SPARLS: A Low Complexity Recursive $\mathcal{L}_1$-Regularized Least Squares Algorithm

We develop a Recursive L1-Regularized Least Squares (SPARLS) algorithm for the estimation of a sparse tap-weight vector in the adaptive filtering setting. The SPARLS algorithm exploits noisy observations of the tap-weight vector output stream and produces its estimate using an ExpectationMaximization type algorithm. Simulation studies in the context of channel estimation, employing multipath wireless channels, show that the SPARLS algorithm has significant improvement over the conventional widely-used Recursive Least Squares (RLS) algorithm, in terms of both mean squared error (MSE) and computational complexity.