Low-rank enhanced Hammerstein-spline adaptive filter for sparsity-aware nonlinear feedback cancellation in hearing aids

Adaptive feedback cancellation (AFC) remains a significant challenge in digital hearing aids due to the correlation between the microphone input and loudspeaker output, leading to biased feedback path estimates. Additionally, loudspeaker-induced non-linearities, such as saturation, further degrade sound quality. This paper proposes an Enhanced Hammerstein-Spline Adaptive Filter (EHSAF) that improves upon the conventional Hammerstein-spline model by modifying the update rule to address convergence issues in sparse feedback paths. The integration of EHSAF within the AFC framework effectively mitigates non-linear distortions, ensuring improved stability and faster convergence. Further performance gains are achieved by incorporating the nearest Kronecker product (NKP) framework, which leverages the low-rank structure of the hearing aid impulse response. Experimental results demonstrate that the proposed EHSAF-based nonlinear AFC (NAFC) and NKP-enhanced EHSAF NAFC algorithms outperform state-of-the-art methods in both accuracy and computational efficiency.