Transient Performance Analysis of Zero-Attracting LMS

Zero-attracting least-mean-square (ZA-LMS) algorithm has been widely used for online sparse system identification. It combines the LMS framework and l1-norm regularization to promote sparsity, and relies on subgradient iterations. Despite the significant interest in ZA-LMS, few works analyzed its transient behavior. The main difficulty lies in the nonlinearity of the update rule. In this study, a detailed analysis in the mean and mean-square sense is carried out in order to examine the behavior of the algorithm. Simulation results illustrate the accuracy of the model and highlight its performance through comparisons with an existing model.

[1]  Antonio J. Plaza,et al.  Sparse Unmixing of Hyperspectral Data , 2011, IEEE Transactions on Geoscience and Remote Sensing.

[2]  Hossein Hassani,et al.  On the Folded Normal Distribution , 2014, 1402.3559.

[3]  E.J. Candes,et al.  An Introduction To Compressive Sampling , 2008, IEEE Signal Processing Magazine.

[4]  Jie Chen,et al.  Variants of Non-Negative Least-Mean-Square Algorithm and Convergence Analysis , 2014, IEEE Transactions on Signal Processing.

[5]  Jie Chen,et al.  Steady-State Performance of Non-Negative Least-Mean-Square Algorithm and Its Variants , 2014, IEEE Signal Processing Letters.

[6]  Michael Elad,et al.  From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images , 2009, SIAM Rev..

[7]  Alfred O. Hero,et al.  Sparse LMS for system identification , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[8]  Jian Wang,et al.  Performance Analysis of $l_0$ Norm Constraint Least Mean Square Algorithm , 2012, IEEE Transactions on Signal Processing.

[9]  Sheng Zhang,et al.  Transient analysis of zero attracting NLMS algorithm without Gaussian inputs assumption , 2014, Signal Process..

[10]  Peng Shi,et al.  Convergence analysis of sparse LMS algorithms with l1-norm penalty based on white input signal , 2010, Signal Process..

[11]  Bhaskar D. Rao,et al.  Sparse channel estimation via matching pursuit with application to equalization , 2002, IEEE Trans. Commun..

[12]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[13]  Michael Elad,et al.  Sparse and Redundant Representations - From Theory to Applications in Signal and Image Processing , 2010 .

[14]  Ali H. Sayed,et al.  Adaptive Filters , 2008 .

[15]  Jeffrey A. Fessler,et al.  Model-Based Image Reconstruction for MRI , 2010, IEEE Signal Processing Magazine.