PRP共轭梯度法在信号恢复问题中的应用
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摘要
对信号恢复问题,提出一个新函数近似l0-范数.相比于经典的Gauss函数,该函数更逼近于l0-范数.进而利用PRP共轭梯度法求解信号恢复问题.在适当的假设下证明了算法的全局收敛性.仿真结果表明新函数具有较好的恢复效果.
For signal reconstruction problem,a new function to approximate l0-norm is proposed.Compared to the classic Gauss function,this function is closer to the l0-norm.Then PRP conjugate gradient method is used to solve signal recovery problem.Under appropriate assumption,the global convergence of new algorithm is proved.The simulation results show that the new function has better recovery effect.
For signal reconstruction problem,a new function to approximate l0-norm is proposed.Compared to the classic Gauss function,this function is closer to the l0-norm.Then PRP conjugate gradient method is used to solve signal recovery problem.Under appropriate assumption,the global convergence of new algorithm is proved.The simulation results show that the new function has better recovery effect.
引文
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[2]Donoho D L.Compressed sensing[J].Trans Information Theory,2006,52(4):1289-1326.
[3]Candes E J,Wakin M B.An introduction to compressive sampling[J].Signal Processing Magazine,2008,25(2):21-30.
[4]Mohimani H,Zadeh M,Jutten C.A fast approach for overcomplete sparse decomposition based on smoothed l0-norm[J].Trans Signal Processing,2009,57(1):289-301.
[5]Hyder M,Mahate K.An improved smoothed l0 approximate algorithm for sparse representation[J].Trans Signal Processing,2010,58(4):2194-2205.
[6]Mohimani H,Zadeh M,Jutten C.Fast sparse representation based on smoothedl0-norm[C]//ICA.London,U.K:2007:389-396.
[7]Hyder M,Mahat K.An approximate l0-norm minimization algorithm for compressed sensing[C]//ICASSP.Taipei:2009:3365-3368.
[8]Mohimani H,Zadeh M,Jutten C.Complex-valued sparse representation based on smoothed l0-norm[C]//ICASSP.Las Vegas,NV:2008:3881-3884.
[9]Pant J K,Lu W-S,Antoniou A.New improved algorithms for compressive sensing based on l0-norm[J].Transactions on circuits and system,2014,61(3):198-202.
[10]袁亚湘,孙文瑜.最优化理论与方法[M].北京:科学出版社,1997:63-64.
[2]Donoho D L.Compressed sensing[J].Trans Information Theory,2006,52(4):1289-1326.
[3]Candes E J,Wakin M B.An introduction to compressive sampling[J].Signal Processing Magazine,2008,25(2):21-30.
[4]Mohimani H,Zadeh M,Jutten C.A fast approach for overcomplete sparse decomposition based on smoothed l0-norm[J].Trans Signal Processing,2009,57(1):289-301.
[5]Hyder M,Mahate K.An improved smoothed l0 approximate algorithm for sparse representation[J].Trans Signal Processing,2010,58(4):2194-2205.
[6]Mohimani H,Zadeh M,Jutten C.Fast sparse representation based on smoothedl0-norm[C]//ICA.London,U.K:2007:389-396.
[7]Hyder M,Mahat K.An approximate l0-norm minimization algorithm for compressed sensing[C]//ICASSP.Taipei:2009:3365-3368.
[8]Mohimani H,Zadeh M,Jutten C.Complex-valued sparse representation based on smoothed l0-norm[C]//ICASSP.Las Vegas,NV:2008:3881-3884.
[9]Pant J K,Lu W-S,Antoniou A.New improved algorithms for compressive sensing based on l0-norm[J].Transactions on circuits and system,2014,61(3):198-202.
[10]袁亚湘,孙文瑜.最优化理论与方法[M].北京:科学出版社,1997:63-64.