  In this paper, we propose sparsity-aware data-selective adaptive filtering
algorithms with adjustable penalties. Prior work incorporates a penalty
function into the cost function used in the optimization that originates the
algorithms to improve their performance by exploiting sparsity. However, the
strength of the penalty function is controlled by a scalar that is often a
fixed parameter. In contrast to prior work, we develop a framework to derive
algorithms that automatically adjust the penalty function parameter and the
step size to achieve a better performance. Simulations for a system
identification application show that the proposed algorithms outperform in
convergence speed existing sparsity-aware algorithms.
