基于选择性测量的压缩感知去噪重构算法

裴立业; 江桦; 麻曰亮

doi:10.11959/j.issn.1000-436x.2017033

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基于选择性测量的压缩感知去噪重构算法

学术论文 | 更新时间：2024-06-05

- 基于选择性测量的压缩感知去噪重构算法
- Denoising recovery for compressive sensing based on selective measure
- 通信学报 2017年38卷第2期页码：106-114
- 作者机构：
  
  解放军信息工程大学，河南郑州 450001
- 作者简介：
  
  [ "裴立业（1987-），男，河北石家庄人，解放军信息工程大学博士生，主要研究方向为通信信号处理、频谱感知。" ]
  [ "江桦（1956-），男，江苏南通人，解放军信息工程大学教授、博士生导师，主要研究方向为通信信号处理、认知无线电。" ]
  [ "麻曰亮（1992-），男，吉林长春人，解放军信息工程大学硕士生，主要研究方向为压缩感知、信号检测。" ]
- 基金信息：
  
  国家自然科学基金资助项目(61401511)
- DOI：10.11959/j.issn.1000-436x.2017033
  中图分类号： TN911.72
- 网络出版日期：2017-02，
  
  纸质出版日期：2017-02-25
- 稿件说明：
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裴立业, 江桦, 麻曰亮. 基于选择性测量的压缩感知去噪重构算法[J]. 通信学报, 2017,38(2):106-114.

Li-ye PEI, Hua JIANG, Yue-liang MA. Denoising recovery for compressive sensing based on selective measure[J]. Journal on communications, 2017, 38(2): 106-114.
裴立业, 江桦, 麻曰亮. 基于选择性测量的压缩感知去噪重构算法[J]. 通信学报, 2017,38(2):106-114. DOI： 10.11959/j.issn.1000-436x.2017033.

Li-ye PEI, Hua JIANG, Yue-liang MA. Denoising recovery for compressive sensing based on selective measure[J]. Journal on communications, 2017, 38(2): 106-114. DOI： 10.11959/j.issn.1000-436x.2017033.

摘要

针对压缩感知中噪声折叠现象严重影响稀疏信号重构性能的问题，提出一种基于选择性测量的压缩感知去噪重构算法。首先从理论上解释了压缩感知中噪声折叠现象；然后提出一种基于测量数据的特征统计量，推导分析其概率密度函数，并基于此构造一种噪声滤波矩阵，用于优化测量矩阵，实现智能地选择信号分量、过滤噪声分量，提高测量数据信噪比；最后，通过增加测量数据获取次数可进一步提升算法重构性能。仿真实验表明，基于选择性测量的压缩感知去噪重构算法明显改善了低信噪比条件下信号的重构性能。

Abstract

In order to reduce the effect of noise folding (NF) phenomenon on the performance of sparse signal recon-struction

a new denoising recovery algorithm based on selective measure was proposed.Firstly

the NF phenomenon in compressive sensing (CS) was explained in theory.Secondly

a new statistic based on compressive measurement data was proposed

and its probability density function (PDF) was deduced and analyzed.Then a noise filter matrix was constructed based on the PDF to guide the optimization of measurement matrix.The optimized measurement matrix can selectively sense the sparse signal and suppress the noise to improve the SNR of the measurement data

resulting in the improvement of sparse reconstruction performance.Finally

it was pointed out that increasing the measurement times can further enhance the performance of denoising reconstruction.Simulation results show that the proposed denoising recon-struction algorithm has a better improvement in the performance of reconstruction of noisy signal

especially under low SNR.

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Keywords

references

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