基于最小化似零伪范数的稀疏信号恢复算法

Sparse Signal Recovery Algorithm Based on the Approximate Zero Pseudo-Norm

针对欠定系统中出现的稀疏信号恢复问题,提出了一种基于最小化近似零伪范数的处理方法,算法首先结合反正切函数构造出代价函数,再融合最速下降法和扩展牛顿迭代法逐步迭代寻优,并给出了算法的收敛性分析,数值仿真实验结果表明,与经典的稀疏信号恢复算法相比,方法有更好的计算速度和恢复精度.

In order to solve underdetermined system sparse signal recovery problem, an approach based on minimizing the approximate zero pseudo-norm is proposed. The algorithm firstly combined arc tangent function to construct a cost function, then adopted the steepest descent method and extended Newton iteration optimization. The convergence analysis of the algorithm was given. Numerical simulation results showed that, compared to the classic sparse signal recovery algorithm, this method has a better computing speed and recovery accuracy.