ISSN 1000-1239 CN 11-1777/TP

• 图形图像 •

### 基于近似l\-0范数的稀疏信号重构

1. (燕山大学理学院 河北秦皇岛 066004) (niedd@ysu.edu.cn)
• 出版日期: 2018-05-01
• 基金资助:
燕山大学基础研究专项课题(理工A类)(15LGA016)

### A Sparse Signal Reconstruction Algorithm Based on Approximate l\-0 Norm

Nie Dongdong,Gong Yaoling

1. (College of Science, Yanshan University, Qinhuangdao, Hebei 066004)
• Online: 2018-05-01

Abstract: The signal reconstruction algorithm is the key to compressed sensing. Signal reconstruction based on approximate l\-0 norm chooses a continuous function to estimate l\-0 norm, thus the minimization problem of l\-0 norm is transformed into an optimization problem of a smooth function. It is critical for the signal reconstruction algorithm to select the appropriate smooth function and optimization algorithm. To improve the accuracy of the sparse signal recovered in the compression sense, the sum of a simple fractional function is proposed to approximate l\-0 norm on the basis of previous work in the paper. Then the sparse solution of an unconstrained optimization problem of the function is solved by Newton iterative algorithm, which effectively integrated the advantages of the fast convergence of approximate l\-0 norm algorithm and the high precision of Newton iteration algorithm. Thus, the minimization of l\-0 norm is approximated smoothly and efficiently within less time. The performance of the proposed algorithm is tested and compared with some existing similar algorithms in the case of different compression ratio, sparseness and noise levels in the simulation experiments. Simulation results show that the performance of the proposed algorithm is better than the existing similar algorithms, and the precision of reconstructed signal is greatly improved, which improves the signal recovery quality in compressed sensing effectively under the same conditions.