Sparse signal reconstruction based on l0 norm approximation minimization

Computer Engineering and Applications ›› 2015, Vol. 51 ›› Issue (10): 200-204.

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Sparse signal reconstruction based on l0 norm approximation minimization

LI Ying1, WANG Ze2, WANG Junhua1, MIAO Gang1, ZHENG Gengle1

1.School of Petty Officer, The Second Artillery Engineering University, Qingzhou, Shandong 262500, China
2.Zhenjiang College of Watercraft, Zhenjiang, Jiangsu 212003, China

Online:2015-05-15 Published:2015-05-15

基于l0范数近似最小化的稀疏信号重构方法

李颖1，王泽2，王军华1，苗刚1，郑耿乐1

1.第二炮兵工程大学士官学院，山东青州 262500
2.镇江船艇学院，江苏镇江 212003

Abstract

Abstract: In this paper, a novel method, called [l0] norm Approximation Minimization, is proposed for sparse signal reconstruction. Firstly, Approximating [l0] norm by arctan function, a nonconvex optimization problem is constructed. Secondly this optimization problem is solved by fast fixed point iterative method, and convergence of the proposed algorithm is analyzed. Finally, it is shown from simulation results that fewer measurements are needed and the better accuracy is provided than existing methods, while the low computational cost is required.

Key words: compressed sensing, sparse signal recovery, basis pursuit, smoothed [l0] norm

摘要： 针对稀疏信号的重构问题，提出了[l0]范数近似最小化算法。利用反正切函数近似[l0]范数建立相应的非凸优化问题。通过构造快速的不动点迭代格式求解该问题，分析了所提出算法的收敛性能。数值仿真表明，该算法具有重构信号需要测量值少、计算精度高且计算量较小的优点。

关键词: 压缩感知, 稀疏信号重构, 基追踪, 平滑[l0]范数

LI Ying1, WANG Ze2, WANG Junhua1, MIAO Gang1, ZHENG Gengle1. Sparse signal reconstruction based on l0 norm approximation minimization[J]. Computer Engineering and Applications, 2015, 51(10): 200-204.

李颖1，王泽2，王军华1，苗刚1，郑耿乐1. 基于l0范数近似最小化的稀疏信号重构方法[J]. 计算机工程与应用, 2015, 51(10): 200-204.

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Sparse signal reconstruction based on l0 norm approximation minimization

基于l0范数近似最小化的稀疏信号重构方法

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