摘要
重构算法是压缩感知理论应用于实际的关键。其中,近似L0范数算法是通过选取一个连续的平滑函数近似逼近L0范数,从而将离散的最小化L0范数问题转为平滑函数求最优值问题。针对现有算法精度不高的缺点,采用了一种逼近程度更高的改进反余切函数族来近似L0范数,并采用修正阻尼牛顿法求解。该算法结合了近似零范数算法的高收敛性和牛顿法的高效寻优,获得了精度较高的重构信号。仿真实验表明,在不同压缩比下,该算法在一维信号重建和二维图像重建的过程中,较SL0算法、NSL0算法和AL0算法的信噪比和重构精度都有了较大的提升,提高了同等条件下信号恢复的质量,有效地改善了重建效果。
Reconstruction algorithm is the key to the application of compression perception theory in practice.The approximate L0 norm algorithm is to approximate the L0 norm by selecting a continuous smoothing function,so that the discrete minimization L0 norm problem can be transformed into the smoothing function to find the optimal value problem.In view of the shortcomings that the low accuracy of existing algorithms,a family of improved inverse cotangent functions with used to approximate the L0 norm,and the modified damping Newton method is used to solve the problem.This algorithm combines the high convergence of the approximate zero norm algorithm and the efficient optimization of Newton′s method to obtain the reconstructed signal with high precision.Simulation experiments show that the signal-to-noise ratio and reconstruction accuracy of the algorithm under different compression ratios,whether in one-dimensional signal reconstruction or two-dimensional image reconstruction,are greatly improved,when compared with the SL0 algorithm(Smoothed L0 Norm),NSL0 algorithm(Smoothed L0 Norm and Revised Newton Method)and AL0(Approximate L0 Norm)algorithm,which improves the quality of signal recovery under the same conditions and effectively improve the reconstruction effect.
作者
卢建宏
刘海鹏
王蒙
陶亮
董士谦
LU Jianhong;LIU Haipeng;WANG Meng;TAO Liang;DONG Shiqian(School of information engineering and automation,Kunming University of Science and Technology,Kunming,Yunnan 650500,China;Huanenglancang River Hydropower Inc,Kunming University of Science and Technology,Kunming,Yunnan 650500,China)
出处
《光电子．激光》
CAS
CSCD
北大核心
2021年第6期595-601,共7页
Journal of Optoelectronics·Laser
基金
国家自然科学基金项目(61563025)项目名称:视觉场景中群体互动轨迹的流形向量场学习与异常判别研究资助项目。
关键词
压缩感知理论
信号重建
修正牛顿法
L0范数
compression sensing theory
signal reconstruction
revised newton method
L0 norm
