冲击噪声下任意稀疏结构的MMV重构算法
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摘要
针对现有多测量向量(multiple measurement vectors,MMV)模型稀疏重构算法在冲击噪声背景下存在的鲁棒性不强、适用性不广等问题,本文提出了一种冲击噪声下任意稀疏结构的MMV模型(ASS-MMV)稀疏重构算法。该算法利用Lorentzian范数和矩阵平滑零范数正则化构造稀疏优化目标函数,建立冲击噪声背景下ASS-MMV重构模型;结合固定步长公式和具有充分下降性质的共轭梯度算法,在统一参数框架下并行重构,以提高算法收敛速度和运行效率。仿真结果表明:本文算法能够在冲击噪声背景下高质量的重构任意稀疏结构的MMV信号,对噪声具有一定的鲁棒性,并且收敛速度较快、计算开销更小。
A novel sparse signal recovery algorithm on multiple measurement vectors of arbitrary sparse structure( ASS-MMV) with impulsive noise was proposed to deal with the robustness and universality issues within most existing sparse signal recovery algorithms. In the beginning,the objective function for sparse optimization was built based on smoothed L0-norm constrained Lorentzian norm regularization,and the ASS-MMV recovery model was set up in the presence of impulsive noise. After that,a parallel recovery which speeds up the convergence and improves the operating efficiency was implemented in a unified parametric framework by combining the fixed-step formula and the conjugate gradient algorithm with sufficient decent property. Simulation results demonstrate that the proposed algorithm can effectively recover the MMV signal with arbitrary sparse structure in impulsive noise environment. It is also proved that the proposed algorithm has faster recovery speed and less computing cost,but better robustness against the noise.
A novel sparse signal recovery algorithm on multiple measurement vectors of arbitrary sparse structure( ASS-MMV) with impulsive noise was proposed to deal with the robustness and universality issues within most existing sparse signal recovery algorithms. In the beginning,the objective function for sparse optimization was built based on smoothed L0-norm constrained Lorentzian norm regularization,and the ASS-MMV recovery model was set up in the presence of impulsive noise. After that,a parallel recovery which speeds up the convergence and improves the operating efficiency was implemented in a unified parametric framework by combining the fixed-step formula and the conjugate gradient algorithm with sufficient decent property. Simulation results demonstrate that the proposed algorithm can effectively recover the MMV signal with arbitrary sparse structure in impulsive noise environment. It is also proved that the proposed algorithm has faster recovery speed and less computing cost,but better robustness against the noise.
引文
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[3]ELDAR Y C,MISHALI M.Robust recovery of signals from a structured union of subspaces[J].IEEE transactions on information theory,2009,55(11):5302-5316.
[4]FANG Hao,VOROBYOV S A,JIANG Hai,et al.Permutation meets parallel compressed sensing:how to relax restricted isometry property for 2D sparse signals[J].IEEE transactions on signal process,2014,62(7):196-210.
[5]ELDAR Y C,RAUHUT H.Average case analysis of multichannel sparse recovery using convex relaxation[J].IEEE transactions on information theory,2010,56(1):505-519.
[6]TANG G,NEHORAI A.Performance analysis for sparse support recovery[J].IEEE transactions on information theory,2010,56(3):1383-1399.
[7]SUN L,LIU J,CHEN J,et al.Efficient recovery of jointly sparse vectors[C]//Advances in Neural Information Processing Systems.Vancouver,British Columbia,Canada,2009:1812-1820.
[8]韩学兵,张颢.模型噪声中的稀疏恢复算法研究[J].电子与信息学报,2012,34(8):1813-1818.HAN Xuebing,ZHANG Hao.Research of sparse recovery algorithm based on model noise[J].Journal of electronics&information technology,2012,34(8):1813-1818.
[9]PENG Xiyuan,ZHANG Miao,ZHANG Jingchao,et al.An alternative recovery algorithm based on SL0 for multiband signals[C]//Instrumentation and Measurement Technology Conference(I2MTC),2013 IEEE International.IEEE,2013:114-117.
[10]WIPF D P,RAO B D.An empirical bayesian strategy for solving the simultaneous sparse approximation problem[J].IEEE transactions on signal processing,2007,55(7):3704-3716.
[11]李少东,陈文峰,杨军,等.任意稀疏结构的多量测向量快速稀疏重构算法研究[J].电子学报,2015,43(4):708-715.LI Shaodong,CHEN Wenfeng,YANG Jun,et al.Study on the fast sparse recovery algorithm via multiple measurement vectors of arbitrary sparse structure[J].ACTA electronica sinica,2015,43(4):708-715.
[12]代林,崔琛,余剑,等.冲击噪声下基于Lorentzian范数的CSR参数估计[J].华中科技大学学报:自然科学版,2015(7):66-71.DAI Lin,CUI Chen,YU Jian,et al.Parameter estimation for CSR under inpulsive noise based on Lorentzian norm[J].Journal of Huazhong University of Science and Technology:natural science edition,2015(7):66-71.
[13]CANDES E,TAO T.The Dantzig selector:statistical estimation when is much larger than n[J].Annals of statistics,2007,35:2313-2351.
[14]CARRILLO R E,BARNER K E,AYSAL T C.Robust sampling and reconstruction methods for sparse signals in the presence of impulsive noise[J].IEEE transactions on selected topics in signal processing,2010,4(2):392-408.
[15]HUANG Jinhong,ZHOU Genjiao.A conjugate gradient method without line search and the convergence analysis[C]//2013 Fourth International Conference on Emerging Intelligent Data and Web Technologies.Xi'an,China,2013:734-736.