Exploiting sparsity in feed-forward active noise control with adaptive Douglas-Rachford splitting

Observing that a typical primary path in Active Noise Control (ANC) system is sparse, i.e., having a few significant coefficients, we propose an adaptive learning which promotes the sparsity of the concatenation of the adaptive filter and the secondary path. More precisely, we propose to suppress a time-varying sum of the data-fidelity term and the weighted ℓ₁ norm of the concatenation by the adaptive Douglas-Rachford splitting scheme. Numerical examples demonstrate that the proposed algorithm shows excellent performance of the ANC by exploiting the sparsity and has robustness against a violation of the sparsity assumption.