Online coordinate descent for adaptive estimation of sparse signals

Two low-complexity sparsity-aware recursive schemes are developed for real-time adaptive signal processing. Both rely on a novel online coordinate descent algorithm which minimizes a time-weighted least-squares cost penalized with the scaled lscr₁ norm of the unknown parameters. In addition to computational savings offered when processing time-invariant sparse parameter vectors, both schemes can be used for tracking slowly varying sparse signals. Analysis and preliminary simulations confirm that when the true signal is sparse the proposed estimators converge to a time-weighted least-absolute shrinkage and selection operator, and both outperform sparsity-agnostic recursive least-squares alternatives.