中文摘要：

针对零范数平滑算法（SL0算法）中最速下降法存在＂锯齿现象＂,尤其是在最优解附近收敛速度较慢的问题,提出一种改进SL0算法的压缩感知重构算法。该算法结合了最速下降法和拟牛顿法的优点,提高了算法的重构精度、收敛速度和信噪比。为了验证该算法的可行性及有效性,对一维离散信号进行了仿真实验。通过仿真实验,得到了重构信号与原信号的重构误差、信噪比、迭代次数等参数之间的对比图,图示的仿真结果表明,较之于SL0算法,改进的SL0算法在重构精度和收敛速度方面均有所改善,信噪比提高了近5 d B,从而证明了该算法的可行性及有效性。

英文摘要：

Aiming at the existing problem named ＂ sawtooth phenomenon＂ of the steepest descent method in zero norm smoothing algorithm（ SL0 algorithm）,especially that its convergence speed is slow in the near of optimal solution,an improved SL0 algorithm based on compressed sensing reconstruction algorithm was proposed. The algorithm combined the advantages of the steepest descent method and quasi-Newton method,which improved the reconstruction precision,the speed of convergence and the Signal-to-Noise Ratio（ SNR）. In order to verify the feasibility and effectiveness of the proposed algorithm,the simulation experiment on the one dimensional discrete signal was carried out. By the simulation experiment,the comparison diagram of the reconstructed signal and the original signal in the aspects of reconstruction error,SNR and iteration times could be obtained. The simulation results show that the improved SL0 algorithm has improved the reconstruction precision and convergence rate compared with SL0 algorithm. Signal-to-noise ratio increases nearly 5 d B at the same time,which can prove the feasibility and effectiveness of the algorithm.