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    07/14/14 | Sparse LMS via online linearized Bregman iteration.
    Hu T, Chklovskii DB
    ICASSP 2014 - 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). 2014 Jul 14:. doi: 10.1109/ICASSP.2014.6855000

    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 l 1 -l 2 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.

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