基于小波框架方法的信号重构  

A wavelet frame based approach for signal reconstruction

作　　者：杨建斌[1] 陶薪竹 YANG Jian-bin;TAO Xin-zhu(College of Science, Hohai University, Nanjin 211100, China)

机构地区：[1]河海大学理学院

出　　处：《高校应用数学学报（A辑）》2019年第3期364-372,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11771120);中央高校基本科研业务费(2018B19614;B190190305)

摘　　要：从含有噪音的离散样本中恢复连续信号是一个基本问题,它在信号,图像处理,医学工程,控制等领域发挥着重要作用.提出了一个基于小波框架方法的信号重构模型,并运用增广Lagrangian乘子法和加速近端梯度法来求解该模型,从而从混合或未知类型噪音的离散样本中恢复连续信号.进一步,给出了重构模型解的L2范数误差分析.最后通过数值实验,从噪音样本中恢复连续信号,突出模型的有效性.Recovering analog signals from noisy samples is a fundamental problem,which plays an important role in signal and image processing,medical engineering,control theory,etc.This paper proposes a wavelet frame based model for recovering signals from discrete samples with mixed or unknown noises,and applies the augmented Lagrangian multiplier and accelerated proximal gradient methods to solve the model.Furthermore,an error analysis of the reconstruction model is given.In the end,numerical experiments for recovering functions from noisy samples are performed to demonstrate the effectiveness of the method.

关 键 词：小波分析 信号重构 增广Lagrangian乘子法 加速近端梯度法 

分 类 号：O174.4[理学—数学]