中文摘要：

光滑l0范数法（SL0）用带参数的高斯光滑函数序列逼近l0范数，可以有效地用于压缩感知信号重构。针对SL0算法在最优解附近收敛速度较慢的问题，由高斯光滑函数梯度及Hesse矩阵的特点，根据牛顿法的基本原理，提出了快速光滑“范数法-FSL0算法。算法的迭代公式十分简洁。仿真结果表明，该算法与已有同类算法的重构精度相当，但重构速度得到了很大地提高。

英文摘要：

Smoothed 10 norm algorithm （SL0） introduced a sequence of smoothed Gaussian functions with parameter to approximate the l0 norm, which could be used efficiently for the compressive sensing reconstruction. But the SL0 algorithm converged rather slowly around the optimal solution. According to the feature of the gradient and Hesse matrix of the smoothed Gaussian function, a fast smoothed l0 norm algorithm is proposed based on the Newton method, which is referred to as FSL0. The iterative formula of the new algorithm is very brief. Simulation results demonstrate that the proposed FSL0 algorithm is competitive to the similar algorithms in the reconstruction accura- cy, but the reconstruction speed is greatly improved.