针对测量值受噪声污染的稀疏重构问题,本文提出了稳健近似l0范数最小化算法.该算法首先利用反正切函数近似l0范数,然后建立基于近似l0范数的含噪稀疏重构模型,最后通过拟牛顿法求解该模型,并分析了算法的收敛性.数值仿真表明,本文提出的算法重构稀疏向量时需要较少的测量值,且具有较高的计算精度.%For the problem of recovering sparse vector with noisy measurements, robust approximate l0 norm minimization algorithm is proposed.Firstly, l0 norm is approximately expressed by arctan function. Secondly,the model of sparse recovery in the present of noise is constructed based on approximate l0 norm. Finally, the model is solved by quasi-Newton method to estimate sparse vector.Simulation results show that our algorithm needs fewer measurements and provides the better accuracy than the existing methods.
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