基于修正近似双曲正切函数的平滑l_0范数算法
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摘要
针对SL0算法中高斯函数对l_0范数的逼近程度较差以及在算法迭代过程中存在"锯齿效应"的问题,提出一种基于修正近似双曲正切函数的平滑l_0范数算法。采用逼近性能更优的修正近似双曲正切函数近似l_0范数,建立基于此函数的稀疏问题模型,利用牛顿法对其进行求解,能够以较高的精度重构出稀疏信号。仿真结果表明,相比于SL0算法、NSL0(newton smoothed l_0norm,NSL0)算法以及ASL0(approximate smoothed l_0norm,ASL0)算法,所提算法能获得更优的重构性能。
Aiming at the poor approximation performance of Gauss functions and the problem of jagged phenomenon during the iterative process,a smoothed l_0 norm algorithm based on modified approximate hyperbolic tangent function was proposed.A modified approximate hyperbolic tangent function with better approximation performance was proposed to approximate the l_0 norm.A sparse problem based on the function was established.A Newton method was utilized to solve the extreme value problem.The accurate reconstruction of sparse signal was then realized using the proposed algorithm.Experimental results show that the proposed algorithm is superior to SL0 algorithm,ASL0 algorithm and NSL0 algorithm in terms of the reconstruction performance.
Aiming at the poor approximation performance of Gauss functions and the problem of jagged phenomenon during the iterative process,a smoothed l_0 norm algorithm based on modified approximate hyperbolic tangent function was proposed.A modified approximate hyperbolic tangent function with better approximation performance was proposed to approximate the l_0 norm.A sparse problem based on the function was established.A Newton method was utilized to solve the extreme value problem.The accurate reconstruction of sparse signal was then realized using the proposed algorithm.Experimental results show that the proposed algorithm is superior to SL0 algorithm,ASL0 algorithm and NSL0 algorithm in terms of the reconstruction performance.
引文
[1]Liu J,Zhou W,Juwono FH,et al.Reweighted smoothed l0-norm based DOA estimation for MIMO radar[J].Signal Processing,2017,137(C):44-51.
[2]Juwono FH,Guo Q,Huang D,et al.Impulsive noise detection in PLC with smoothed L0-norm[C]//IEEE International Conferenceon Acoustics,Speech and Signal Processing.IEEE,2015:3232-3236.
[3]Lv J,Huang L,Shi Y,et al.Inverse synthetic aperture radar imaging via modified smoothedl0norm[J].IEEE Antennas&Wireless Propagation Letters,2014,13(6):1235-1238.
[4]LIU Ting,ZHOU Jie.Fast channel estimation for partial sparse multi-path based on SL0algorithm[J].Computer Engineering&Design,2014,35(3):785-790(in Chinese).[刘婷,周杰.基于SL0算法的快速局部稀疏多径信道估计[J].计算机工程与设计,2014,35(3):785-790.]
[5]Shi B,Lian Q,Chen S.Compressed sensing magnetic resonance imaging based on dictionary updating and block-matching and three-dimensional filtering regularization[J].IET Image Processing,2016,10(1):68-79.
[6]Wan P J.Greedy Approximation Algorithms[M]//Handbook of Combinatorial Optimization,2013:1599-1629.
[7]Khajehnejad MA,Xu W,Avestimehr AS,et al.Improving the thresholds of sparse recovery:An analysis of a two-step reweighted basis pursuit algorithm[J].IEEE Transactions on Information Theory,2015,61(9):5116-5128.
[8]Sajjad M,Mehmood I,Abbas N,et al.Basis pursuit denoi-singbased image superresolution using a redundant set of atoms[J].Signal,Image and Video Processing,2016,10(1):181-188.
[9]Fornasier M,Peter S,Rauhut H,et al.Conjugate gradient acceleration of iteratively re-weighted least squares methods[J].Computational Optimization&Applications,2016,65(1):205-259.
[10]Saadat SA,Safari A,Needell D.Sparse reconstruction of regional gravity signal based on stabilized orthogonal matching pursuit(SOMP)[J].Pure&Applied Geophysics,2016,173(6):2087-2099.
[11]Chen J,Zhou Y,Jin L,et al.An adaptive regularized smoothed norm algorithm for sparse signal recovery in noisy environments[J].Signal Processing,2017,135(C):153-157.
[12]Ramli DA,Tan WC.Fast kernel sparse representation classifier using improved smoothed-l0norm[J].Procedia Computer Science,2017,112:494-503.
[13]Zhang Y,Yu J,Bai H,et al.Improved sparse signal reconstruction based on approximate hyperbolic tangent function with smoothedl0norm[J].International Journal of Science,2017,4(2):201-210.
[14]Feng JJ,Zhang G,Wen FQ.MIMO radar imaging based on smoothed l0 norm[J]. Mathematical Problems in Engineering,2015(8):1-10.
[15]Gerdts M,Horn S,Kimmerle SJ.Line search globalization of a semismooth Newton method for operator equations in Hilbert spaces with applications in optimal control[J].Journal of Industrial&Management Optimization,2017,13(1):47-62.
[16]WU Feiyun,ZHOU Yuehai,TONG Feng.A fast sparse signal recovery algorith-m based on approximate l0norm and hybrid optimization[J].Acta Automatica Sinica,2014,40(10):2145-2150(in Chinese).[伍飞云,周跃海,童峰.基于似零范数和混合优化的压缩感知信号快速重构算法[J].自动化学报,2014,40(10):2145-2150.]
[2]Juwono FH,Guo Q,Huang D,et al.Impulsive noise detection in PLC with smoothed L0-norm[C]//IEEE International Conferenceon Acoustics,Speech and Signal Processing.IEEE,2015:3232-3236.
[3]Lv J,Huang L,Shi Y,et al.Inverse synthetic aperture radar imaging via modified smoothedl0norm[J].IEEE Antennas&Wireless Propagation Letters,2014,13(6):1235-1238.
[4]LIU Ting,ZHOU Jie.Fast channel estimation for partial sparse multi-path based on SL0algorithm[J].Computer Engineering&Design,2014,35(3):785-790(in Chinese).[刘婷,周杰.基于SL0算法的快速局部稀疏多径信道估计[J].计算机工程与设计,2014,35(3):785-790.]
[5]Shi B,Lian Q,Chen S.Compressed sensing magnetic resonance imaging based on dictionary updating and block-matching and three-dimensional filtering regularization[J].IET Image Processing,2016,10(1):68-79.
[6]Wan P J.Greedy Approximation Algorithms[M]//Handbook of Combinatorial Optimization,2013:1599-1629.
[7]Khajehnejad MA,Xu W,Avestimehr AS,et al.Improving the thresholds of sparse recovery:An analysis of a two-step reweighted basis pursuit algorithm[J].IEEE Transactions on Information Theory,2015,61(9):5116-5128.
[8]Sajjad M,Mehmood I,Abbas N,et al.Basis pursuit denoi-singbased image superresolution using a redundant set of atoms[J].Signal,Image and Video Processing,2016,10(1):181-188.
[9]Fornasier M,Peter S,Rauhut H,et al.Conjugate gradient acceleration of iteratively re-weighted least squares methods[J].Computational Optimization&Applications,2016,65(1):205-259.
[10]Saadat SA,Safari A,Needell D.Sparse reconstruction of regional gravity signal based on stabilized orthogonal matching pursuit(SOMP)[J].Pure&Applied Geophysics,2016,173(6):2087-2099.
[11]Chen J,Zhou Y,Jin L,et al.An adaptive regularized smoothed norm algorithm for sparse signal recovery in noisy environments[J].Signal Processing,2017,135(C):153-157.
[12]Ramli DA,Tan WC.Fast kernel sparse representation classifier using improved smoothed-l0norm[J].Procedia Computer Science,2017,112:494-503.
[13]Zhang Y,Yu J,Bai H,et al.Improved sparse signal reconstruction based on approximate hyperbolic tangent function with smoothedl0norm[J].International Journal of Science,2017,4(2):201-210.
[14]Feng JJ,Zhang G,Wen FQ.MIMO radar imaging based on smoothed l0 norm[J]. Mathematical Problems in Engineering,2015(8):1-10.
[15]Gerdts M,Horn S,Kimmerle SJ.Line search globalization of a semismooth Newton method for operator equations in Hilbert spaces with applications in optimal control[J].Journal of Industrial&Management Optimization,2017,13(1):47-62.
[16]WU Feiyun,ZHOU Yuehai,TONG Feng.A fast sparse signal recovery algorith-m based on approximate l0norm and hybrid optimization[J].Acta Automatica Sinica,2014,40(10):2145-2150(in Chinese).[伍飞云,周跃海,童峰.基于似零范数和混合优化的压缩感知信号快速重构算法[J].自动化学报,2014,40(10):2145-2150.]