电子学报 ›› 2016, Vol. 44 ›› Issue (4): 780-787.DOI: 10.3969/j.issn.0372-2112.2016.04.005

• 学术论文 • 上一篇    下一篇

联合稀疏信号恢复的贪婪增强贝叶斯算法

王友华1,2, 张建秋1   

  1. 1. 复旦大学电子工程系, 上海 200433;
    2. 模拟集成电路重点实验室, 重庆 400060
  • 收稿日期:2014-08-18 修回日期:2014-12-14 出版日期:2016-04-25
    • 作者简介:
    • 王友华 男,1981年生,重庆人.2011年进入复旦大学电子工程系,现为博士生,从事压缩感知信号恢复,混合信号集成电路设计等工作. E-mail:wangyouhua@fudan.edu.cn;张建秋 男,1962年生于湖南隆回县,现任复旦大学电子工程系教授、博士生导师、IEEE高级会员,主要研究领域有信息处理理论及其在测量和仪器、新型传感器、控制和通信中的应用. E-mail:jqzhang01@fudan.edu.cn
    • 基金资助:
    • 国家自然科学基金 (No.61171127,No.61571131); 模拟集成电路重点实验室基金 (No.9140C090110130C09003)

A Greedy Refinement Bayesian Approach to Joint Sparse Signal Recovery

WANG You-hua1,2, ZHANG Jian-qiu1   

  1. 1. Department of Electronic Engineering, Fudan University, Shanghai 200433, China;
    2. Science and Technology on Analog Integrated Circuits Laboratory, Chongqing 400060, China
  • Received:2014-08-18 Revised:2014-12-14 Online:2016-04-25 Published:2016-04-25
    • Supported by:
    • National Natural Science Foundation of China (No.61171127, No.61571131); Fund of State Key Laboratory of Analog Integrated Circuits (No.9140C090110130C09003)

摘要:

本文针对联合稀疏信号恢复问题,提出了一种贪婪增强贝叶斯算法.算法首先利用联合稀疏的特点对信号进行建模,然后在贝叶斯框架下,提出一种贪婪推理方式对信号恢复问题进行迭代求解.在迭代过程中,提出算法利用贝叶斯估计的方差信息来增强支撑恢复的结果,极大地提高了算法对信号恢复性能.理论分析表明:提出算法与同步正交匹配追踪算法具有相同的计算复杂度,远低于其他联合稀疏信号恢复算法.提出方法在具有高恢复精度和较低计算复杂度的同时,兼具贝叶斯方法和贪婪算法的优点.数值仿真验证了理论分析的有效性.

关键词: 联合稀疏, 信号恢复, 贪婪算法, 贪婪增强贝叶斯算法

Abstract:

In this paper,a new greedy refinement bayesian approach (GRBA),used to solve the joint sparse signal recovery problem,is proposed.The joint sparse property of signals is first used to model the signals.Based on the model,a greedy Bayesian inference method used to estimate the signals is then presented.In order to enhance the performance of the recovery,the covariance matrix got by the Bayesian inference is utilized to refine the support recovery results in our inference process.The analytical results show that GRBA outperforms the reported algorithms in the literature in terms of both the signal recovery accuracy and computational complexity.It keeps both the advantages of Bayesian methods and greedy methods.Numerical simulations verify the effectiveness of the analytical results.

Key words: joint sparsity, signal recovery, greedy algorithm, greedy refinement Bayesian approach

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