lp范数约束的去冲击干扰优化算法

doi:10.19665/j.issn1001-2400.2020.01.005

西安电子科技大学学报 ›› 2020, Vol. 47 ›› Issue (1): 30-36.doi: 10.19665/j.issn1001-2400.2020.01.005

l_p范数约束的去冲击干扰优化算法

黎力^1,²,闫利¹,周磊³(),李东⁴,刘宏清³

^1. 武汉大学测绘学院,湖北武汉 430072
^2. 重庆市自然资源安全调度中心,重庆401147
^3. 重庆邮电大学通信与信息工程学院,重庆 400065
^4. 重庆大学通信和跟踪遥测指挥中心,重庆400044

收稿日期:2019-07-29 出版日期:2020-02-20 发布日期:2020-03-19
作者简介:黎力(1982—),男,高级工程师,E?mail: llywhu@whu.edu.cn
基金资助:
重庆市规划和自然资源局科技项目(KJ-2019038);重庆市技术创新与应用示范专项基金(CSTC2018JSCX-MSZDX0074)

l_p-norm regularization optimization of impulsive disturbance removal

LI Li^1,²,YAN Li¹,ZHOU Lei³(),LI Dong⁴,LIU Hongqing³

^1. School of Geodesy and Geomatics, Wuhan University, Wuhan 430072, China
^2. Chongqing Natural Resources Safety Dispatch Center, Chongqing 401147, China
^3. School of Communication and Information Engineering, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
^4. Center of Communication and Tracking Telemetering Command, Chongqing University, Chongqing 400044, China

Received:2019-07-29 Online:2020-02-20 Published:2020-03-19

摘要/Abstract

摘要：

为解决在冲击干扰下信号的恢复问题,提出了一种利用l_p范数约束的优化算法。因为l_p(0<p<1)范数约束的引入会导致提出的优化模型退化为难以求解的非凸优化问题, 因此利用交替方向乘子法来有效解决该优化问题。文中分别利用迭代重加权最小二乘法和内点法求得了优化问题中对应优化变量的迭代方程, 并将该算法用于图像增强。数值仿真结果说明了相比于l_p-ADM算法,加权l_p范数约束优化算法有更好的恢复性能。

关键词: 冲击干扰, l_p范数, 非凸问题, 迭代重加权, 内点法

Abstract:

This work addresses the signal recovery problem in the presence of impulsive disturbance utilizing l_p-norm optimization. In doing so, the resultant optimization is difficult to solve, especially when 0<p< 1, because it is nonconvex. In this work, the alternating direction method for multipliers steps is developed to efficiently obtain the solution from this optimization. In each step of the alternating direction method for multipliers, the corresponding solutions are respectively obtained by utilizing the iteratively reweighted least squares and interior-point approach. Numerical studies including an application of image enhancement demonstrate the superior performance of the proposed weighted estimation algorithms compared to the l_p-ADM approach.

Key words: impulsive disturbance, l_p-norm, nonconvex, iteratively reweighted least squares, interior-point method

中图分类号:

TN911.72

黎力,闫利,周磊,李东,刘宏清. l_p范数约束的去冲击干扰优化算法[J]. 西安电子科技大学学报, 2020, 47(1): 30-36.

LI Li,YAN Li,ZHOU Lei,LI Dong,LIU Hongqing. l_p-norm regularization optimization of impulsive disturbance removal[J]. Journal of Xidian University, 2020, 47(1): 30-36.

图/表 5

表1

仿真实验参数设置"

参数名称	初始化	更新方法
式(10)中的惩罚项参数ρ	ρ₀=1	$ρ l + 1 = 1.01 ρ l 直到 ρ max = 6$
式(10)中的平滑参数ε	ε₀=5	$ε l + 1 = min {ε l, γ · d (x l + 1) χ + 1}$
衰减系数γ	γ∈(0,1)	常数用于衰减ε
信号稀疏度水平χ	χ取x维数的一半
运算操作符d(·)		将x中的元素递减排列

表1

图1

图2

图3

图4

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l_p范数约束的去冲击干扰优化算法

l_p-norm regularization optimization of impulsive disturbance removal

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lp范数约束的去冲击干扰优化算法

lp-norm regularization optimization of impulsive disturbance removal

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l_p范数约束的去冲击干扰优化算法

l_p-norm regularization optimization of impulsive disturbance removal