中文摘要：

欠定系统（又称超完备系统）的稀疏信号恢复在压缩感知、源信号分离和信号采集等领域中被广泛研究.目前这类问题主要采用l1范数约束结合线性规划优化或贪婪算法进行求解,但这些方法存在收敛速度慢、恢复精度不高等缺陷.提出一种快速恢复稀疏信号的算法,该算法采用一种新的近似l0范数代替l1范数构造代价函数,并融合牛顿法和最陡梯度法推导出寻优迭代式,以获得似零范数代价函数的最优解.仿真实验和真实数据实验结果表明,与经典算法相比,该算法在能提供相同精度、甚至更好精度的条件下,收敛速度更快.

英文摘要：

Obtaining sparse solutions of under-determined, or over-complete, linear systems of equations has found extensive applications in signal processing of compressive sensing, source separation and signal acquisition. However, the previous approaches to this problem, which generally minimize the 11 norm using linear programming （LP） techniques or greedy methods, are subject to drawbacks such as low accuracy and slow convergence. This paper proposes to replace the 11 norm with a newly defined approximate 10 norm （AL0）, the optimization of which leads to the derivation of a hybrid approach by incorporating the steepest descent method with the Newton iteration. Numerical simulations and real data experiment show that the proposed algorithm is about two to three orders of magnitude faster than the state-of-the-art interior-point LP solvers, while providing the same （or better） accuracy.