自适应权重的GPSR压缩感知重构算法
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摘要
在压缩感知信号重构的过程中,为使投影梯度稀疏重构算法(GPSR)在保持低复杂度的同时,能有效提高重构性能,引入了自适应思想,给重构模型添加具有惩罚意义的权重系数,以寻找算法复杂度和精度之间的最佳平衡点;根据解的收敛进程不断调整权重值,以加速收敛.仿真实验表明:在相同条件下,该算法的计算效率优于传统的GPSR算法和典型的OMP算法,能在较短的运行时间内大幅度提高重构精度.
In order to improve the performance of gradient projection for sparse reconstruction(GPSR)algorithm effectively during the process of compressed sensing signal reconstruction,the weight coefficients for penalty is introduced into the reconstruction model.Its advantage is to find the best balance between the complexity and the construction precision.The weights are adaptively adjusted during every iterative step to accelerate the convergence.Simulation experiment results show that the proposed algorithm has a better performance on computational efficiency than that of the traditional GPSR algorithm and the typical OMP algorithm,enabling high precision reconstruction in less time.
In order to improve the performance of gradient projection for sparse reconstruction(GPSR)algorithm effectively during the process of compressed sensing signal reconstruction,the weight coefficients for penalty is introduced into the reconstruction model.Its advantage is to find the best balance between the complexity and the construction precision.The weights are adaptively adjusted during every iterative step to accelerate the convergence.Simulation experiment results show that the proposed algorithm has a better performance on computational efficiency than that of the traditional GPSR algorithm and the typical OMP algorithm,enabling high precision reconstruction in less time.
引文
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[2]GEORGE S N,AUGUSTINE N,PATTATHIL D P.Audio security through compressive sampling and cellular automata[J].Multimedia Tools and Applications,2015,74(23):10393-10417.
[3]LIU Z,LI Z,LI M,et al.Path reconstruction in dynamic wireless sensor networks using compressive sensing[J].IEEE/ACM Transactions on Networking,2016,24(4):1948-1960.
[4]TROPP J A,GILBERT A C.Signal recovery from random measurements via orthogonal matching pursuit[J].IEEE Transactions on Information Theory,2007,53(12):4655-4666.
[5]NEEDELL D,TROPP J A.CoSaMP:Iterative signal recovery from incomplete and inaccurate samples[J].Applied and Computational Harmonic Analysis,2009,26(3):301-321.
[6]BLUMENSATH T,DAVIES M E.Iterative hard thresholding for compressed sensing[J].Applied and Computational Harmonic Analysis,2009,27(3):265-274.
[7]李珅,马彩文,李艳,等.压缩感知重构算法综述[J].红外与激光工程,2013,42(S1):225-232.LI K,MA C W,LI Y,et al.Survey on reconstruction algorithm based on compressive sensing[J].Infrared and Laser Engineering,2013,42(S1):225-232.
[8]WRIGHT S J,NOWAK R D,FIGUEIREDO M A T.Sparse reconstruction by separable approximation[J].IEEE Transactions on Signal Processing,2009,57(7):2479-2493.
[9]BABACAN S D,NAKAJIMA S,DO M N.Bayesian group-sparse modeling and variation an inference[J].IEEE Transactions on Signal Processing,2014,62(11):2906-2921.
[10]OLIVERI G,CARLIN M,MASSA A.Complexweight sparse linear array synthesis by Bayesian compressive sampling[J].IEEE Transactions on Antennas and Propagation,2012,60(5):2309-2326.
[11]YU L,WEI C,JIA J,et al.Compressive sensing for cluster structured sparse signals:Variational Bayes approach[J].Let Signal Processing,2016,10(7):770-779.
[12]ZAYYANI H,BABAIE-ZADEH M,JUTTEN C.Decoding real-field codes by an iterative expectationmaximization(EM)algorithm[C]//IEEE International Conference on Acoustics,Speech and Signal Processing.Las Vegas:IEEE,2008:3169-3172.
[13]BARANIUK R G,CEVHER V,DUARTE M F,et al.Model-based compressive sensing[J].IEEE Transactions on Information Theory,2010,56(4):1982-2001.
[14]FIGUEIREDO M A T,NOWAK R D,WRIGHT S J.Gradient projection for sparse reconstruction:Application to compressed sensing and other inverse problems[J].IEEE Journal of Selected Topics in Signal Processing,2007,1(4):586-597.
[15]FOUCART S,RAUHUT H.A mathematical introduction to compressive sensing[C]//Applied and Numerical Analysis.NewYork:Spring,2013.
[16]CAI T T,JIANG T.Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices[J].The Annals of Statistics,2011,39(3):1496-1525.
[17]CANDES E J,PLAN Y.A probabilistic and RIPless theory of compressed sensing[J].IEEE Transactions on Information Theory,2011,57(11):7235-7254.
[18]ASIF M S,ROMBERG J.Fast and accurate algorithms for re-weighted L1-norm minimization[J].IEEE Transactions on Signal Processing,2013,61(23):5905-5916.
[19]刘建伟,崔立鹏,刘泽宇,等.正则化稀疏模型[J].计算机学报,2015,38(7):1307-1325.LIU J W,CUI L P,LIU Z Y,et al.Survey on the regularized sparse models[J].Chinese Journal of Computers,2015,38(7):1307-1325.
[20]CHEN W,RODRIGUES M R D,WASSELL I.A fréchet mean approach for compressive sensing date acquisition and reconstruction in wireless sensor networks[J].IEEE Transactions on Wireless Communications,2012,11(10):3598-3606.