稀疏重构的一种新的加速动量梯度投影法  

A new momentum gradient projection method for sparse reconstruction

作　　者：武高玉 李慧云[2] 

机构地区：[1]河北工业大学理学院,天津300401 [2]河北工业大学控制科学与工程学院,天津300130

出　　处：《河北工业大学学报》2017年第1期59-64,共6页Journal of Hebei University of Technology

基　　金：河北省自然科学基金(A2015202365)

摘　　要：提出了一种新的应用于稀疏信号重构的加速动量梯度投影法.该方法是把负梯度方向与动量项的凸组合作为搜索方向,步长采取滞后最速下降法(LSD)的步长选取规则.与加速动量梯度投影法取固定的学习速率和动量参数不同,该方法是动态地选取动量参数和步长,从而加速了算法的收敛.数值试验表明,与已有求解大规模l1正则化最小二乘问题的一些方法相比较,本文提出的算法无论是在时间上还是在信号重构的质量上都是有竞争力的.A new momentum gradient projection method for sparse reconstruction is proposed by using the convex combination of the negative gradient direction and the momentum term as the search direction, and the same step length selection rule as the lagged steepest decent method. Different from the momentum based gradient projection method with fixed learning rate and momentum parameters, the proposed method employs dynamic selection of momentum parameters and step length, which accelerates its convergence. Experiment results demonstrate that the proposed method outperforms its competitors both in time efficiency and in the quality of signal reconstruction.

关 键 词：动量梯度投影法 滞后最速下降法 L1正则化 信号重构 图像复原 

分 类 号：O224[理学—运筹学与控制论]