平滑零范数稀疏度约束下的盲稀疏回溯重构算法
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摘要
现有的回溯迭代类算法具有重构速度快、精度高等优点,但实际中其需要已知信号稀疏度的条件有时难以满足。针对以上不足,提出了一种基于平滑零范数稀疏度约束的盲稀疏回溯重构算法,并证明了其收敛性。该算法不需已知稀疏度先验,在截断过程中以平滑零范数来估计信号的稀疏度并确定支撑集。新算法继承了现有回溯迭代类算法的有效性,同时避免了因稀疏度未知或估计不足导致的重构失败。理论分析和实验表明,新算法在无需信号稀疏度先验的条件下,重构性能优于现有典型回溯迭代类算法。
The existing back-track iterative reconstruction algorithms for reconstructing the original signal fast and well always require the prior information of signal sparsity for accurate recovery.But sometimes it's hard to meet the requirement in practice.Aiming at this problem,a new blind sparsity back-track reconstruction algorithm based on smooth 0-norm constraint is proposed and its convergence is demonstrated.The new algorithm does not need the sparse prior and the smooth 0-norm issued to estimate the sparsity of signal and determine the support set in the truncation process.The new algorithm is effective as other back-track ones and is able to avoid recovery failure due to unknown or underestimated sparsity as well.The theoretical analysis and experiment simulation prove that the performance of the new algorithm is better than that of the existing back-track iterative reconstruction algorithms in the sparsity unknown conditions.
The existing back-track iterative reconstruction algorithms for reconstructing the original signal fast and well always require the prior information of signal sparsity for accurate recovery.But sometimes it's hard to meet the requirement in practice.Aiming at this problem,a new blind sparsity back-track reconstruction algorithm based on smooth 0-norm constraint is proposed and its convergence is demonstrated.The new algorithm does not need the sparse prior and the smooth 0-norm issued to estimate the sparsity of signal and determine the support set in the truncation process.The new algorithm is effective as other back-track ones and is able to avoid recovery failure due to unknown or underestimated sparsity as well.The theoretical analysis and experiment simulation prove that the performance of the new algorithm is better than that of the existing back-track iterative reconstruction algorithms in the sparsity unknown conditions.
引文
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[4]杨萌,张弓.基于CS的SAR图像自动目标分割算法[J].宇航学报.2011,32(12):2575-2581.[Yang Meng,ZhangGong.Automatic target segmentation in SAR images using CS[J].Journal of Astronautics,2011,32(12):2575-2581.]
[5]韦顺军,张晓玲.基于压缩传感的线阵SAR三维成像方法研究[J].宇航学报,2011,32(11):2403-2409.[Wei Shun-jun,Zhang Xiao-ling.Linear array SAR 3-D imaging based oncompressed sensing[J].Journal of Astronautics,2011,32(11):2403-2409.]
[6]贺亚鹏,李洪涛,王克让,等.基于压缩感知的高分辨DOA估计[J].宇航学报,2011,32(6):1344-1349.[He Ya-peng,Li Hong-tao,Wang Ke-ang,et al.Compressive sensing basedhigh resolution DOA estimation[J].Journal of Astronautics,2011,32(6):1344-1349.]
[7]何劲,张群,杨小优,等.基于压缩感知理论的合成孔径激光雷达成像算法[J].宇航学报,2011,32(11):2395-2402.[He Jin,Zhang Qun,Yang Xiao-you,et al.SAL imagingalgorithm based on compressed sensing theory[J].Journal ofAstronautics,2011,32(11):2395-2402.]
[8]Dai W,Milenkovic O.Subspace pursuit for compressive sensingsignal reconstruction[J].IEEE Trans.on Information Theory,2009,55(5):2230-2249.
[9]Needell D,Tropp J A.CoSaMP:Iterative signal recovery fromincomplete and inaccurate samples[J].Communications of theACM,2010,53(12):93-100.
[10]张宗念,黄仁泰,闫敬文.压缩感知信号盲稀疏度重构算法[J].电子学报,2011,39(1):18-22.[Zhang Zong-nian,Huang Ren-tai,Yan Jing-wen.A blind sparsity reconstructionalgorithm for compressed sensing signal[J].Acta ElectronicaSinica,2011,39(1):18-22.]
[11]杨成,冯巍,冯辉,等.一种压缩采样中的稀疏度自适应子空间追踪算法[J].电子学报,2010,38(8):1914-1917.[Yang Cheng,Feng Wei,Feng Hui,et al.A sparsity adaptivesubspace pursuit algorithm for compressive sampling[J].ActaElectronica Sinica,2010,38(8):1914-1917.]
[12]Do T T,Gan L,Nguyen N S.Sparsity adaptive matching pursuitalgorithm for practical compressed sensing[C].AsilomarConference on Signals,Systems and Computers,Pacific Grove,California,2008.
[13]Huang H,Makur A.Backtracking-based matching pursuitmethod for sparse signal reconstruction[J].IEEE SignalProcessing Letters,2011,18(7):391-394.
[14]Mohimani H,Babaie-Zadeh M,Jutten C.A fast approach forovercomplete sparse decomposition based on smoothed0 norm[J].IEEE Transactions on Signal Processing,2009,57(1):289-301.
[15]Mohimani G,Babaie-Zadeh M,Jutten C.Fast sparse representationbased on smoothed0 norm[J].Independent Component Analysisand Signal Separation,2007:389-396.
[16]Chen S S,Donoho D L,Saunders M A.Atomic decomposition bybasis pursuit[J].SIAM Journal on Scientific Computing,1998,20(1):33-61.
[17]Candès E J.The restricted isometry property and its implicationsfor compressed sensing[J].Compte Rendus de l'Academie desSciences,2008,Series I(346):589-592.
[18]李小波.基于压缩感知的测量矩阵研究[D].北京:北京交通大学,2010.[Li Xiao-bo.Research on measurement matrixbased on compressed sensing[D].Beijing:Beijing JiaotongUniversity,2010.]