Title :
Sparse LMS via online linearized Bregman iteration
Author :
Tao Hu ; Chklovskii, Dmitri B.
Author_Institution :
Center for Bioinformatical & Genomic Syst. Eng, Texas A&M, College Station, TX, USA
Abstract :
We propose a version of least-mean-square (LMS) algorithm for sparse system identification. Our algorithm called online linearized Bregman iteration (OLBI) is derived from minimizing the cumulative prediction error squared along with an l1-l2 norm regularizer. By systematically treating the non-differentiable regularizer we arrive at a simple two-step iteration. We demonstrate that OLBI is bias free and compare its operation with existing sparse LMS algorithms by rederiving them in the online convex optimization framework. We perform convergence analysis of OLBI for white input signals and derive theoretical expressions for the steady state mean square deviations (MSD). We demonstrate numerically that OLBI improves the performance of LMS type algorithms for signals generated from sparse tap weights.
Keywords :
convergence of numerical methods; convex programming; identification; iterative methods; least mean squares methods; signal processing; MSD; OLBI; convergence analysis; cumulative prediction error minimization; l1-l2 norm regularizer; least-mean-square algorithm; nondifferentiable regularizer; online convex optimization framework; online linearized Bregman iteration; sparse LMS algorithm; sparse system identification; sparse tap weights; steady state mean square deviations; two-step iteration; white input signals; Algorithm design and analysis; Filtering theory; Least squares approximations; Signal processing algorithms; Standards; Steady-state; Vectors; LMS; Sparse; online;
Conference_Titel :
Acoustics, Speech and Signal Processing (ICASSP), 2014 IEEE International Conference on
Conference_Location :
Florence
DOI :
10.1109/ICASSP.2014.6855000