点而收敛于误差较小的点成为可能,提高了重构信号的成功率。对该算法进行了信号重构和图像重构2个方面的实验,结果表明,与半阈值算法及相关算法比较,无论是对高斯信号、符号信号还是自然图像信号,该算法重构信号的成功率都有明显提高,较半阈值算法平均提高了约30％～40％,表现出较强的鲁棒性。
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