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Block Sparse Signal Reconstruction Algorithm Based on Improved Smoothed l0 Norm

QI Rui 1a,2,LI Hongwei 1b,ZHANG Yujie 1b   

  1. (1a.Institute of Geophysics and Geomatics; 1b.School of Mathematics and Physics,China University of Geosciences,Wuhan 430074,China; 2.School of Science,Naval University of Engineering,Wuhan 430033,China)
  • Received:2014-10-28 Online:2015-11-15 Published:2015-11-13

基于改进光滑l0范数的块稀疏信号重构算法

祁锐 1a,2,李宏伟 1b,张玉洁 1b   

  1. (1.中国地质大学 a.地球物理与空间信息学院; b.数学与物理学院,武汉 430074;2.海军工程大学理学院,武汉 430033)
  • 作者简介:祁锐(1981-),男,讲师、博士研究生,主研方向:盲信号处理,压缩感知;李宏伟,教授、博士;张玉洁,讲师、博士。
  • 基金资助:

    国家自然科学基金资助项目(61071188);中央高校基本科研业务费专项基金资助项目(CUGL130247);海军工程大学青年基金资助项目(HGDQNEQJJ15004)。

Abstract: Smoothed l0 norm(SL0) algorithm utilizes a sequence of smoothed Gaussian function with parameter to approximate the l0 norm,which can be used efficiently for the compressive sensing reconstruction.Block-sparse signal is a typical sparse signal whose non-zero coefficients occur in a few blocks.This paper proposes a block sparse signal reconstruction based on improved SL0 algorithm with respect to the block sparse signals.The smoothed Gaussian function is substituted by inverse tangent function,and the convergence equality is further improved by optimizing the decreasing factor.Simulation results show that,compared with Block Smoothed l0 Norm(BSL0) algorithm,Smoothed l0 Norm(SL0) algorithm,and Orthogonal Matching Pursuit(OMP) algorithm,the proposed method has better robustness and higher Signal to Noise Ratio(SNR).

Key words: compressive sensing, block-sparse, Smoothed l0 Norm(SL0), signal reconstruction

摘要: 光滑l0范数算法用带参数的高斯光滑函数序列逼近l0范数,可以用于压缩感知信号重构。块稀疏信号是一种典型的稀疏信号,它的非零元素成块出现。为此,基于改进的光滑l0范数提出一种块稀疏信号重构算法。利用反正切函数取代高斯函数序列,通过对下降因子的 优化处理进一步提高收敛效果。仿真实验结果表明,相比块光滑l0范数算法、光滑l0范数算法以及正交匹配追踪算法,该算法具有更好的鲁棒性和更高的信噪比。

关键词: 压缩感知, 块稀疏, 光滑l0范数, 信号重构

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