北京航空航天大学学报 ›› 2017, Vol. 43 ›› Issue (7): 1336-1347.doi: 10.13700/j.bh.1001-5965.2016.0518

• 论文 • 上一篇    下一篇

电路测试响应信号的GP-KSVD稀疏重构算法

聂静1, 苏东林1, 李红裔2, 赵迪2   

  1. 1. 北京航空航天大学 电子信息与工程学院, 北京 100083;
    2. 北京航空航天大学 数学与系统科学学院, 北京 100083
  • 收稿日期:2016-06-15 修回日期:2016-09-21 出版日期:2017-07-20 发布日期:2016-12-13
  • 通讯作者: 赵迪,E-mail:zdzz@buaa.edu.cn E-mail:zdzz@buaa.edu.cn
  • 作者简介:聂静 女,博士研究生。主要研究方向:系统级电磁兼容性评估;苏东林 女,博士,教授,博士生导师。主要研究方向:系统级电磁兼容;李红裔 女,博士,教授,博士生导师。主要研究方向:矩阵理论与应用、多复变与几何;赵迪 男,博士,教授,博士生导师。主要研究方向:矩阵理论与应用、多复变与几何。
  • 基金资助:
    国家自然科学基金(61379001)

Circuitry test response signal reconstruction based on GP-KSVD algorithm

NIE Jing1, SU Donglin1, LI Hongyi2, ZHAO Di2   

  1. 1. School of Electronic and Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
    2. School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
  • Received:2016-06-15 Revised:2016-09-21 Online:2017-07-20 Published:2016-12-13
  • Supported by:
    National Natural Science Foundation of China (61379001)

摘要: 电路系统测试响应信号具有周期性强、分布较稀疏的特点,针对电路系统测试响应信号的压缩重构问题进行了研究,提出了基于梯度方向追踪的K奇异值分解(GP-KSVD) 稀疏重构算法。结合单一响应信号以及混合信号其自身特点进行字典训练,利用更新后字典对含噪信号进行梯度追踪稀疏表征,通过对含噪信号的重构,实现了去噪的目的,算法计算复杂度低,储存量小,具有较好的重构效果。仿真中将GP-KSVD表征与使用随机字典、离散余弦字典(DCT)的表征进行比较,从信噪比(SNR)以及相对均方误差(RMSE)2项指标中得出使用KSVD字典具有更好的重构去噪效果;此外将GP-KSVD稀疏重构算法与正交匹配追踪正交匹配追踪(OMP)-KSVD、预处理共轭梯度追踪(PCGP)算法进行比较,得出GP-KSVD的计算时间最短、重构精度更高的结论,并且进行了实测验证。算法可用来对测试响应信号进行预处理,为电路系统设备性能的评估分析提供了理论依据。

关键词: 压缩感知, GP-KSVD, 稀疏表征, 电路测试响应信号重构, 去噪

Abstract: Response signals in circuitry system always have the characteristics of high periodicity and sparse distribution. In order to realize response signals reconstruction in circuitry system, an algorithm combining gradient pursuit and K singular value decomposition (GP-KSVD) was proposed. Dictionary was trained according to the features of single and mixed signal. Making use of the updated dictionary and gradient pursuit to sparse representation on noisy signal, the reconstruction achieves the aim of de-noising. The algorithm has excellent reconstruction results with low computing complexity and storage capacity. In simulation, GP-KSVD dictionary was compared with both random and discrete cosine dictionary (DCT) dictionary, and the results show that the denoising effect of sparse representation with KSVD dictionary is the best depending on the indices of signal to noise ratio (SNR) and root mean square error (RMSE). GP-KSVD sparse representation was compared with orthogonal matching pursuit(OMP)-KSVD and preconditioning conjugate gradient pursuit(PCGP) algorithms. The simulation results prove that GP-KSVD has the minimum computer running time and the highest reconstruction precision, and the measurement verification proves the universality of the algorithm. This algorithm can be applied to response signal preprocessing, which provides theoretical basis for circuitry system equipment performance evaluation analysis.

Key words: compressive sensing, (GP-KSVD), sparse representation, circuitry test response signal reconstruction, denoising

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