基于变步长的正则化回溯自适应追踪算法
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摘要
在压缩感知重构算法中,稀疏度未知及步长大小固定是影响算法精度及运行时间的因素.针对以上不足,本文提出一种基于变步长的正则化回溯自适应追踪算法.该算法首先通过原子匹配测试的方式获得信号的稀疏度估计;将正则化思想和子空间追踪算法的回溯思想相结合,实现原子的二次筛选并筛除不合适的原子;最后,利用变化的步长选择候选集中的原子,帮助完成信号的完整重构.通过仿真实验证明,本文提出的重构算法在重构速度和重构精度上均优于同类算法.
In the compressive sensing reconstruction algorithm,the unknown sparsity and the fixed step-size are the factors that affect the reconstruction accuracy and running time of the algorithm. In viewof the above shortcomings,we propose a regularized backtracking adaptive pursuit algorithm based variable step-size. Firstly,the sparsity of the signal is obtained by the way of atomic matching test. Then we combine the regularization method with the subspace tracking algorithm to achieve the second screening and remove the atoms which are not appropriate. Finally,we use a variable step-size to select atoms in the candidate set so that we can complete the signal reconstruction. The simulation results showthat the proposed algorithm is superior to other algorithms in speed and reconstruction accuracy.
In the compressive sensing reconstruction algorithm,the unknown sparsity and the fixed step-size are the factors that affect the reconstruction accuracy and running time of the algorithm. In viewof the above shortcomings,we propose a regularized backtracking adaptive pursuit algorithm based variable step-size. Firstly,the sparsity of the signal is obtained by the way of atomic matching test. Then we combine the regularization method with the subspace tracking algorithm to achieve the second screening and remove the atoms which are not appropriate. Finally,we use a variable step-size to select atoms in the candidate set so that we can complete the signal reconstruction. The simulation results showthat the proposed algorithm is superior to other algorithms in speed and reconstruction accuracy.
引文
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[12]倪加明,孙钦者,陆家明.一种改进的稀疏度自适应压缩采样匹配追踪算法[J].通信技术,2016,49(8):992-996.Ni Jiaming,Sun Qinzhe,Lu Jiaming.A modified adaptive compressive sampling matching pursuit algorithm[J].Communications Technology,2016,49(8):992-996.(in Chinese)
[13]Tropp J,Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Transactions on Information Theory,2008,53(12):4655-4666.
[14]Gui G,Mehbodniya A,Wan Q,et al.Sparse signal recovery w ith OM P algorithm using sensing measurement matrix[J].Ieice Electron Express,2011,8(5):285-290.
[15]Luo Y,Gui G,Cong X,et al.Sparse estimation based on a new random regularized matching pursuit generalized approximate message passing algorithm[J].Entropy,2016,18(6):207-241.
[16]Candès E,Romberg J.Sparsity and incoherence in compressive sampling[J].Inverse Problems,2006,23(3):969-985.
[17]Luo C,Wu F,Sun J,et al.Efficient measurement generation and pervasive sparsity for compressive data gathering[J].IEEE Transactions on Wireless Communications,2010,9(12):3728-3738.
[18]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 adaptive subspace pursuit algorithm for compressive sampling[J].Acta Electronica Sinica,2010,38(8):1914-1917.(in Chinese)
[2]石光明,刘丹华,高大化,等.压缩感知理论及其研究进展[J].电子学报,2009,37(5):1070-1081.Shi Guangming,Liu Danhua,Gao Dahua,et al.Advances in theory and application of compressed sensing[J].Acta Electronica Sinica,2009,37(5):1070-1081.(in Chinese)
[3]芮国胜,王林,田文飚.一种基于基追踪压缩感知信号重构的改进算法[J].电子测量技术,2010,33(4):38-41.Rui Guosheng,Wang Lin,Tian Wenbiao.Improved algorithm basis pursuit for compressive sensing reconstruction[J].Electronic Measurement Technology,2010,33(4):38-41.(in Chinese)
[4]Tropp J A,Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEETrans on Information Theory,2007,53(12):4655-4666.
[5]Needell D,Vershynin R.Uniform uncertainty principle and signal recovery via regularized orthogonal matching pursuit[J].Foundations of Computational Mathematics,2007,9(3):317-334.
[6]Dai W,Milenkovic O.Subspace pursuit for compressive sensing signal reconstruction[J].IEEE Trans on Information Theory,2009,55(5):2230-2249.
[7]Needell D,Tropp J A.Co Sa MP:Iterative signal recovery from incomplete and inaccurate samples[J].Applied&Computational Harmonic Analysis,2009,26(3):301-321.
[8]Do T T,Lu G,Nguyen N,et al.Sparsity adaptive matching pursuit algorithm for practical compressed sensing[A]Signals,Systems and Computers,2008 42nd Asilomar Conference on[C].Pacific Grove:IEEE,2008.581-587.
[9]Zhao Ruizhen,Ren Xiaoxin,Han Xuelian,et al.An improved sparsity adaptive matching pursuit algorithm for compressive sensing based on regularized backtracking[J].Chinese Journal of Electronics,2012,29(6):580-584.
[10]Bi X,Chen X D,Zhang Y,et al.Variable step size stagew ise adaptive matching pursuit algorithm for image compressed sensing[A].International Conference on Signal Processing,Communication and Computing[C].Kunming:IEEE,2013.1-4.
[11]Yu Z.Variable step-size compressed sensing-based sparsity adaptive matching pursuit algorithm for speech reconstruction[A].Control Conference 2014[C].Nanjing:IEEE,2014.7344-7349.
[12]倪加明,孙钦者,陆家明.一种改进的稀疏度自适应压缩采样匹配追踪算法[J].通信技术,2016,49(8):992-996.Ni Jiaming,Sun Qinzhe,Lu Jiaming.A modified adaptive compressive sampling matching pursuit algorithm[J].Communications Technology,2016,49(8):992-996.(in Chinese)
[13]Tropp J,Gilbert A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Transactions on Information Theory,2008,53(12):4655-4666.
[14]Gui G,Mehbodniya A,Wan Q,et al.Sparse signal recovery w ith OM P algorithm using sensing measurement matrix[J].Ieice Electron Express,2011,8(5):285-290.
[15]Luo Y,Gui G,Cong X,et al.Sparse estimation based on a new random regularized matching pursuit generalized approximate message passing algorithm[J].Entropy,2016,18(6):207-241.
[16]Candès E,Romberg J.Sparsity and incoherence in compressive sampling[J].Inverse Problems,2006,23(3):969-985.
[17]Luo C,Wu F,Sun J,et al.Efficient measurement generation and pervasive sparsity for compressive data gathering[J].IEEE Transactions on Wireless Communications,2010,9(12):3728-3738.
[18]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 adaptive subspace pursuit algorithm for compressive sampling[J].Acta Electronica Sinica,2010,38(8):1914-1917.(in Chinese)