Combined sparse regularization for nonlinear adaptive filters

Nonlinear adaptive filters often show some sparse behavior due to the fact that not all the coefficients are equally useful for the modeling of any nonlinearity. Recently, a class of proportionate algorithms has been proposed for nonlinear filters to leverage sparsity of their coefficients. However, the choice of the norm penalty of the cost function may be not always appropriate depending on the problem. In this paper, we introduce an adaptive combined scheme based on a block-based approach involving two nonlinear filters with different regularization that allows to achieve always superior performance than individual rules. The proposed method is assessed in nonlinear system identification problems, showing its effectiveness in taking advantage of the online combined regularization.