压缩感知后引入噪声的信号恢复

胡辽林; 王斌; 薛瑞洋

doi:10.3788/OPE.20142210.2840

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压缩感知后引入噪声的信号恢复

信息科学 | 更新时间：2020-08-13

- 压缩感知后引入噪声的信号恢复
- Signal recovery of noise introduced after compressed sensing
- 光学精密工程 2014年22卷第10期页码：2840-2846
- 作者机构：
  
  西安理工大学机械与精密仪器工程学院,陕西西安,710048
- 作者简介：
- 基金信息：
  
  陕西省自然科学基金资助项目(No.1014JM7273)()
- DOI：10.3788/OPE.20142210.2840
  中图分类号： TP391.4
- 收稿日期：2014-03-04，
  
  修回日期：2014-04-08，
  
  纸质出版日期：2014-10-25
- 稿件说明：
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胡辽林, 王斌, 薛瑞洋. 压缩感知后引入噪声的信号恢复[J]. 光学精密工程, 2014,22(10): 2840-2846

HU Liao-lin, WANG Bin, XUE Rui-yang. Signal recovery of noise introduced after compressed sensing[J]. Editorial Office of Optics and Precision Engineering, 2014,22(10): 2840-2846
胡辽林, 王斌, 薛瑞洋. 压缩感知后引入噪声的信号恢复[J]. 光学精密工程, 2014,22(10): 2840-2846 DOI： 10.3788/OPE.20142210.2840.

HU Liao-lin, WANG Bin, XUE Rui-yang. Signal recovery of noise introduced after compressed sensing[J]. Editorial Office of Optics and Precision Engineering, 2014,22(10): 2840-2846 DOI： 10.3788/OPE.20142210.2840.

摘要

将压缩感知后引入噪声的信号恢复作为研究对象

建立了信号恢复模型

以解决工程领域中广泛存在的噪声问题.由于传统的算法无法实现压缩后引入噪声的信号恢复

本文提出了用阈值收缩迭代算法来实现含噪信号的恢复.分析了算法原理

对压缩感知后加入高斯随机噪声、5%和10%密度的脉冲噪声分别进行了信号恢复仿真

并与正交匹配追踪(OMP)算法和平行坐标下降(PCD)算法进行了比较.结果表明

阈值收缩迭代算法对无噪稀疏信号基本可以做到完全恢复;对压缩后含噪信号的恢复具有较强的鲁棒性

只在峰值处出现了较明显的误差

通过增加测量矩阵行数和迭代次数可以提高抗噪性能.实验显示:本算法在处理高斯噪声和低密度脉冲噪声时具有明显优势

在处理高密度脉冲噪声时略优于另两种算法.

Abstract

To explore the signal recovery of a noisy image after compressed sensing

a signal recovery model was established to solve the noise problems in engineering applications. As traditional greedy algorithm can not recover the signals added into noise after compressed sensing

this paper proposes an iterative shrinkage-thresholding method to implement the signal recovery. Details of this algorithm were analyzed

and the signal recovery of noise after compressed sensing which contains Gaussian noise and 10% impulse noise

5% impulse noise was simulated. Then

it was compared with the Orthogonal Matching Pursuit(OMP) and the Parallel Coordinate Descent (PCD) algorithms. Simulation results show that this proposed method completely recovers noise-free sparse signal. It has a strong robustness for recovering signal with noise after compressed sensing

and the recovery error occurs mainly at the peak .It is also worth mentioning that increasing the number of measurement rows and iterations is able to enhance the anti-noise performance of this method. The result also indicates that this algorithm shows excellent characteristics when the Gaussian noise and low-desity impulse noise are processed

but has no many advantages while dealing with high-density impulse noise.

关键词

Keywords

references

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